Monograph records
https://feeds.library.caltech.edu/people/Bhattacharya-K/monograph.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 12 Apr 2024 23:18:01 +0000A coarse-grained model of the myofibril: overall dynamics and the evolution of sarcomere non-uniformities
https://resolver.caltech.edu/CaltechSOLIDS:2008.002
Authors: {'items': [{'id': 'Givli-S', 'name': {'family': 'Givli', 'given': 'Sefi'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2008
A theoretical framework for predicting the macroscopic behavior of a muscle myofibril based on the collective behavior of sarcomeres is presented. The analysis is accomplished by rigorously transforming the nonlinear dynamics of an assemblage of sarcomeres into a partial differential equation for the probability distribution function of sarcomere lengths in the presence of stochastic temporal fluctuations and biological variability. This enables the study of biologically relevant specimens with reasonable computational effort. The model is validated by a comparison to quantitative experimental results. Further, it reproduces experimental observations that can not be explained by standard single sarcomere models, and provides new insights into muscle function and muscle damage during cyclic loading. We show that the accumulation of overstretched sarcomeres, which is related to muscle damage, depends on a delicate interplay between the dynamics of a large number of sarcomeres and the load characteristics, such as its magnitude and frequency. Further, we show that biological variability rather than stochastic fluctuations are the main source for sarcomere non-uniformities.https://authors.library.caltech.edu/records/46y76-5bg40A sharp interface model for the propagation of martensitic phase boundaries
https://resolver.caltech.edu/CaltechSOLIDS:2008.003
Authors: {'items': [{'id': 'Dondl-P-W', 'name': {'family': 'Dondl', 'given': 'Patrick W.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2008
A model for the quasistatic evolution of martensitic phase boundaries is presented. The model is essentially the gradient flow of an energy that can contains elastic energy due to the underlying change in crystal structure in the course of the phase transformation and surface energy penalizing the area of the phase boundary. This leads to a free boundary problem with a nonlocal velocity that arises from the coupling to the elasticity equation. We show existence of solutions under a technical convergence condition using an implicit time-discretization.https://authors.library.caltech.edu/records/ehbhb-36c73Stress-induced phase transformations in shape-memory polycrystals
https://resolver.caltech.edu/CaltechSOLIDS:2008.005
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Schlömerkemper-A', 'name': {'family': 'Schlömerkemper', 'given': 'Anja'}}]}
Year: 2008
Shape-memory alloys undergo a solid-to-solid phase transformation involving a change of crystal structure. We examine model problems in the scalar setting motivated by the situation when this transformation is induced by the application of stress in a polycrystalline material made of numerous grains of the same crystalline solid with varying orientations. We show that the onset of transformation in a granular polycrystal with homogeneous elasticity is in fact predicted accurately by the so-called Sachs bound based on the ansatz of uniform stress. We also present a simple example where the onset of phase transformation is given by the Sachs bound, and the extent of phase transformation is given by the constant strain Taylor bound. Finally we discuss the stress-strain relations of the general problem using Milton-Serkov bounds.https://authors.library.caltech.edu/records/s7889-26981Characterization of soft stripe-domain deformations in SmC and SmC* liquid-crystal elastomers
https://resolver.caltech.edu/CaltechSOLIDS:2008.004
Authors: {'items': [{'id': 'Biggins-J-S', 'name': {'family': 'Biggins', 'given': 'J. S.'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2008
The neo-classical model of SmC (and SmC*) elastomers developed by Warner and Adams predicts a class of "soft" (zero energy) deformations. We find and describe the full set of stripe-domains – laminate structures in which the laminates alternate between two different deformations – that can form between pairs of these soft deformations. All the stripe-domains fall into two classes, one in which the smectic layers are not bent at the interfaces, but for which, in the SmC* case, the interfaces are charged, and one in which the smectic layers are bent but the interfaces are never charged. Striped deformations significantly enhance the softness of the macroscopic elastic response.https://authors.library.caltech.edu/records/dwtww-vnd56Origin of undesirable cracks during layer transfer
https://resolver.caltech.edu/CaltechAUTHORS:20160322-074244346
Authors: {'items': [{'id': 'Ponson-L', 'name': {'family': 'Ponson', 'given': 'L.'}}, {'id': 'Diest-K', 'name': {'family': 'Diest', 'given': 'K.'}}, {'id': 'Atwater-H-A', 'name': {'family': 'Atwater', 'given': 'H. A.'}, 'orcid': '0000-0001-9435-0201'}, {'id': 'Ravichandran-G', 'name': {'family': 'Ravichandran', 'given': 'G.'}, 'orcid': '0000-0002-2912-0001'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'K.'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2016
DOI: 10.48550/arXiv.0810.5053
We investigate the origin of undesirable transverse cracks often observed in thin films obtained by the layer transfer technique. During this process, two crystals bonded to each other containing a weak plan produced by ion implantation are heated to let a thin layer of one of the material on the other. The level of stress imposed on the film during the heating phase due to the mismatch of thermal expansion coefficients of the substrate and the film is shown to be the relevant parameter of the problem. In particular, it is shown that if the film is submitted to a tensile stress, the microcracks produced by ion implantation are not stable and deviate from their straight trajectory making the layer transfer process impossible. However, if the compressive stress exceeds a threshold value, after layer transfer, the film can buckle and delaminate, leading to transverse cracks induced by bending. As a result, we show that the imposed stress σ_m - or equivalently the heating temperature - must be within the range -σ_c < σ_m < 0 to produce an intact thin film where σ_c depends on the interfacial fracture energy and the size of defects at the interface between film and substrate.https://authors.library.caltech.edu/records/3b0d5-g6s72A threshold-force model for adhesion and mode I fracture
https://resolver.caltech.edu/CaltechAUTHORS:20161012-160619944
Authors: {'items': [{'id': 'Hulikal-S', 'name': {'family': 'Hulikal', 'given': 'Srivatsan'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Lapusta-N', 'name': {'family': 'Lapusta', 'given': 'Nadia'}, 'orcid': '0000-0001-6558-0323'}]}
Year: 2016
DOI: 10.48550/arXiv.1606.03166
We study the relation between a threshold-force based model at the microscopic scale and mode I fracture at the macroscopic scale in a system of discrete interacting springs. Specifically, we idealize the contact between two surfaces as that between a rigid surface and a collection of springs with long-range interaction and a constant tensile threshold force. We show that a particular scaling similar to that of crack-tip stress in Linear Elastic Fracture Mechanics leads to a macroscopic limit behavior. The model also reproduces the scaling behaviors of the JKR model of adhesive contact. We determine how the threshold force depends on the fracture energy and elastic properties of the material. The model can be used to study rough-surface adhesion.https://authors.library.caltech.edu/records/k0b54-psh43Optimizing Bone Scaffold Porosity Distributions
https://resolver.caltech.edu/CaltechAUTHORS:20190123-111634389
Authors: {'items': [{'id': 'Poh-P-S-P', 'name': {'family': 'Poh', 'given': 'Patrina S. P.'}}, {'id': 'Valainis-D', 'name': {'family': 'Valainis', 'given': 'Dvina'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'van-Griensven-M', 'name': {'family': 'van Griensven', 'given': 'Martijn'}, 'orcid': '0000-0001-5104-9881'}, {'id': 'Dondl-P-W', 'name': {'family': 'Dondl', 'given': 'Patrick'}}]}
Year: 2019
DOI: 10.48550/arXiv.1809.08179
We consider a simple one-dimensional time-dependent model for bone regeneration in the presence of a bio-resorbable polymer scaffold. Within the framework of the model, we optimize the effective mechanical stiffness of the polymer scaffold together with the regenerated bone matrix. The result of the optimization procedure is a scaffold porosity distribution which maximizes the stiffness of the scaffold-bone system over the regeneration time, such that the propensity for mechanical failure is reduced.https://authors.library.caltech.edu/records/rtqr7-q7986Photo-Motile Structures
https://resolver.caltech.edu/CaltechAUTHORS:20191111-090332268
Authors: {'items': [{'id': 'Korner-K', 'name': {'family': 'Korner', 'given': 'Kevin'}}, {'id': 'Audoly-B', 'name': {'family': 'Audoly', 'given': 'Basile'}, 'orcid': '0000-0002-0534-1467'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2019
DOI: 10.48550/arXiv.1909.02643
Actuation remains a signifcant challenge in soft robotics. Actuation by light has important advantages: objects can be actuated from a distance, distinct frequencies can be used to actuate and control distinct modes with minimal interference and signifcant power can be transmitted over long distances through corrosion-free, lightweight fiber optic cables. Photo-chemical processes that directly convert photons to configurational changes are particularly attractive for actuation. Various researchers have demonstrated light-induced actuation with liquid crystal elastomers combined with azobenzene photochromes. We present a simple modeling framework and a series of examples that studies actuation by light. Of particular interest is the generation of cyclic or periodic motion under steady illumination. We show that this emerges as a result of a coupling between light absorption and deformation. As the structure absorbs light and deforms, the conditions of illumination change, and this in turn changes the nature of further deformation. This coupling can be exploited in either closed structures or with structural instabilities to generate cyclic motion.https://authors.library.caltech.edu/records/ybrf8-w3b07Neural Operator: Graph Kernel Network for Partial Differential Equations
https://resolver.caltech.edu/CaltechAUTHORS:20200402-133318521
Authors: {'items': [{'id': 'Li-Zongyi', 'name': {'family': 'Li', 'given': 'Zongyi'}, 'orcid': '0000-0003-2081-9665'}, {'id': 'Kovachki-Nikola-B', 'name': {'family': 'Kovachki', 'given': 'Nikola'}, 'orcid': '0000-0002-3650-2972'}, {'id': 'Azizzadenesheli-Kamyar', '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'}}, {'id': 'Anandkumar-A', 'name': {'family': 'Anandkumar', 'given': 'Anima'}, 'orcid': '0000-0002-6974-6797'}]}
Year: 2020
DOI: 10.48550/arXiv.2003.03485
The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Euclidean spaces. The purpose of this work is to generalize neural networks so that they can learn mappings between infinite-dimensional spaces (operators). The key innovation in our work is that a single set of network parameters, within a carefully designed network architecture, may be used to describe mappings between infinite-dimensional spaces and between different finite-dimensional approximations of those spaces. We formulate approximation of the infinite-dimensional mapping by composing nonlinear activation functions and a class of integral operators. The kernel integration is computed by message passing on graph networks. This approach has substantial practical consequences which we will illustrate in the context of mappings between input data to partial differential equations (PDEs) and their solutions. In this context, such learned networks can generalize among different approximation methods for the PDE (such as finite difference or finite element methods) and among approximations corresponding to different underlying levels of resolution and discretization. Experiments confirm that the proposed graph kernel network does have the desired properties and show competitive performance compared to the state of the art solvers.https://authors.library.caltech.edu/records/k3t18-we744Model Reduction and Neural Networks for Parametric PDEs
https://resolver.caltech.edu/CaltechAUTHORS:20200527-074228185
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Hosseini-Bamdad', 'name': {'family': 'Hosseini', 'given': 'Bamdad'}}, {'id': 'Kovachki-N-B', 'name': {'family': 'Kovachki', 'given': 'Nikola B.'}, 'orcid': '0000-0002-3650-2972'}, {'id': 'Stuart-A-M', 'name': {'family': 'Stuart', 'given': 'Andrew M.'}}]}
Year: 2020
DOI: 10.48550/arXiv.2005.03180
We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with ideas from model reduction. This combination results in a neural network approximation which, in principle, is defined on infinite-dimensional spaces and, in practice, is robust to the dimension of finite-dimensional approximations of these spaces required for computation. For a class of input-output maps, and suitably chosen probability measures on the inputs, we prove convergence of the proposed approximation methodology. Numerically we demonstrate the effectiveness of the method on a class of parametric elliptic PDE problems, showing convergence and robustness of the approximation scheme with respect to the size of the discretization, and compare our method with existing algorithms from the literature.https://authors.library.caltech.edu/records/0e45m-qwh51Fourier Neural Operator for Parametric Partial Differential Equations
https://resolver.caltech.edu/CaltechAUTHORS:20201106-120140981
Authors: {'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'}}, {'id': 'Anandkumar-A', 'name': {'family': 'Anandkumar', 'given': 'Anima'}}]}
Year: 2020
DOI: 10.48550/arXiv.2010.08895
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.https://authors.library.caltech.edu/records/hpbg9-9ea84Accelerated computational micromechanics
https://resolver.caltech.edu/CaltechAUTHORS:20201110-073310991
Authors: {'items': [{'id': 'Zhou-Hao', 'name': {'family': 'Zhou', 'given': 'Hao'}}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2020
DOI: 10.48550/arXiv.2010.06697
We present an approach to solving problems in micromechanics that is amenable to massively parallel calculations through the use of graphical processing units and other accelerators. The problems lead to nonlinear differential equations that are typically second order in space and first order in time. This combination of nonlinearity and nonlocality makes such problems difficult to solve in parallel. However, this combination is a result of collapsing nonlocal, but linear and universal physical laws (kinematic compatibility, balance laws), and nonlinear but local constitutive relations. We propose an operator-splitting scheme inspired by this structure. The governing equations are formulated as (incremental) variational problems, the differential constraints like compatibility are introduced using an augmented Lagrangian, and the resulting incremental variational principle is solved by the alternating direction method of multipliers. The resulting algorithm has a natural connection to physical principles, and also enables massively parallel implementation on structured grids. We present this method and use it to study two examples. The first concerns the long wavelength instability of finite elasticity, and allows us to verify the approach against previous numerical simulations. We also use this example to study convergence and parallel performance. The second example concerns microstructure evolution in liquid crystal elastomers and provides new insights into some counter-intuitive properties of these materials. We use this example to validate the model and the approach against experimental observations.https://authors.library.caltech.edu/records/y5khy-p2w24Learning Dissipative Dynamics in Chaotic Systems
https://resolver.caltech.edu/CaltechAUTHORS:20210719-210135878
Authors: {'items': [{'id': 'Li-Zongyi', 'name': {'family': 'Li', 'given': 'Zongyi'}, 'orcid': '0000-0003-2081-9665'}, {'id': 'Kovachki-Nikola-B', 'name': {'family': 'Kovachki', 'given': 'Nikola'}, 'orcid': '0000-0002-3650-2972'}, {'id': 'Azizzadenesheli-Kamyar', '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'}]}
Year: 2021
DOI: 10.48550/arXiv.2106.06898
Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many dissipative systems the statistics of the long term trajectories are governed by an invariant measure supported on a set, known as the global attractor; for many problems this set is finite dimensional, even if the state space is infinite dimensional. For Markovian systems, the statistical properties of long-term trajectories are uniquely determined by the solution operator that maps the evolution of the system over arbitrary positive time increments. In this work, we propose a machine learning framework to learn the underlying solution operator for dissipative chaotic systems, showing that the resulting learned operator accurately captures short-time trajectories and long-time statistical behavior. Using this framework, we are able to predict various statistics of the invariant measure for the turbulent Kolmogorov Flow dynamics with Reynolds numbers up to 5000.https://authors.library.caltech.edu/records/wm6xz-zgz78Concurrent goal-oriented materials-by-design
https://resolver.caltech.edu/CaltechAUTHORS:20210713-212259269
Authors: {'items': [{'id': 'Sun-Xingsheng', 'name': {'family': 'Sun', 'given': 'Xingsheng'}, 'orcid': '0000-0003-1527-789X'}, {'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': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}]}
Year: 2021
DOI: 10.48550/arXiv.2106.06074
The development of new materials and structures for extreme conditions including impact remains a continuing challenge despite steady advances. Design is currently accomplished using a sequential approach: an optimal material is first developed using the process-structure-properties paradigm, where performance is measured against a blended measure. Then, the structure is optimized while holding the material properties fixed. In this paper, we propose an alternative concurrent and goal-oriented optimization approach where both the material properties and the structure are optimized simultaneously against an overall system-wide performance measure. We develop a non-intrusive, high-performance computational framework based on DAKOTA and GMSH and use it to study the ballistic impact of a double-layer plate of strong AZ31B magnesium alloy and soft polyurea. We show that the proposed concurrent and goal-oriented optimization strategy can provide significant advantage over the traditional sequential optimization approach.https://authors.library.caltech.edu/records/3nqk7-yhe03Tuning acoustic impedance in load-bearing structures
https://resolver.caltech.edu/CaltechAUTHORS:20210716-222546164
Authors: {'items': [{'id': 'Injeti-Sai-Sharan', 'name': {'family': 'Injeti', 'given': 'Sai Sharan'}, 'orcid': '0000-0003-1941-9752'}, {'id': 'Celli-Paolo', 'name': {'family': 'Celli', 'given': 'Paolo'}, 'orcid': '0000-0001-7839-7472'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Daraio-C', 'name': {'family': 'Daraio', 'given': 'Chiara'}, 'orcid': '0000-0001-5296-4440'}]}
Year: 2021
DOI: 10.48550/arXiv.2106.10573
Acoustic transparency is the capability of a medium to transmit mechanical waves to adjacent media, without scattering. This characteristic can be achieved by carefully engineering the acoustic impedance of the medium -- a combination of wave speed and density, to match that of the surroundings. Owing to the strong correlation between acoustic wave speed and static stiffness, it is challenging to design acoustically transparent materials in a fluid, while maintaining their high structural rigidity. In this work, we propose a method to design architected lattices with independent control of the elastic wave speed at a chosen frequency, the mass density, and the static stiffness, along a chosen loading direction. We provide a sensitivity analysis to optimize these properties with respect to design parameters of the structure, that include localized masses at specific positions. We demonstrate the method on five different periodic, three dimensional lattices, to calculate bounds on the longitudinal wave speed as a function of their density and stiffness. We then perform experiments on 3-D printed structures, to validate our numerical simulations. The tools developed in this work can be used to design lightweight and stiff materials with optimized acoustic impedance for a plethora of applications, including ultrasound imaging, wave filtering and waveguiding.https://authors.library.caltech.edu/records/ed6ms-7ze27Neural Operator: Learning Maps Between Function Spaces
https://resolver.caltech.edu/CaltechAUTHORS:20210831-204010794
Authors: {'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'}}]}
Year: 2021
DOI: 10.48550/arXiv.2108.08481
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.https://authors.library.caltech.edu/records/h5ry0-fsp13Accurate approximations of density functional theory for large systems with applications to defects in crystalline solids
https://resolver.caltech.edu/CaltechAUTHORS:20220119-233956787
Authors: {'items': [{'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}, {'id': 'Gavini-Vikram', 'name': {'family': 'Gavini', 'given': 'Vikram'}, 'orcid': '0000-0002-9451-2300'}, {'id': 'Ortiz-M', 'name': {'family': 'Ortiz', 'given': 'Michael'}, 'orcid': '0000-0001-5877-4824'}, {'id': 'Ponga-Mauricio', 'name': {'family': 'Ponga', 'given': 'Mauricio'}, 'orcid': '0000-0001-5058-1454'}, {'id': 'Suryanarayana-Phanish', 'name': {'family': 'Suryanarayana', 'given': 'Phanish'}, 'orcid': '0000-0001-5172-0049'}]}
Year: 2021
DOI: 10.48550/arXiv.2112.06016
This chapter presents controlled approximations of Kohn-Sham density functional theory (DFT) that enable very large scale simulations. The work is motivated by the study of defects in crystalline solids, though the ideas can be used in other applications. The key idea is to formulate DFT as a minimization problem over the density operator, and to cast spatial and spectral discretization as systematically convergent approximations. This enables efficient and adaptive algorithms that solve the equations of DFT with no additional modeling, and up to desired accuracy, for very large systems, with linear and sublinear scaling. Various approaches based on such approximations are presented, and their numerical performance demonstrated through selected examples. These examples also provide important insight about the mechanics and physics of defects in crystalline solids.https://authors.library.caltech.edu/records/gb81e-r3t46Interaction between deformation twinning and dislocation slip in polycrystalline solids
https://resolver.caltech.edu/CaltechAUTHORS:20220304-171248075
Authors: {'items': [{'id': 'Ocegueda-Eric', 'name': {'family': 'Ocegueda', 'given': 'Eric'}, 'orcid': '0000-0001-7845-6890'}, {'id': 'Bhattacharya-K', 'name': {'family': 'Bhattacharya', 'given': 'Kaushik'}, 'orcid': '0000-0003-2908-5469'}]}
Year: 2022
DOI: 10.48550/arXiv.2202.02908
Deformation twinning is a form of permanent deformation that is commonly observed in low symmetry crystals such as hexagonal close-packed (hcp) metals. With recent increased interest in using hcp metals, such as magnesium, in structural, automotive, and armor applications due to their high strength to weight ratio, there is a need for a comprehensive understanding of deformation twinning and its interaction with dislocation slip. A great deal has been learned at the microscopic level where individual dislocations interact with twin boundaries through atomistic simulations, and at the macroscopic level by ignoring morphology and treating twinning as `pseudo-slip'. However, twins form collectively across multiple grains with complex morphology that affects the bulk behavior. These mesoscale aspects have been less studied and are the focus of this paper. We present a model that describes the twin and slip morphology, its evolution, and interactions in a unified manner at the scale of several grains and use it to study the implications on macroscopic behavior. The key ideas are to combine a phase-field model of twinning with a crystal plasticity model of slip, and to implement it in parallel on graphic processing units for fast computations.https://authors.library.caltech.edu/records/4dsdm-4y873