Submitted - 2301.08290.pdf
", "abstract": "We apply Fourier neural operators (FNOs), a state-of-the-art operator learning technique, to forecast the temporal evolution of experimentally measured velocity fields. FNOs are a recently developed machine learning method capable of approximating solution operators to systems of partial differential equations through data alone. The learned FNO solution operator can be evaluated in milliseconds, potentially enabling faster-than-real-time modeling for predictive flow control in physical systems. Here we use FNOs to predict how physical fluid flows evolve in time, training with particle image velocimetry measurements depicting cylinder wakes in the subcritical vortex shedding regime. We train separate FNOs at Reynolds numbers ranging from Re = 240 to Re = 3060 and study how increasingly turbulent flow phenomena impact prediction accuracy. We focus here on a short prediction horizon of ten non-dimensionalized time-steps, as would be relevant for problems of predictive flow control. We find that FNOs are capable of accurately predicting the evolution of experimental velocity fields throughout the range of Reynolds numbers tested (L2 norm error < 0.1) despite being provided with limited and imperfect flow observations. Given these results, we conclude that this method holds significant potential for real-time predictive flow control of physical systems.", "date": "2023-01-19", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20230316-153752294", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230316-153752294", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF Graduate Research Fellowship", "grant_number": "DGE-1745301" }, { "agency": "Bren Professor of Computing and Mathematical Sciences" }, { "agency": "Kortschak Scholars Program" }, { "agency": "PIMCO" }, { "agency": "Amazon AI4Science Fellowship" }, { "agency": "Center for Autonomous Systems and Technologies" } ] }, "local_group": { "items": [ { "id": "GALCIT" }, { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "primary_object": { "basename": "2301.08290.pdf", "url": "https://authors.library.caltech.edu/records/1ya2r-9a428/files/2301.08290.pdf" }, "pub_year": "2023", "author_list": "Renn, Peter I; Wang, Cong; et al." }, { "id": "https://authors.library.caltech.edu/records/ecrs2-f1625", "eprint_id": 118471, "eprint_status": "archive", "datestamp": "2023-08-20 08:53:01", "lastmod": "2025-11-21 03:13:05", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Akella-Prithvi", "name": { "family": "Akella", "given": "Prithvi" }, "orcid": "0000-0003-4375-0015" }, { "id": "Wei-Skylar-X", "name": { "family": "Wei", "given": "Skylar X." }, "orcid": "0000-0002-6336-9433" }, { "id": "Burdick-J-W", "name": { "family": "Burdick", "given": "Joel W." }, "orcid": "0000-0002-3091-540X" }, { "id": "Ames-A-D", "name": { "family": "Ames", "given": "Aaron D." }, "orcid": "0000-0003-0848-3177" } ] }, "title": "Learning Disturbances Online for Risk-Aware Control: Risk-Aware Flight with Less Than One Minute of Data", "ispublished": "unpub", "full_text_status": "public", "note": "Attribution 4.0 International (CC BY 4.0).\n\nThe work of Prithvi Akella was supported by the Air Force Office of Scientific Research, grant FA9550-19-1-0302, and the National Science Foundation, grant 1932091. The work of Skylar Wei was supported in part by DARPA, through the Learning and Introspective Control program. We would also like to thank the Caltech Center for Autonomous Systems and Technologies for the use of the wind tunnel in our experiments.\n\nAccepted Version - 2212.06253.pdf
", "abstract": "Recent advances in safety-critical risk-aware control are predicated on apriori knowledge of the disturbances a system might face. This paper proposes a method to efficiently learn these disturbances online, in a risk-aware context. First, we introduce the concept of a Surface-at-Risk, a risk measure for stochastic processes that extends Value-at-Risk -- a commonly utilized risk measure in the risk-aware controls community. Second, we model the norm of the state discrepancy between the model and the true system evolution as a scalar-valued stochastic process and determine an upper bound to its Surface-at-Risk via Gaussian Process Regression. Third, we provide theoretical results on the accuracy of our fitted surface subject to mild assumptions that are verifiable with respect to the data sets collected during system operation. Finally, we experimentally verify our procedure by augmenting a drone's controller and highlight performance increases achieved via our risk-aware approach after collecting less than a minute of operating data.", "date": "2022-12-12", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20221219-234112304", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221219-234112304", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-19-1-0302" }, { "agency": "NSF", "grant_number": "CNS-1932091" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)" } ] }, "local_group": { "items": [ { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "doi": "10.48550/arXiv.2212.06253", "primary_object": { "basename": "2212.06253.pdf", "url": "https://authors.library.caltech.edu/records/ecrs2-f1625/files/2212.06253.pdf" }, "pub_year": "2022", "author_list": "Akella, Prithvi; Wei, Skylar X.; et al." }, { "id": "https://authors.library.caltech.edu/records/pnp9k-akm20", "eprint_id": 118468, "eprint_status": "archive", "datestamp": "2023-08-20 08:39:52", "lastmod": "2025-11-21 03:03:14", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Badithela-Apurva", "name": { "family": "Badithela", "given": "Apurva" } }, { "id": "Graebener-Josefine-B", "name": { "family": "Graebener", "given": "Josefine B." } }, { "id": "Ubellacker-Wyatt-L", "name": { "family": "Ubellacker", "given": "Wyatt" }, "orcid": "0000-0002-4732-6185" }, { "id": "Mazumdar-Eric", "name": { "family": "Mazumdar", "given": "Eric V." }, "orcid": "0000-0002-1815-269X" }, { "id": "Ames-A-D", "name": { "family": "Ames", "given": "Aaron D." }, "orcid": "0000-0003-0848-3177" }, { "id": "Murray-R-M", "name": { "family": "Murray", "given": "Richard M." }, "orcid": "0000-0002-5785-7481" } ] }, "title": "Synthesizing Reactive Test Environments for Autonomous Systems: Testing Reach-Avoid Specifications with Multi-Commodity Flows", "ispublished": "unpub", "full_text_status": "public", "note": "Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0).\n\nWe acknowledge funding from AFOSR Test and Evaluation Program, grant FA9550-19-1-0302, National Science Foundation award CNS-1932091, and Dow (#227027AT). \n\nThe authors would like to acknowledge Mani Chandy, Tichakorn Wongpiromsarn, Qiming Zhao, Michel Ingham, Joel Burdick, Leonard Schulman, Shih-Hao Tseng, Ioannis Filippidis, and Ugo Rosolia for insightful discussions.\n\nSubmitted - 2210.10304.pdf
", "abstract": "We study automated test generation for verifying discrete decision-making modules in autonomous systems. We utilize linear temporal logic to encode the requirements on the system under test in the system specification and the behavior that we want to observe during the test is given as the test specification which is unknown to the system. First, we use the specifications and their corresponding non-deterministic B\u00fcchi automata to generate the specification product automaton. Second, a virtual product graph representing the high-level interaction between the system and the test environment is constructed modeling the product automaton encoding the system, the test environment, and specifications. The main result of this paper is an optimization problem, framed as a multi-commodity network flow problem, that solves for constraints on the virtual product graph which can then be projected to the test environment. Therefore, the result of the optimization problem is reactive test synthesis that ensures that the system meets the test specifications along with satisfying the system specifications. This framework is illustrated in simulation on grid world examples, and demonstrated on hardware with the Unitree A1 quadruped, wherein dynamic locomotion behaviors are verified in the context of reactive test environments.", "date": "2022-10-19", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20221219-234102223", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221219-234102223", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-19-1-0302" }, { "agency": "NSF", "grant_number": "CNS-1932091" }, { "agency": "Dow Chemical Company", "grant_number": "227027AT" } ] }, "local_group": { "items": [ { "id": "GALCIT" }, { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" }, { "id": "Division-of-Biology-and-Biological-Engineering" } ] }, "doi": "10.48550/arXiv.2210.10304", "primary_object": { "basename": "2210.10304.pdf", "url": "https://authors.library.caltech.edu/records/pnp9k-akm20/files/2210.10304.pdf" }, "pub_year": "2022", "author_list": "Badithela, Apurva; Graebener, Josefine B.; et al." }, { "id": "https://authors.library.caltech.edu/records/8gvvt-tg512", "eprint_id": 118466, "eprint_status": "archive", "datestamp": "2023-08-20 08:34:45", "lastmod": "2025-11-21 01:36:19", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Csomay-Shanklin-Noel-V", "name": { "family": "Csomay-Shanklin", "given": "Noel" }, "orcid": "0000-0002-2361-1694" }, { "id": "Dorobantu-Victor-D", "name": { "family": "Dorobantu", "given": "Victor D." }, "orcid": "0000-0002-2797-7802" }, { "id": "Ames-A-D", "name": { "family": "Ames", "given": "Aaron D." }, "orcid": "0000-0003-0848-3177" } ] }, "title": "Nonlinear Model Predictive Control of a 3D Hopping Robot: Leveraging Lie Group Integrators for Dynamically Stable Behaviors", "ispublished": "unpub", "full_text_status": "public", "note": "This research was supported by NSF Graduate Research Fellowship No. DGE-1745301 and Raytheon, Beyond Limits, JPL RTD 1643049. \n\nThe authors would like to especially thank Igor Sadalski, as well as Sergio Esteban and Adrian Boedtker Ghansah for their help with simulation and hardware implementation, and Will Compton for his experimental assistance.\n\nSubmitted - 2209.11808.pdf
", "abstract": "Achieving stable hopping has been a hallmark challenge in the field of dynamic legged locomotion. Controlled hopping is notably difficult due to extended periods of underactuation, combined with very short ground phases wherein ground interactions must be modulated to regulate global state. In this work, we explore the use of hybrid nonlinear model predictive control, paired with a low-level feedback controller in a multi-rate hierarchy, to achieve dynamically stable motions on a novel 3D hopping robot. In order to demonstrate richer behaviors on the manifold of rotations, both the planning and feedback layers must be done in a geometrically consistent fashion; therefore, we develop the necessary tools to employ Lie group integrators and an appropriate feedback controller. We experimentally demonstrate stable 3D hopping on a novel robot, as well as trajectory tracking and flipping in simulation.", "date": "2022-09-23", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20221219-234055506", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221219-234055506", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF Graduate Research Fellowship", "grant_number": "DGE-1745301" }, { "agency": "Raytheon Company" }, { "agency": "Beyond Limits" }, { "agency": "JPL Research and Technology Development Fund", "grant_number": "1643049" } ] }, "local_group": { "items": [ { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "doi": "10.48550/arXiv.2209.11808", "primary_object": { "basename": "2209.11808.pdf", "url": "https://authors.library.caltech.edu/records/8gvvt-tg512/files/2209.11808.pdf" }, "pub_year": "2022", "author_list": "Csomay-Shanklin, Noel; Dorobantu, Victor D.; et al." }, { "id": "https://authors.library.caltech.edu/records/m3zrt-p6h47", "eprint_id": 115568, "eprint_status": "archive", "datestamp": "2023-08-20 08:11:21", "lastmod": "2025-02-01 19:40:02", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dorobantu-Victor-D", "name": { "family": "Dorobantu", "given": "Victor D." }, "orcid": "0000-0002-2797-7802" }, { "id": "Azizzadenesheli-Kamyar", "name": { "family": "Azizzadenesheli", "given": "Kamyar" }, "orcid": "0000-0001-8507-1868" }, { "id": "Yue-Yisong", "name": { "family": "Yue", "given": "Yisong" }, "orcid": "0000-0001-9127-1989" } ] }, "title": "Compactly Restrictable Metric Policy Optimization Problems", "ispublished": "unpub", "full_text_status": "public", "keywords": "Continuous Markov Decision Processes, Reinforcement Learning, Optimal Control, Value Iteration, Selection Theorems, Sampled-Data, Physical Systems", "note": "Submitted May 15th, 2021. Resubmitted July 6th, 2022. This work was supported in part by DARPA and Beyond Limits. Victor D. Dorobantu was also supported in part by a Kortschak Fellowship.\n\nSubmitted - 2207.05850.pdf
", "abstract": "We study policy optimization problems for deterministic Markov decision processes (MDPs) with metric state and action spaces, which we refer to as Metric Policy Optimization Problems (MPOPs). Our goal is to establish theoretical results on the well-posedness of MPOPs that can characterize practically relevant continuous control systems. To do so, we define a special class of MPOPs called Compactly Restrictable MPOPs (CR-MPOPs), which are flexible enough to capture the complex behavior of robotic systems but specific enough to admit solutions using dynamic programming methods such as value iteration. We show how to arrive at CR-MPOPs using forward-invariance. We further show that our theoretical results on CR-MPOPs can be used to characterize feedback linearizable control affine systems.", "date": "2022-07-12", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20220714-212414777", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220714-212414777", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Defense Advanced Research Projects Agency (DARPA)" }, { "agency": "Beyond Limits" }, { "agency": "Kortschak Scholars Program" } ] }, "local_group": { "items": [ { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "doi": "10.48550/arXiv.arXiv.2207.05850", "primary_object": { "basename": "2207.05850.pdf", "url": "https://authors.library.caltech.edu/records/m3zrt-p6h47/files/2207.05850.pdf" }, "pub_year": "2022", "author_list": "Dorobantu, Victor D.; Azizzadenesheli, Kamyar; et al." }, { "id": "https://authors.library.caltech.edu/records/3b3tb-r2g71", "eprint_id": 115561, "eprint_status": "archive", "datestamp": "2023-08-20 07:29:03", "lastmod": "2025-02-01 19:39:50", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ong-Pio", "name": { "family": "Ong", "given": "Pio" }, "orcid": "0000-0002-9665-1320" }, { "id": "Bahati-Gilbert", "name": { "family": "Bahati", "given": "Gilbert" } }, { "id": "Ames-A-D", "name": { "family": "Ames", "given": "Aaron D." }, "orcid": "0000-0003-0848-3177" } ] }, "title": "Stability and Safety through Event-Triggered Intermittent Control with Application to Spacecraft Orbit Stabilization", "ispublished": "unpub", "full_text_status": "public", "note": "Attribution 4.0 International (CC BY 4.0) \n\nThis research is supported in part by Raytheon Technologies and the National Science Foundation (CPS Award #1932091). \n\nThe authors would like to thank JPL for their feedback on the application of these ideas to spacecraft, and Saptarshi Bandyopadhyay in particular for discussions and providing the eighth-order harmonics gravity model used in our simulation results.\n\nSubmitted - 2204.03110.pdf
", "abstract": "In systems where the ability to actuate is a scarce resource, e.g., spacecrafts, it is desirable to only apply a given controller in an intermittent manner--with periods where the controller is on and periods where it is off. Motivated by the event-triggered control paradigm, where state-dependent triggers are utilized in a sample-and-hold context, we generalize this concept to include state triggers where the controller is off thereby creating a framework for intermittent control. Our approach utilizes certificates--either Lyapunov or barrier functions--to design intermittent trigger laws that guarantee stability or safety; the controller is turned on for the period for which is beneficial with regard to the certificate, and turned off until a performance threshold is reached. The main result of this paper is that the intermittent controller scheme guarantees (set) stability when Lyapunov functions are utilized, and safety (forward set invariance) in the setting of barrier functions. As a result, our trigger designs can leverage the intermittent nature of the actuator, and at the same time, achieve the task of stabilization or safety. We further demonstrate the application and benefits of intermittent control in the context of the spacecraft orbit stabilization problem.", "date": "2022-04-06", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20220714-194256328", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220714-194256328", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Raytheon Company" }, { "agency": "NSF", "grant_number": "CNS-1932091" } ] }, "local_group": { "items": [ { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "doi": "10.48550/arXiv.arXiv.2204.03110", "primary_object": { "basename": "2204.03110.pdf", "url": "https://authors.library.caltech.edu/records/3b3tb-r2g71/files/2204.03110.pdf" }, "pub_year": "2022", "author_list": "Ong, Pio; Bahati, Gilbert; et al." }, { "id": "https://authors.library.caltech.edu/records/jz2q3-n3386", "eprint_id": 115560, "eprint_status": "archive", "datestamp": "2023-08-20 07:27:34", "lastmod": "2025-02-01 19:39:48", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Taylor-Andrew-J", "name": { "family": "Taylor", "given": "Andrew J." }, "orcid": "0000-0002-5990-590X" }, { "id": "Ong-Pio", "name": { "family": "Ong", "given": "Pio" }, "orcid": "0000-0002-9665-1320" }, { "id": "Moln\u00e1r-Tam\u00e1s-G", "name": { "family": "Moln\u00e1r", "given": "Tam\u00e1s G." }, "orcid": "0000-0002-9379-7121" }, { "id": "Ames-A-D", "name": { "family": "Ames", "given": "Aaron D." }, "orcid": "0000-0003-0848-3177" } ] }, "title": "Safe Backstepping with Control Barrier Functions", "ispublished": "unpub", "full_text_status": "public", "note": "This research is supported in part by Ford, the National Science Foundation (CPS Award #1932091, CMMI Award #1923239), Raytheon Technologies, Aerovironment and Dow (#227027AT).\n\nSubmitted - 2204.00653.pdf
", "abstract": "Complex control systems are often described in a layered fashion, represented as higher-order systems where the inputs appear after a chain of integrators. While Control Barrier Functions (CBFs) have proven to be powerful tools for safety-critical controller design of nonlinear systems, their application to higher-order systems adds complexity to the controller synthesis process -- it necessitates dynamically extending the CBF to include higher order terms, which consequently modifies the safe set in complex ways. We propose an alternative approach for addressing safety of higher-order systems through Control Barrier Function Backstepping. Drawing inspiration from the method of Lyapunov backstepping, we provide a constructive framework for synthesizing safety-critical controllers and CBFs for higher-order systems from a top-level dynamics safety specification and controller design. Furthermore, we integrate the proposed method with Lyapunov backstepping, allowing the tasks of stability and safety to be expressed individually but achieved jointly. We demonstrate the efficacy of this approach in simulation.", "date": "2022-04-01", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20220714-194252464", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220714-194252464", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ford Motor Company" }, { "agency": "NSF", "grant_number": "CNS-1932091" }, { "agency": "NSF", "grant_number": "CMMI-1923239" }, { "agency": "Raytheon Company" }, { "agency": "AeroVironment" }, { "agency": "Dow Chemical Company", "grant_number": "227027AT" } ] }, "local_group": { "items": [ { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "doi": "10.48550/arXiv.arXiv.2204.00653", "primary_object": { "basename": "2204.00653.pdf", "url": "https://authors.library.caltech.edu/records/jz2q3-n3386/files/2204.00653.pdf" }, "pub_year": "2022", "author_list": "Taylor, Andrew J.; Ong, Pio; et al." }, { "id": "https://authors.library.caltech.edu/records/aeg7b-hbw77", "eprint_id": 114900, "eprint_status": "archive", "datestamp": "2023-08-20 06:13:28", "lastmod": "2026-03-30 15:21:02", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hamze-Bajgiran-Hamed", "name": { "family": "Hamze Bajgiran", "given": "Hamed" }, "orcid": "0000-0002-6246-2783" }, { "id": "Owhadi-H", "name": { "family": "Owhadi", "given": "Houman" }, "orcid": "0000-0002-5677-1600" } ] }, "title": "Aggregation of Pareto optimal models", "ispublished": "unpub", "full_text_status": "public", "note": "The authors gratefully acknowledge support from Beyond Limits (Learning Optimal Models) through CAST (The Caltech Center for Autonomous Systems and Technologies) and partial support from the Air Force Office of Scientific Research under awards number FA9550-18-1-0271 (Games for Computation and Learning) and FA9550-20-1-0358 (Machine Learning and Physics-Based Modeling and Simulation).\n\nSubmitted - 2112.04161.pdf
", "abstract": "In statistical decision theory, a model is said to be Pareto optimal (or admissible) if no other model carries less risk for at least one state of nature while presenting no more risk for others. How can you rationally aggregate/combine a finite set of Pareto optimal models while preserving Pareto efficiency? This question is nontrivial because weighted model averaging does not, in general, preserve Pareto efficiency. This paper presents an answer in four logical steps: (1) A rational aggregation rule should preserve Pareto efficiency (2) Due to the complete class theorem, Pareto optimal models must be Bayesian, i.e., they minimize a risk where the true state of nature is averaged with respect to some prior. Therefore each Pareto optimal model can be associated with a prior, and Pareto efficiency can be maintained by aggregating Pareto optimal models through their priors. (3) A prior can be interpreted as a preference ranking over models: prior \u03c0 prefers model A over model B if the average risk of A is lower than the average risk of B. (4) A rational/consistent aggregation rule should preserve this preference ranking: If both priors \u03c0 and \u03c0\u2032 prefer model A over model B, then the prior obtained by aggregating \u03c0 and \u03c0\u2032 must also prefer A over B. Under these four steps, we show that all rational/consistent aggregation rules are as follows: Give each individual Pareto optimal model a weight, introduce a weak order/ranking over the set of Pareto optimal models, aggregate a finite set of models S as the model associated with the prior obtained as the weighted average of the priors of the highest-ranked models in S. This result shows that all rational/consistent aggregation rules must follow a generalization of hierarchical Bayesian modeling. Following our main result, we present applications to Kernel smoothing, time-depreciating models, and voting mechanisms.", "date": "2021-12-08", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20220524-180318744", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220524-180318744", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Beyond Limits" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-18-1-0271" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-20-1-0358" } ] }, "local_group": { "items": [ { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "doi": "10.48550/arXiv.2112.04161", "primary_object": { "basename": "2112.04161.pdf", "url": "https://authors.library.caltech.edu/records/aeg7b-hbw77/files/2112.04161.pdf" }, "pub_year": "2021", "author_list": "Hamze Bajgiran, Hamed and Owhadi, Houman" }, { "id": "https://authors.library.caltech.edu/records/g0k6z-gvr57", "eprint_id": 114898, "eprint_status": "archive", "datestamp": "2023-08-20 06:01:45", "lastmod": "2026-03-30 14:24:32", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hamze-Bajgiran-Hamed", "name": { "family": "Hamze Bajgiran", "given": "Hamed" } }, { "id": "Owhadi-H", "name": { "family": "Owhadi", "given": "Houman" }, "orcid": "0000-0002-5677-1600" } ] }, "title": "Aggregation of Models, Choices, Beliefs, and Preferences", "ispublished": "unpub", "full_text_status": "public", "note": "The authors gratefully acknowledge support from Beyond Limits (Learning Optimal Models) through CAST (The Caltech Center for Autonomous Systems and Technologies) and partial support from the Air Force Office of Scientific Research under awards number FA9550-18-1-0271 (Games for Computation and Learning) and FA9550-20-1-0358 (Machine Learning and Physics-Based Modeling and Simulation). \n\nThe first version of the paper was written during the first author's Ph.D. studies with many helpful comments from Federico Echenique and Kota Saito. The first author thanks his Ph.D. advisors Jaksa Cvitanic, Federico Echenique, Kota Saito, and Robert Sherman. For helpful discussions, the first author thanks Itai Ashlagi, Kim Border, Martin Cripps, David Dillenberger, Drew Fudenberg, Simone Galperti, Michihiro Kandori, Igor Kopylov, Jay Lu, Fabio Maccheroni, Thomas Palfrey, Charles Plott, Luciano Pomatto, Antonio Rangel, Pablo Schenone, Omer Tamuz, and Leeat Yariv.\n\nSubmitted - 2111.11630.pdf
", "abstract": "A natural notion of rationality/consistency for aggregating models is that, for all (possibly aggregated) models A and B, if the output of model A is f(A) and if the output model B is f(B), then the output of the model obtained by aggregating A and B must be a weighted average of f(A) and f(B). Similarly, a natural notion of rationality for aggregating preferences of ensembles of experts is that, for all (possibly aggregated) experts A and B, and all possible choices x and y, if both A and B prefer x over y, then the expert obtained by aggregating A and B must also prefer x over y. Rational aggregation is an important element of uncertainty quantification, and it lies behind many seemingly different results in economic theory: spanning social choice, belief formation, and individual decision making. Three examples of rational aggregation rules are as follows. (1) Give each individual model (expert) a weight (a score) and use weighted averaging to aggregate individual or finite ensembles of models (experts). (2) Order/rank individual model (expert) and let the aggregation of a finite ensemble of individual models (experts) be the highest-ranked individual model (expert) in that ensemble. (3) Give each individual model (expert) a weight, introduce a weak order/ranking over the set of models/experts, aggregate A and B as the weighted average of the highest-ranked models (experts) in A or B. Note that (1) and (2) are particular cases of (3). In this paper, we show that all rational aggregation rules are of the form (3). This result unifies aggregation procedures across different economic environments. Following the main representation, we show applications and extensions of our representation in various separated economics topics such as belief formation, choice theory, and social welfare economics.", "date": "2021-11-23", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20220524-180312022", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220524-180312022", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Beyond Limits" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-18-1-0271" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-20-1-0358" } ] }, "local_group": { "items": [ { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "doi": "10.48550/arXiv.2111.11630", "primary_object": { "basename": "2111.11630.pdf", "url": "https://authors.library.caltech.edu/records/g0k6z-gvr57/files/2111.11630.pdf" }, "pub_year": "2021", "author_list": "Hamze Bajgiran, Hamed and Owhadi, Houman" }, { "id": "https://authors.library.caltech.edu/records/3j1pw-an266", "eprint_id": 115614, "eprint_status": "archive", "datestamp": "2023-08-20 05:03:15", "lastmod": "2025-02-02 01:05:10", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Wen-Gege", "name": { "family": "Wen", "given": "Gege" }, "orcid": "0000-0003-1668-3777" }, { "id": "Li-Zongyi", "name": { "family": "Li", "given": "Zongyi" }, "orcid": "0000-0003-2081-9665" }, { "id": "Azizzadenesheli-Kamyar", "name": { "family": "Azizzadenesheli", "given": "Kamyar" }, "orcid": "0000-0001-8507-1868" }, { "id": "Anandkumar-A", "name": { "family": "Anandkumar", "given": "Anima" }, "orcid": "0000-0002-6974-6797" }, { "id": "Benson-Sally-M", "name": { "family": "Benson", "given": "Sally M." }, "orcid": "0000-0002-3733-4296" } ] }, "title": "U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow", "ispublished": "unpub", "full_text_status": "public", "keywords": "Multiphase flow, Fourier neural operator, Convolutional neural network, Carbon capture and storage, Deep learning", "note": "Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) \n\nG. Wen and S. M. Benson gratefully acknowledges the supported by ExxonMobil through the Strategic Energy Alliance at Stanford University and the Stanford Center for Carbon Storage. Z. Li gratefully acknowledges the financial support from the Kortschak Scholars Program. A. Anandkumar is supported in part by Bren endowed chair, LwLL grants, Beyond Limits, Raytheon, Microsoft, Google, Adobe faculty fellowships, and DE Logi grant. The authors would like to acknowledge the reviewers and editors for the constructive comments. \n\nCode and data availability. The python code for U-FNO model architecture and the data set used in training is available at https://github.com/gegewen/ufno. Web application https://ccsnet.ai hosts the trained U-FNO models to provide real time predictions.\n\nSubmitted - 2109.03697.pdf
", "abstract": "Numerical simulation of multiphase flow in porous media is essential for many geoscience applications. Machine learning models trained with numerical simulation data can provide a faster alternative to traditional simulators. Here we present U-FNO, a novel neural network architecture for solving multiphase flow problems with superior accuracy, speed, and data efficiency. U-FNO is designed based on the newly proposed Fourier neural operator (FNO), which has shown excellent performance in single-phase flows. We extend the FNO-based architecture to a highly complex CO\u2082-water multiphase problem with wide ranges of permeability and porosity heterogeneity, anisotropy, reservoir conditions, injection configurations, flow rates, and multiphase flow properties. The U-FNO architecture is more accurate in gas saturation and pressure buildup predictions than the original FNO and a state-of-the-art convolutional neural network (CNN) benchmark. Meanwhile, it has superior data utilization efficiency, requiring only a third of the training data to achieve the equivalent accuracy as CNN. U-FNO provides superior performance in highly heterogeneous geological formations and critically important applications such as gas saturation and pressure buildup \"fronts\" determination. The trained model can serve as a general-purpose alternative to routine numerical simulations of 2D-radial CO\u2082 injection problems with significant speed-ups than traditional simulators.", "date": "2021-09-03", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20220714-224722475", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220714-224722475", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "ExxonMobil" }, { "agency": "Stanford University" }, { "agency": "Kortschak Scholars Program" }, { "agency": "Bren Professor of Computing and Mathematical Sciences" }, { "agency": "Learning with Less Labels (LwLL)" }, { "agency": "Beyond Limits" }, { "agency": "Raytheon Company" }, { "agency": "Microsoft Faculty Fellowship" }, { "agency": "Google Faculty Research Award" }, { "agency": "Adobe" }, { "agency": "Caltech De Logi Fund" } ] }, "local_group": { "items": [ { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "doi": "10.48550/arXiv.arXiv.2109.03697", "primary_object": { "basename": "2109.03697.pdf", "url": "https://authors.library.caltech.edu/records/3j1pw-an266/files/2109.03697.pdf" }, "pub_year": "2021", "author_list": "Wen, Gege; Li, Zongyi; et al." }, { "id": "https://authors.library.caltech.edu/records/v0cp5-ykc35", "eprint_id": 114897, "eprint_status": "archive", "datestamp": "2023-08-20 04:47:15", "lastmod": "2025-02-01 19:36:44", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hamze-Bajgiran-Hamed", "name": { "family": "Hamze Bajgiran", "given": "Hamed" } }, { "id": "Batlle-Franch-Pau", "name": { "family": "Batlle Franch", "given": "Pau" } }, { "id": "Owhadi-H", "name": { "family": "Owhadi", "given": "Houman" }, "orcid": "0000-0002-5677-1600" }, { "id": "Scovel-Clint", "name": { "family": "Scovel", "given": "Clint" }, "orcid": "0000-0001-7757-3411" }, { "id": "Shirdel-Mahdy", "name": { "family": "Shirdel", "given": "Mahdy" } }, { "id": "Stanley-Michael", "name": { "family": "Stanley", "given": "Michael" } }, { "id": "Tavallali-Peyman", "name": { "family": "Tavallali", "given": "Peyman" }, "orcid": "0000-0001-7166-5489" } ] }, "title": "Uncertainty Quantification of the 4th kind; optimal posterior accuracy-uncertainty tradeoff with the minimum enclosing ball", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2021. California Institute of Technology. Government sponsorship acknowledged. \n\nPart of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. The authors gratefully acknowledge support from Beyond Limits (Learning Optimal Models) through CAST (The Caltech Center for Autonomous Systems and Technologies) and partial support from the Air Force Office of Scientific Research under award number FA9550-18-1-0271 (Games for Computation and Learning).\n\nSubmitted - 2108.10517.pdf
", "abstract": "There are essentially three kinds of approaches to Uncertainty Quantification (UQ): (A) robust optimization, (B) Bayesian, (C) decision theory. Although (A) is robust, it is unfavorable with respect to accuracy and data assimilation. (B) requires a prior, it is generally brittle and posterior estimations can be slow. Although (C) leads to the identification of an optimal prior, its approximation suffers from the curse of dimensionality and the notion of risk is one that is averaged with respect to the distribution of the data. We introduce a 4th kind which is a hybrid between (A), (B), (C), and hypothesis testing. It can be summarized as, after observing a sample x, (1) defining a likelihood region through the relative likelihood and (2) playing a minmax game in that region to define optimal estimators and their risk. The resulting method has several desirable properties (a) an optimal prior is identified after measuring the data, and the notion of risk is a posterior one, (b) the determination of the optimal estimate and its risk can be reduced to computing the minimum enclosing ball of the image of the likelihood region under the quantity of interest map (which is fast and not subject to the curse of dimensionality). The method is characterized by a parameter in [0,1] acting as an assumed lower bound on the rarity of the observed data (the relative likelihood). When that parameter is near 1, the method produces a posterior distribution concentrated around a maximum likelihood estimate with tight but low confidence UQ estimates. When that parameter is near 0, the method produces a maximal risk posterior distribution with high confidence UQ estimates. In addition to navigating the accuracy-uncertainty tradeoff, the proposed method addresses the brittleness of Bayesian inference by navigating the robustness-accuracy tradeoff associated with data assimilation.", "date": "2021-08-24", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20220524-180308552", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220524-180308552", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NASA/JPL/Caltech" }, { "agency": "Beyond Limits" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-18-1-0271" } ] }, "local_group": { "items": [ { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "doi": "10.48550/arXiv.2108.10517", "primary_object": { "basename": "2108.10517.pdf", "url": "https://authors.library.caltech.edu/records/v0cp5-ykc35/files/2108.10517.pdf" }, "pub_year": "2021", "author_list": "Hamze Bajgiran, Hamed; Batlle Franch, Pau; et al." }, { "id": "https://authors.library.caltech.edu/records/h5ry0-fsp13", "eprint_id": 110666, "eprint_status": "archive", "datestamp": "2023-08-20 04:44:45", "lastmod": "2026-03-30 06:17:00", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kovachki-Nikola-B", "name": { "family": "Kovachki", "given": "Nikola" }, "orcid": "0000-0002-3650-2972" }, { "id": "Li-Zongyi", "name": { "family": "Li", "given": "Zongyi" }, "orcid": "0000-0003-2081-9665" }, { "id": "Liu-Burigede", "name": { "family": "Liu", "given": "Burigede" }, "orcid": "0000-0002-6518-3368" }, { "id": "Azizzadenesheli-Kamyar", "name": { "family": "Azizzadenesheli", "given": "Kamyar" }, "orcid": "0000-0001-8507-1868" }, { "id": "Bhattacharya-K", "name": { "family": "Bhattacharya", "given": "Kaushik" }, "orcid": "0000-0003-2908-5469" }, { "id": "Stuart-A-M", "name": { "family": "Stuart", "given": "Andrew" }, "orcid": "0000-0001-9091-7266" }, { "id": "Anandkumar-A", "name": { "family": "Anandkumar", "given": "Anima" } } ] }, "title": "Neural Operator: Learning Maps Between Function Spaces", "ispublished": "unpub", "full_text_status": "public", "keywords": "Deep Learning, Operator Inference, Partial Differential Equations, Navier-Stokes Equation", "note": "Z. Li gratefully acknowledges the financial support from the Kortschak Scholars Program. A. Anandkumar is supported in part by Bren endowed chair, LwLL grants, Beyond Limits, Raytheon, Microsoft, Google, Adobe faculty fellowships, and DE Logi grant. K. Bhattacharya, N. B. Kovachki, B. Liu and A. M. Stuart gratefully acknowledge the financial support of the Army Research Laboratory through the Cooperative Agreement Number W911NF-12-0022. Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-12-2-0022. AMS is also supported by NSF (award DMS-1818977). \n\nThe views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. \n\nThe computations presented here were conducted on the Caltech High Performance Cluster, partially supported by a grant from the Gordon and Betty Moore Foundation.\n\nSubmitted - 2108.08481.pdf
", "abstract": "The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks tailored to learn operators mapping between infinite dimensional function spaces. We formulate the approximation of operators by composition of a class of linear integral operators and nonlinear activation functions, so that the composed operator can approximate complex nonlinear operators. Furthermore, we introduce four classes of operator parameterizations: graph-based operators, low-rank operators, multipole graph-based operators, and Fourier operators and describe efficient algorithms for computing with each one. The proposed neural operators are resolution-invariant: they share the same network parameters between different discretizations of the underlying function spaces and can be used for zero-shot super-resolutions. Numerically, the proposed models show superior performance compared to existing machine learning based methodologies on Burgers' equation, Darcy flow, and the Navier-Stokes equation, while being several order of magnitude faster compared to conventional PDE solvers.", "date": "2021-08-19", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20210831-204010794", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210831-204010794", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Kortschak Scholars Program" }, { "agency": "Bren Professor of Computing and Mathematical Sciences" }, { "agency": "Learning with Less Labels (LwLL)" }, { "agency": "Beyond Limits" }, { "agency": "Raytheon Company" }, { "agency": "Microsoft Faculty Fellowship" }, { "agency": "Google Faculty Research Award" }, { "agency": "Adobe" }, { "agency": "Caltech De Logi Fund" }, { "agency": "Army Research Laboratory", "grant_number": "W911NF-12-0022" }, { "agency": "NSF", "grant_number": "DMS-1818977" }, { "agency": "Gordon and Betty Moore Foundation" } ] }, "local_group": { "items": [ { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "doi": "10.48550/arXiv.2108.08481", "primary_object": { "basename": "2108.08481.pdf", "url": "https://authors.library.caltech.edu/records/h5ry0-fsp13/files/2108.08481.pdf" }, "pub_year": "2021", "author_list": "Kovachki, Nikola; Li, Zongyi; et al." }, { "id": "https://authors.library.caltech.edu/records/1b23n-q5002", "eprint_id": 108529, "eprint_status": "archive", "datestamp": "2023-08-20 02:21:47", "lastmod": "2026-03-29 21:13:56", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Tavallali-Peyman", "name": { "family": "Tavallali", "given": "Peyman" }, "orcid": "0000-0001-7166-5489" }, { "id": "Hamze-Bajgiran-Hamed", "name": { "family": "Hamze Bajgiran", "given": "Hamed" } }, { "id": "Esaid-Danial-J", "name": { "family": "Esaid", "given": "Danial J." } }, { "id": "Owhadi-H", "name": { "family": "Owhadi", "given": "Houman" }, "orcid": "0000-0002-5677-1600" } ] }, "title": "Decision Theoretic Bootstrapping", "ispublished": "unpub", "full_text_status": "public", "note": "Attribution 4.0 International (CC BY 4.0).\n\n\u00a9 2021. California Institute of Technology. Government sponsorship acknowledged.\n\nThis research was carried out at the Jet Propulsion Laboratory, California Institute\nof Technology, under a contract with the National Aeronautics and Space Administration\nand support from Beyond Limits (Learning Optimal Models) and AFOSR (Grant number\nFA9550-18-1-0271, Games for Computation and Learning). The authors are thankful to\nAmy Braverman, Lukas Mandrake and Kiri Wagstaff, for their insights.\n\nSubmitted - 2103.09982.pdf
", "abstract": "The design and testing of supervised machine learning models combine two fundamental distributions: (1) the training data distribution (2) the testing data distribution. Although these two distributions are identical and identifiable when the data set is infinite; they are imperfectly known (and possibly distinct) when the data is finite (and possibly corrupted) and this uncertainty must be taken into account for robust Uncertainty Quantification (UQ). We present a general decision-theoretic bootstrapping solution to this problem: (1) partition the available data into a training subset and a UQ subset (2) take m subsampled subsets of the training set and train m models (3) partition the UQ set into n sorted subsets and take a random fraction of them to define n corresponding empirical distributions \u03bc_j (4) consider the adversarial game where Player I selects a model i\u2208{1,\u2026,m}, Player II selects the UQ distribution \u03bc_j and Player I receives a loss defined by evaluating the model i against data points sampled from \u03bc_j (5) identify optimal mixed strategies (probability distributions over models and UQ distributions) for both players. These randomized optimal mixed strategies provide optimal model mixtures and UQ estimates given the adversarial uncertainty of the training and testing distributions represented by the game. The proposed approach provides (1) some degree of robustness to distributional shift in both the distribution of training data and that of the testing data (2) conditional probability distributions on the output space forming aleatory representations of the uncertainty on the output as a function of the input variable.", "date": "2021-03-18", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20210323-130821498", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210323-130821498", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NASA/JPL/Caltech" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-18-1-0271" } ] }, "local_group": { "items": [ { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "doi": "10.48550/arXiv.2103.09982", "primary_object": { "basename": "2103.09982.pdf", "url": "https://authors.library.caltech.edu/records/1b23n-q5002/files/2103.09982.pdf" }, "pub_year": "2021", "author_list": "Tavallali, Peyman; Hamze Bajgiran, Hamed; et al." }, { "id": "https://authors.library.caltech.edu/records/ya4es-0tj28", "eprint_id": 109397, "eprint_status": "archive", "datestamp": "2023-08-20 00:24:54", "lastmod": "2026-03-30 15:46:59", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cardona-Jennifer-L", "name": { "family": "Cardona", "given": "Jennifer L." } }, { "id": "Bouman-K-L", "name": { "family": "Bouman", "given": "Katherine L." }, "orcid": "0000-0003-0077-4367" }, { "id": "Dabiri-J-O", "name": { "family": "Dabiri", "given": "John O." }, "orcid": "0000-0002-6722-9008" } ] }, "title": "Wind speed inference from environmental flow-structure interactions", "ispublished": "unpub", "full_text_status": "public", "keywords": "Flow imaging and velocimetry, optical based flow diagnostics, fluid-structure interactions", "note": "The authors would like to thank Peter Gunnarson, Berthy Feng, and Emily de Jong for their assistance in running wind tunnel experiments, and Matthew Fu for his thoughtful comments and discussion. \n\nThis work was supported by the National Science Foundation (grant CBET-2019712), and by the Center for Autonomous Systems and Technologies at Caltech. \n\nThe authors report no conflict of interest. \n\nData Availability Statement. The data discussed in this work will be made available at the Stanford Digital Repository at\nhttps://purl.stanford.edu/tp480sx4819. \n\nAuthor Contributions. Conceptualization: JLC; KLB; JOD. Methodology: JLC; JOD. Investigation: JLC. Software: JLC. Data analysis: JLC; JOD. Funding acquisition: KLB; JOD. \n\nSupplementary Material. Additional information can be found in the supplementary material.\n\nSubmitted - 2011.09609.pdf
", "abstract": "This study aims to leverage the relationship between fluid dynamic loading and resulting structural deformation to infer the incident flow speed from measurements of time-dependent structure kinematics. Wind tunnel studies are performed on cantilevered cylinders and trees. Tip deflections of the wind-loaded structures are captured in time series data, and a physical model of the relationship between force and deflection is applied to calculate the instantaneous wind speed normalized with respect to a known reference wind speed. Wind speeds inferred from visual measurements showed consistent agreement with ground truth anemometer measurements for different cylinder and tree configurations. These results suggest an approach for non-intrusive, quantitative flow velocimetry that eliminates the need to directly visualize or instrument the flow itself.", "date": "2020-11-19", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20210604-142548826", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210604-142548826", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CBET-2019712" }, { "agency": "Center for Autonomous Systems and Technologies" } ] }, "local_group": { "items": [ { "id": "Astronomy-Department" }, { "id": "GALCIT" }, { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "doi": "10.48550/arXiv.2011.09609", "primary_object": { "basename": "2011.09609.pdf", "url": "https://authors.library.caltech.edu/records/ya4es-0tj28/files/2011.09609.pdf" }, "pub_year": "2020", "author_list": "Cardona, Jennifer L.; Bouman, Katherine L.; et al." }, { "id": "https://authors.library.caltech.edu/records/f8x2p-rtc42", "eprint_id": 106584, "eprint_status": "archive", "datestamp": "2023-08-19 23:56:46", "lastmod": "2025-02-01 23:14:59", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marino-Joseph-L", "name": { "family": "Marino", "given": "Joseph" }, "orcid": "0000-0001-6387-8062" }, { "id": "Pich\u00e9-Alexandre", "name": { "family": "Pich\u00e9", "given": "Alexandre" } }, { "id": "Ialongo-Alessandro-Davide", "name": { "family": "Ialongo", "given": "Alessandro Davide" } }, { "id": "Yue-Yisong", "name": { "family": "Yue", "given": "Yisong" }, "orcid": "0000-0001-9127-1989" } ] }, "title": "Iterative Amortized Policy Optimization", "ispublished": "unpub", "full_text_status": "public", "note": "JM acknowledges Scott Fujimoto for helpful discussions. This work was funded in part by NSF #1918839 and Beyond Limits. JM is currently employed by Google DeepMind. The authors declare no other competing interests related to this work.\n\nAccepted Version - 2010.10670.pdf
", "abstract": "Policy networks are a central feature of deep reinforcement learning (RL) algorithms for continuous control, enabling the estimation and sampling of high-value actions. From the variational inference perspective on RL, policy networks, when employed with entropy or KL regularization, are a form of amortized optimization, optimizing network parameters rather than the policy distributions directly. However, this direct amortized mapping can empirically yield suboptimal policy estimates. Given this perspective, we consider the more flexible class of iterative amortized optimizers. We demonstrate that the resulting technique, iterative amortized policy optimization, yields performance improvements over conventional direct amortization methods on benchmark continuous control tasks.", "date": "2020-10-20", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20201110-082336091", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201110-082336091", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CCF-1918839" }, { "agency": "Beyond Limits" } ] }, "local_group": { "items": [ { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "doi": "10.48550/arXiv.2010.10670", "primary_object": { "basename": "2010.10670.pdf", "url": "https://authors.library.caltech.edu/records/f8x2p-rtc42/files/2010.10670.pdf" }, "pub_year": "2020", "author_list": "Marino, Joseph; Pich\u00e9, Alexandre; et al." }, { "id": "https://authors.library.caltech.edu/records/hpbg9-9ea84", "eprint_id": 106480, "eprint_status": "archive", "datestamp": "2023-08-19 23:55:01", "lastmod": "2026-03-30 17:20:38", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Li-Zongyi", "name": { "family": "Li", "given": "Zongyi" }, "orcid": "0000-0003-2081-9665" }, { "id": "Kovachki-N-B", "name": { "family": "Kovachki", "given": "Nikola" }, "orcid": "0000-0002-3650-2972" }, { "id": "Azizzadenesheli-K", "name": { "family": "Azizzadenesheli", "given": "Kamyar" }, "orcid": "0000-0001-8507-1868" }, { "id": "Liu-Burigede", "name": { "family": "Liu", "given": "Burigede" }, "orcid": "0000-0002-6518-3368" }, { "id": "Bhattacharya-K", "name": { "family": "Bhattacharya", "given": "Kaushik" }, "orcid": "0000-0003-2908-5469" }, { "id": "Stuart-A-M", "name": { "family": "Stuart", "given": "Andrew" }, "orcid": "0000-0001-9091-7266" }, { "id": "Anandkumar-A", "name": { "family": "Anandkumar", "given": "Anima" }, "orcid": "0000-0002-6974-6797" } ] }, "title": "Fourier Neural Operator for Parametric Partial Differential Equations", "ispublished": "unpub", "full_text_status": "public", "note": "Z. Li gratefully acknowledges the financial support from the Kortschak Scholars Program. A. Anandkumar is supported in part by Bren endowed chair, LwLL grants, Beyond Limits, Raytheon, Microsoft, Google, Adobe faculty fellowships, and De Logi grant. K. Bhattacharya, N. B. Kovachki, B. Liu and A. M. Stuart gratefully acknowledge the financial support of the Army Research Laboratory through the Cooperative Agreement Number W911NF-12-0022. Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-12-2-0022. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.
\n\nSubmitted - 2010.08895.pdf
", "abstract": "The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For partial differential equations (PDEs), neural operators directly learn the mapping from any functional parametric dependence to the solution. Thus, they learn an entire family of PDEs, in contrast to classical methods which solve one instance of the equation. In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on Burgers' equation, Darcy flow, and the Navier-Stokes equation (including the turbulent regime). Our Fourier neural operator shows state-of-the-art performance compared to existing neural network methodologies and it is up to three orders of magnitude faster compared to traditional PDE solvers.
", "date": "2020-10-18", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20201106-120140981", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201106-120140981", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Kortschak Scholars Program" }, { "agency": "Bren Professor of Computing and Mathematical Sciences" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)" }, { "agency": "Learning with Less Labels (LwLL)" }, { "agency": "Beyond Limits" }, { "agency": "Raytheon Company" }, { "agency": "Microsoft Faculty Fellowship" }, { "agency": "Google Faculty Research Award" }, { "agency": "Adobe" }, { "agency": "Caltech De Logi Fund" }, { "agency": "Army Research Laboratory", "grant_number": "W911NF-12-0022" } ] }, "local_group": { "items": [ { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "doi": "10.48550/arXiv.2010.08895", "primary_object": { "basename": "2010.08895.pdf", "url": "https://authors.library.caltech.edu/records/hpbg9-9ea84/files/2010.08895.pdf" }, "pub_year": "2020", "author_list": "Li, Zongyi; Kovachki, Nikola; et al." }, { "id": "https://authors.library.caltech.edu/records/7sv9q-5fv63", "eprint_id": 103473, "eprint_status": "archive", "datestamp": "2023-08-19 20:39:18", "lastmod": "2026-03-30 06:24:31", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "Song-Jialin", "name": { "family": "Song", "given": "Jialin" } }, { "id": "Lanka-Ravi", "name": { "family": "Lanka", "given": "Ravi" } }, { "id": "Yue-Yisong", "name": { "family": "Yue", "given": "Yisong" }, "orcid": "0000-0001-9127-1989" }, { "id": "Dilkina-Bistra", "name": { "family": "Dilkina", "given": "Bistra" }, "orcid": "0000-0002-6784-473X" } ] }, "title": "A General Large Neighborhood Search Framework for Solving Integer Programs", "ispublished": "unpub", "full_text_status": "public", "note": "We thank the anonymous reviewers for their suggestions for improvements. Dilkina was supported partially by NSF #1763108, DARPA, DHS Center of Excellence \"Critical Infrastructure Resilience Institute\", and Microsoft. This research was also supported in part by funding from NSF #1645832, Raytheon, Beyond Limits, and JPL.\n\nAccepted Version - 2004.00422v3.pdf
", "abstract": "This paper studies how to design abstractions of large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general purpose ways, and that are amenable to data-driven design. The goal is to arrive at new approaches that can reliably outperform existing solvers in wall-clock time. We focus on solving integer programs, and ground our approach in the large neighborhood search (LNS) paradigm, which iteratively chooses a subset of variables to optimize while leaving the remainder fixed. The appeal of LNS is that it can easily use any existing solver as a subroutine, and thus can inherit the benefits of carefully engineered heuristic approaches and their software implementations. We also show that one can learn a good neighborhood selector from training data. Through an extensive empirical validation, we demonstrate that our LNS framework can significantly outperform, in wall-clock time, compared to state-of-the-art commercial solvers such as Gurobi.", "date": "2020-03-29", "date_type": "published", "publisher": "arXiv", "id_number": "CaltechAUTHORS:20200526-151215262", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200526-151215262", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "CMMI-1763108" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)" }, { "agency": "Department of Homeland Security" }, { "agency": "Microsoft Research" }, { "agency": "NSF", "grant_number": "CNS-1645832" }, { "agency": "Raytheon Company" }, { "agency": "Beyond Limits" }, { "agency": "JPL" } ] }, "local_group": { "items": [ { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "doi": "10.48550/arXiv.2004.00422", "primary_object": { "basename": "2004.00422v3.pdf", "url": "https://authors.library.caltech.edu/records/7sv9q-5fv63/files/2004.00422v3.pdf" }, "pub_year": "2020", "author_list": "Song, Jialin; Lanka, Ravi; et al." }, { "id": "https://authors.library.caltech.edu/records/wjr0t-sh732", "eprint_id": 99547, "eprint_status": "archive", "datestamp": "2023-08-19 17:40:18", "lastmod": "2025-02-01 17:11:33", "type": "monograph", "metadata_visibility": "show", "creators": { "items": [ { "id": "O'Connell-Michael", "name": { "family": "O'Connell", "given": "Michael" } }, { "id": "Shi-Guanya", "name": { "family": "Shi", "given": "Guanya" }, "orcid": "0000-0002-9075-3705" }, { "id": "Shi-Xichen", "name": { "family": "Shi", "given": "Xichen" } }, { "id": "Chung-Soon-Jo", "name": { "family": "Chung", "given": "Soon-Jo" }, "orcid": "0000-0002-6657-3907" } ] }, "title": "Meta-Learning-Based Robust Adaptive Flight Control Under Uncertain Wind Conditions", "ispublished": "unpub", "full_text_status": "public", "note": "We thank Yisong Yue, Animashree Anandkumar, Kamyar Azizzadenesheli, Joel Burdick, Mory Gharib, Daniel Pastor Moreno, and Anqi Liu for helpful discussions. The work is funded in part by Caltech's Center for Autonomous Systems and Technologies and Raytheon Company.\n\nSubmitted - 2103.01932v1.pdf
", "abstract": "Realtime model learning proves challenging for complex dynamical systems, such as drones flying in variable wind conditions. Machine learning technique such as deep neural networks have high representation power but is often too slow to update onboard. On the other hand, adaptive control relies on simple linear parameter models can update as fast as the feedback control loop. We propose an online composite adaptation method that treats outputs from a deep neural network as a set of basis functions capable of representing different wind conditions. To help with training, meta-learning techniques are used to optimize the network output useful for adaptation. We validate our approach by flying a drone in an open air wind tunnel under varying wind conditions and along challenging trajectories. We compare the result with other adaptive controller with different basis function sets and show improvement over tracking and prediction errors.", "date": "2019-09", "date_type": "published", "id_number": "CaltechAUTHORS:20191029-154625952", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191029-154625952", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Center for Autonomous Systems and Technologies" }, { "agency": "Raytheon Company" } ] }, "local_group": { "items": [ { "id": "GALCIT" }, { "id": "Center-for-Autonomous-Systems-and-Technologies-(CAST)" } ] }, "doi": "10.48550/arXiv.2103.01932", "primary_object": { "basename": "2103.01932v1.pdf", "url": "https://authors.library.caltech.edu/records/wjr0t-sh732/files/2103.01932v1.pdf" }, "pub_year": "2019", "author_list": "O'Connell, Michael; Shi, Guanya; et al." } ]