@article{https://authors.library.caltech.edu/records/1fbsq-jcx05, title = "Bridging Algorithmic Information Theory and Machine Learning: A new approach to kernel learning", journal = "Physica D: Nonlinear Phenomena", year = "2024", url = "https://authors.library.caltech.edu/records/1fbsq-jcx05", id = "record", issn = "0167-2789", doi = "10.1016/j.physd.2024.134153", volume = "464" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20230502-759894900.1, title = "Gaussian process hydrodynamics", journal = "Applied Mathematics and Mechanics", year = "2023", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230502-759894900.1", id = "record", issn = "0253-4827", doi = "10.1007/s10483-023-2990-9" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20230605-334829000.12, title = "A note on microlocal kernel design for some slow–fast stochastic differential equations with critical transitions and application to EEG signals", journal = "Physica A", year = "2023", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230605-334829000.12", id = "record", issn = "0378-4371", doi = "10.1016/j.physa.2023.128583", volume = "616" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20230307-205876300.5, title = "Do ideas have shape? Idea registration as the continuous limit of artificial neural networks", journal = "Physica D", year = "2023", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230307-205876300.5", id = "record", issn = "0167-2789", doi = "10.1016/j.physd.2022.133592", volume = "444" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20230307-205876300.8, title = "One-shot learning of stochastic differential equations with data adapted kernels", journal = "Physica D", year = "2023", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230307-205876300.8", id = "record", issn = "0167-2789", doi = "10.1016/j.physd.2022.133583", volume = "444" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20221122-564647900.3, title = "Learning dynamical systems from data: A simple cross-validation perspective, Part III: Irregularly-sampled time series", journal = "Physica D", year = "2023", url = "https://resolver.caltech.edu/CaltechAUTHORS:20221122-564647900.3", id = "record", issn = "0167-2789", doi = "10.1016/j.physd.2022.133546", volume = "443" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20221020-727675300.1, title = {Learning "best" kernels from data in Gaussian process regression. With application to aerodynamics}, journal = "Journal of Computational Physics", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20221020-727675300.1", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2022.111595", volume = "470" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20230603-041912328, title = "Mean-field limits of trained weights in deep learning: A dynamical systems perspective", journal = "Dolomites Research Notes on Approximation", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20230603-041912328", id = "record", issn = "2035-6803", doi = "10.14658/pupj-drna-2022-3-12", volume = "15" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20220511-647768900, title = "Computational graph completion", journal = "Research in the Mathematical Sciences", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20220511-647768900", id = "record", issn = "2522-0144", doi = "10.1007/s40687-022-00320-8", volume = "9" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20220524-180318744, title = "Aggregation of Pareto optimal models", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20220524-180318744", id = "record", doi = "10.48550/arXiv.2112.04161" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20220524-180305206, title = "Data-driven geophysical forecasting: Simple, low-cost, and accurate baselines with kernel methods", year = "2022", url = "https://resolver.caltech.edu/CaltechAUTHORS:20220524-180305206", id = "record", doi = "10.48550/arXiv.2103.10935" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20220524-180308552, title = "Uncertainty Quantification of the 4th kind; 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Plato's theory of forms as the continuous limit of artificial neural networks", year = "2020", url = "https://resolver.caltech.edu/CaltechAUTHORS:20201109-155524397", id = "record", doi = "10.48550/arXiv.2008.03920" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20201106-120218966, title = "Competitive Mirror Descent", year = "2020", url = "https://resolver.caltech.edu/CaltechAUTHORS:20201106-120218966", id = "record", doi = "10.48550/arXiv.2006.10179" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20190923-154306921, title = "Fast eigenpairs computation with operator adapted wavelets and hierarchical subspace correction", journal = "SIAM Journal on Numerical Analysis", year = "2019", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190923-154306921", id = "record", issn = "0036-1429", doi = "10.1137/18M1194079", volume = "57" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20191111-134055447, title = "Material-adapted refinable basis functions for elasticity simulation", journal = "ACM Transactions on Graphics", year = "2019", url = "https://resolver.caltech.edu/CaltechAUTHORS:20191111-134055447", id = "record", issn = "0730-0301", doi = "10.1145/3355089.3356567", volume = "38" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20190923-104545857, title = "De-noising by thresholding operator adapted wavelets", journal = "Statistics and Computing", year = "2019", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190923-104545857", id = "record", issn = "0960-3174", doi = "10.1007/s11222-019-09893-x", volume = "29" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20190923-153747161, title = "Kernel Mode Decomposition and programmable/interpretable regression networks", year = "2019", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190923-153747161", id = "record", doi = "10.48550/arXiv.1907.08592" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20190109-090349439, title = "Multiresolution Operator Decomposition for Flow Simulation in Fractured Porous Media", journal = "Journal of Computational Physics", year = "2019", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190109-090349439", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2018.12.032", volume = "391" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20190328-180953225, title = "Kernel Flows: From learning kernels from data into the abyss", journal = "Journal of Computational Physics", year = "2019", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190328-180953225", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2019.03.040", volume = "389" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20190315-100824617, title = "Operator-adapted wavelets for finite-element differential forms", journal = "Journal of Computational Physics", year = "2019", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190315-100824617", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2019.02.018", volume = "388" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20190109-112815344, title = "On testing the simulation theory", year = "2019", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190109-112815344", id = "record", doi = "10.48550/arXiv.1703.00058" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160223-152453383, title = "Qualitative Robustness in Bayesian Inference", journal = "ESAIM: Probability and Statistics", year = "2017", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160223-152453383", id = "record", issn = "1292-8100", doi = "10.1051/ps/2017014", volume = "21" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170707-092240450, title = "Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients", journal = "Journal of Computational Physics", year = "2017", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170707-092240450", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2017.06.037", volume = "347" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170825-144657432, title = "Self-Powered Dynamic Systems in the Framework of Optimal Uncertainty Quantification", journal = "Journal of Dynamic Systems, Measurement, and Control", year = "2017", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170825-144657432", id = "record", issn = "0022-0434", doi = "10.1115/1.4036367", volume = "139" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20170710-085210757, title = "Universal Scalable Robust Solvers from Computational Information Games and fast eigenspace adapted Multiresolution Analysis", year = "2017", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170710-085210757", id = "record", doi = "10.48550/arXiv.1703.10761" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20160224-064915023, title = "Handbook of Uncertainty Quantification", chapter = "Toward Machine Wald", year = "2017", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-064915023", id = "record", isbn = "978-3-319-12384-4", doi = "10.1007/978-3-319-12385-1\_3" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160224-070508936, title = "Separability of reproducing kernel Hilbert spaces", journal = "Proceedings of the American Mathematical Society", year = "2017", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-070508936", id = "record", issn = "0002-9939", doi = "10.1090/proc/13354", volume = "145" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160223-133809979, title = "Multigrid with rough coefficients and Multiresolution operator decomposition from Hierarchical Information Games", journal = "SIAM Review", year = "2017", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160223-133809979", id = "record", issn = "0036-1445", doi = "10.1137/15M1013894", volume = "59" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20190816-144341264, title = "AIAA SciTech Forum : 19th AIAA Non-Deterministic Approaches Conference", chapter = "The game theoretic approach to Uncertainty Quantification, reduced order modeling and numerical analysis", year = "2017", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190816-144341264", id = "record", isbn = "9781624104527", doi = "10.2514/6.2017-1092" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160223-151629237, title = "Extreme points of a ball about a measure with finite support", journal = "Communications in Mathematical Sciences", year = "2017", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160223-151629237", id = "record", issn = "1539-6746", doi = "10.4310/CMS.2017.v15.n1.a4", volume = "15" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20170602-084400992, title = "ASME 2016 International Mechanical Engineering Congress and Exposition", chapter = "Self-Powered and Bio-Inspired Dynamic Systems: Research and Education", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170602-084400992", id = "record", isbn = "978-0-7918-5054-1", doi = "10.1115/IMECE2016-65276" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20160224-094627612, title = "Metric based up-scaling", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-094627612", id = "record", doi = "10.48550/arXiv.0505223" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20160224-073833523, title = "Brittleness of Bayesian inference and new Selberg formulas", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-073833523", id = "record", doi = "10.48550/arXiv.1304.7046" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20160224-100431574, title = "Stochastic Variational Partitioned Runge-Kutta Integrators for Constrained Systems", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-100431574", id = "record", doi = "10.48550/arXiv.0709.2222" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20160224-090906859, title = "Temperature and Friction Accelerated Sampling of Boltzmann-Gibbs Distribution", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-090906859", id = "record", doi = "10.48550/arXiv.1007.0995" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20160224-080348129, title = "The optimal uncertainty algorithm in the mystic framework", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-080348129", id = "record", doi = "10.48550/arXiv.1202.1055" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20160224-065740350, title = "Conditioning Gaussian measure on Hilbert space", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-065740350", id = "record", doi = "10.48550/arXiv.1506.04208" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20160224-101438724, title = "Ballistic Transport at Uniform Temperature", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-101438724", id = "record", doi = "10.48550/arXiv.0710.1565" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20160224-103320707, title = "Ergodicity of Langevin Processes with Degenerate Diffusion in Momentums", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-103320707", id = "record", doi = "10.48550/arXiv.0710.4259" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20160224-082333411, title = "Equivalence of concentration inequalities for linear and non-linear functions", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-082333411", id = "record", doi = "10.48550/arXiv.1009.4913" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20160224-085934570, title = "Structure preserving Stochastic Impulse Methods for stiff Langevin systems with a uniform global error of order 1 or 1/2 on position", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-085934570", id = "record", doi = "10.48550/arXiv.1006.4657" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160317-083434102, title = "Variational and linearly implicit integrators, with applications", journal = "IMA Journal of Numerical Analysis", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160317-083434102", id = "record", issn = "0272-4979", doi = "10.1093/imanum/dru064", volume = "36" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20170615-123732747, title = "Handbook of Uncertainty Quantification", chapter = "Introduction to Uncertainty Quantification", year = "2016", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170615-123732747", id = "record", isbn = "978-3-319-11259-6", doi = "10.1007/978-3-319-11259-6\_1-1" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160224-071627521, title = "Temporal homogenization of linear ODEs, with applications to parametric super-resonance and energy harvest", journal = "Archive for Rational Mechanics and Analysis", year = "2015", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-071627521", id = "record", issn = "0003-9527", doi = "10.1007/s00205-015-0932-4", volume = "220" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20151030-084615377, title = "Convex Optimal Uncertainty Quantification", journal = "SIAM Journal of Optimization", year = "2015", url = "https://resolver.caltech.edu/CaltechAUTHORS:20151030-084615377", id = "record", issn = "1052-6234", doi = "10.1137/13094712X", volume = "25" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20151023-105214463, title = "Bayesian Numerical Homogenization", journal = "Multiscale Modeling and Simulation", year = "2015", url = "https://resolver.caltech.edu/CaltechAUTHORS:20151023-105214463", id = "record", issn = "1540-3459", doi = "10.1137/140974596", volume = "13" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160108-105121903, title = "On the Brittleness of Bayesian Inference", journal = "SIAM Review", year = "2015", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160108-105121903", id = "record", issn = "0036-1445", doi = "10.1137/130938633", volume = "57" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160108-101302184, title = "Brittleness of Bayesian inference under finite information in a continuous world", journal = "Electronic Journal of Statistics", year = "2015", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160108-101302184", id = "record", issn = "1935-7524", doi = "10.1214/15-EJS989", volume = "9" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20141201-081327318, title = "Optimal uncertainty quantification with model uncertainty and legacy data", journal = "Journal of the Mechanics and Physics of Solids", year = "2014", url = "https://resolver.caltech.edu/CaltechAUTHORS:20141201-081327318", id = "record", issn = "0022-5096", doi = "10.1016/j.jmps.2014.07.007", volume = "72" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160223-143844457, title = "Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization", journal = "ESAIM-Mathematical Modelling and Numerical Analysis", year = "2014", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160223-143844457", id = "record", issn = "0764-583X", doi = "10.1051/m2an/2013118", volume = "48" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160224-085030779, title = "Preface", journal = "ESAIM: Mathematical Modelling and Numerical Analysis", year = "2014", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-085030779", id = "record", issn = "0764-583X", doi = "10.1051/m2an/2013108", volume = "48" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20131119-093417975, title = "Optimal Uncertainty Quantification for Legacy Data Observations of Lipschitz Functions", journal = "ESAIM-Mathematical Modelling and Numerical Analysis", year = "2013", url = "https://resolver.caltech.edu/CaltechAUTHORS:20131119-093417975", id = "record", issn = "0764-583X", doi = "10.1051/m2an/2013083", volume = "47" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20210224-145143008, title = "Multiscale Analysis and Nonlinear Dynamics", chapter = "Modeling Across Scales: Discrete Geometric Structures in Homogenization and Inverse Homogenization", year = "2013", url = "https://resolver.caltech.edu/CaltechAUTHORS:20210224-145143008", id = "record", isbn = "9783527671632", doi = "10.1002/9783527671632.ch02" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20130829-153504635, title = "On the equilibrium of simplicial masonry structures", journal = "ACM Transactions on Graphics", year = "2013", url = "https://resolver.caltech.edu/CaltechAUTHORS:20130829-153504635", id = "record", issn = "0730-0301", doi = "10.1145/2461912.2461932", volume = "32" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20130628-141442082, title = "Variational integrators for electric circuits", journal = "Journal of Computational Physics", year = "2013", url = "https://resolver.caltech.edu/CaltechAUTHORS:20130628-141442082", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2013.02.006", volume = "242" } @inbook{https://resolver.caltech.edu/CaltechCDSTR:2012.002, title = "2013 American Control Conference (ACC)", chapter = "Convex optimal uncertainty quantification: Algorithms and a case study in energy storage placement for power grids", year = "2013", url = "https://resolver.caltech.edu/CaltechCDSTR:2012.002", id = "record", isbn = "978-1-4799-0177-7" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20130618-075057070, title = "Optimal Uncertainty Quantification", journal = "SIAM Review", year = "2013", url = "https://resolver.caltech.edu/CaltechAUTHORS:20130618-075057070", id = "record", issn = "0036-1445", doi = "10.1137/10080782X", volume = "55" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20130502-133827036, title = "Control of a model of DNA division via parametric resonance", journal = "Chaos", year = "2013", url = "https://resolver.caltech.edu/CaltechAUTHORS:20130502-133827036", id = "record", issn = "1054-1500", doi = "10.1063/1.4790835", volume = "23" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20120430-133945935, title = "Rigorous model-based uncertainty quantification with application to terminal ballistics—Part II. Systems with uncontrollable inputs and large scatter", journal = "Journal of the Mechanics and Physics of Solids", year = "2012", url = "https://resolver.caltech.edu/CaltechAUTHORS:20120430-133945935", id = "record", issn = "0022-5096", doi = "10.1016/j.jmps.2011.12.002", volume = "60" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20120502-091106236, title = "Rigorous model-based uncertainty quantification with application to terminal ballistics, part I: Systems with controllable inputs and small scatter", journal = "Journal of the Mechanics and Physics of Solids", year = "2012", url = "https://resolver.caltech.edu/CaltechAUTHORS:20120502-091106236", id = "record", issn = "0022-5096", doi = "10.1016/j.jmps.2011.12.001", volume = "60" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20120126-112528320, title = "Localized Bases for Finite-Dimensional Homogenization Approximations with Nonseparated Scales and High Contrast", journal = "Multiscale Modeling and Simulation", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20120126-112528320", id = "record", issn = "1540-3459", doi = "10.1137/100813968", volume = "9" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20111011-163848887, title = "Discrete Geometric Structures in Homogenization and Inverse Homogenization with Application to EIT", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20111011-163848887", id = "record", doi = "10.7907/XR8W-EA85" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20111012-113158874, title = "Optimal Uncertainty Quantification", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20111012-113158874", id = "record", doi = "10.7907/TTW6-QD19" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20111012-110532817, title = "Non-intrusive and structure preserving multiscale integration of stiff ODEs, SDEs and Hamiltonian systems with hidden slow dynamics via flow averaging", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20111012-110532817", id = "record", doi = "10.7907/QZNP-SR14" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20111012-113719601, title = "Localized bases for finite dimensional homogenization approximations with non-separated scales and high-contrast", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20111012-113719601", id = "record" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20111012-105135181, title = "Flux Norm Approach to Homogenization Problems with non-separated Scales", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20111012-105135181", id = "record", doi = "10.7907/T5DC-SN48" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20110822-140452319, title = "Rigorous uncertainty quantification without integral testing", journal = "Reliability Engineering and System Safety", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20110822-140452319", id = "record", issn = "0951-8320", doi = "10.1016/j.ress.2010.07.013", volume = "96" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20110414-085411000, title = "A non-adapted sparse approximation of PDEs with stochastic inputs", journal = "Journal of Computational Physics", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20110414-085411000", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2011.01.002", volume = "230" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20110315-151154130, title = "Uncertainty quantification via codimension-one partitioning", journal = "International Journal for Numerical Methods in Engineering", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20110315-151154130", id = "record", issn = "0029-5981", doi = "10.1002/nme.3030", volume = "85" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20110502-134102771, title = "Space-time FLAVORS: finite difference, multisymlectic, and pseudospectral integrators for multiscale PDEs", journal = "Dynamics of Partial Differential Equations", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20110502-134102771", id = "record", issn = "1548-159X", doi = "10.48550/arXiv.1104.0272", volume = "8" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20120215-101206163, title = "From efficient symplectic exponentiation of matrices to symplectic integration of high-dimensional Hamiltonian systems with slowly varying quadratic stiff potentials", journal = "Applied Mathematics Research eXpress", year = "2011", url = "https://resolver.caltech.edu/CaltechAUTHORS:20120215-101206163", id = "record", issn = "1687-1200", doi = "10.1093/amrx/abr008", volume = "2011" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20110318-145129123, title = "A cutoff phenomenon in accelerated stochastic simulations of chemical kinetics via flow averaging (FLAVOR-SSA)", journal = "Journal of Chemical Physics", year = "2010", url = "https://resolver.caltech.edu/CaltechAUTHORS:20110318-145129123", id = "record", issn = "0021-9606", doi = "10.1063/1.3518419", volume = "133" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20101025-093609352, title = "Flux Norm Approach to Finite Dimensional Homogenization Approximations with Non-Separated Scales and High Contrast", journal = "Archive for Rational Mechanics and Analysis", year = "2010", url = "https://resolver.caltech.edu/CaltechAUTHORS:20101025-093609352", id = "record", issn = "0003-9527", doi = "10.1007/s00205-010-0302-1", volume = "198" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20100927-105248361, title = "Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging", journal = "Multiscale Modeling and Simulation", year = "2010", url = "https://resolver.caltech.edu/CaltechAUTHORS:20100927-105248361", id = "record", issn = "1540-3459", doi = "10.1137/090771648", volume = "8" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20100709-105908209, title = "Optimal Control Strategies for Robust Certification", journal = "Journal of Computational and Nonlinear Dynamics", year = "2010", url = "https://resolver.caltech.edu/CaltechAUTHORS:20100709-105908209", id = "record", issn = "1555-1423", doi = "10.1115/1.4001375", volume = "5" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20190109-104739732, title = "Uncertainty quantification via codimension one domain partitioning and a new concentration inequality", journal = "Procedia - Social and Behavioral Sciences", year = "2010", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190109-104739732", id = "record", issn = "1877-0428", doi = "10.1016/j.sbspro.2010.05.211", volume = "2" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20100609-111014824, title = "Long-Run Accuracy of Variational Integrators in the Stochastic Context", journal = "SIAM Journal on Numerical Analysis", year = "2010", url = "https://resolver.caltech.edu/CaltechAUTHORS:20100609-111014824", id = "record", issn = "0036-1429", doi = "10.1137/090758842", volume = "48" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20110526-090344006, title = "Global Energy Matching Method for Atomistic-to-Continuum Modeling of Self-Assembling Biopolymer Aggregates", journal = "Multiscale Modeling \& Simulation", year = "2010", url = "https://resolver.caltech.edu/CaltechAUTHORS:20110526-090344006", id = "record", issn = "1540-3459", doi = "10.1137/090781619", volume = "8" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20170328-173555191, title = "Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference", chapter = "Multiple target detection using Bayesian learning", year = "2009", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170328-173555191", id = "record", isbn = "978-1-4244-3871-6", doi = "10.1109/CDC.2009.5399565" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20090911-153604312, title = "Numerical coarsening of inhomogeneous elastic materials", journal = "ACM Transactions on Graphics", year = "2009", url = "https://resolver.caltech.edu/CaltechAUTHORS:20090911-153604312", id = "record", issn = "0730-0301", doi = "10.1145/1531326.1531357", volume = "28" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20161116-134645591, title = "SIGGRAPH '09 ACM SIGGRAPH 2009 papers", chapter = "Numerical coarsening of inhomogeneous elastic materials", year = "2009", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161116-134645591", id = "record", isbn = "978-1-60558-726-4", doi = "10.1145/1576246.1531357" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20090713-115112523, title = "Stochastic variational integrators", journal = "IMA Journal of Numerical Analysis", year = "2009", url = "https://resolver.caltech.edu/CaltechAUTHORS:20090713-115112523", id = "record", issn = "0272-4979", doi = "10.1093/imanum/drn018", volume = "29" } @article{https://resolver.caltech.edu/CaltechAUTHORS:OWHcmame08, title = "Numerical homogenization of the acoustic wave equations with a continuum of scales", journal = "Computer Methods in Applied Mechanics and Engineering", year = "2008", url = "https://resolver.caltech.edu/CaltechAUTHORS:OWHcmame08", id = "record", issn = "0045-7825", doi = "10.1016/j.cma.2008.08.012", volume = "198" } @article{https://resolver.caltech.edu/CaltechAUTHORS:LUCcmame08, title = "Rigorous verification, validation, uncertainty quantification and certification through concentration-of-measure inequalities", journal = "Computer Methods in Applied Mechanics and Engineering", year = "2008", url = "https://resolver.caltech.edu/CaltechAUTHORS:LUCcmame08", id = "record", issn = "0045-7825", doi = "10.1016/j.cma.2008.06.008", volume = "197" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160226-104801314, title = "Bistable Equilibrium Points of Mercury Body Burden", journal = "Journal of Biological Systems", year = "2008", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160226-104801314", id = "record", issn = "0218-3390", doi = "10.1142/S0218339008002459", volume = "16" } @article{https://resolver.caltech.edu/CaltechAUTHORS:OWHsiamjna07, title = "Homogenization of Parabolic Equations with a Continuum of Space and Time Scales", journal = "SIAM Journal on Numerical Analysis", year = "2007", url = "https://resolver.caltech.edu/CaltechAUTHORS:OWHsiamjna07", id = "record", issn = "0036-1429", doi = "10.1137/060670420", volume = "46" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20190109-105904110, title = "From a market of dreamers to economical shocks", journal = "Physica A", year = "2004", url = "https://resolver.caltech.edu/CaltechAUTHORS:20190109-105904110", id = "record", issn = "0378-4371", doi = "10.1016/j.physa.2004.05.078", volume = "343" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160224-131618930, title = "Averaging Versus Chaos in Turbulent Transport?", journal = "Communications in Mathematical Physics", year = "2004", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-131618930", id = "record", issn = "0010-3616", doi = "10.1007/s00220-004-1069-8", volume = "247" } @article{https://resolver.caltech.edu/CaltechAUTHORS:OWHaop03, title = "Anomalous slow diffusion from perpetual homogenization", journal = "Annals of Probability", year = "2003", url = "https://resolver.caltech.edu/CaltechAUTHORS:OWHaop03", id = "record", issn = "0091-1798", doi = "10.1214/aop/1068646372", volume = "31" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160224-124326510, title = "Approximation of the effective conductivity of ergodic media by periodization", journal = "Probability Theory and Related Fields", year = "2003", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-124326510", id = "record", issn = "0178-8051", doi = "10.1007/s00440-002-0240-4", volume = "125" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160224-121708361, title = "Multi-scale homogenization with bounded ratios and Anomalous Slow Diffusion", journal = "Communications on Pure and Applied Mathematics", year = "2003", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-121708361", id = "record", issn = "0010-3640", doi = "10.1002/cpa.10053", volume = "56" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160224-110658762, title = "Super-diffusivity in a shear flow model from perpetual homogenization", journal = "Communications in Mathematical Physics", year = "2002", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160224-110658762", id = "record", issn = "0010-3616", doi = "10.1007/s002200200640", volume = "227" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170408-142731157, title = "Distances and diameters in concentration inequalities: from geometry to optimal assignment of sampling resources", journal = "International Journal for Uncertainty Quantification", year = "2002", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170408-142731157", id = "record", issn = "2152-5080", doi = "10.1615/Int.J.UncertaintyQuantification.2011003433", volume = "2" }