A data-driven peridynamic continuum model for upscaling molecular dynamics

• URL: http://arxiv.org/abs/2108.04883v1
• Date: Wed, 4 Aug 2021 07:07:47 GMT
• Title: A data-driven peridynamic continuum model for upscaling molecular dynamics
• Authors: Huaiqian You, Yue Yu, Stewart Silling, Marta D'Elia
• Abstract summary: We propose a learning framework to extract, from molecular dynamics data, an optimal Linear Peridynamic Solid model. We provide sufficient well-posedness conditions for discretized LPS models with sign-changing influence functions. This framework guarantees that the resulting model is mathematically well-posed, physically consistent, and that it generalizes well to settings that are different from the ones used during training.
• Score: 3.1196544696082613
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Nonlocal models, including peridynamics, often use integral operators that embed lengthscales in their definition. However, the integrands in these operators are difficult to define from the data that are typically available for a given physical system, such as laboratory mechanical property tests. In contrast, molecular dynamics (MD) does not require these integrands, but it suffers from computational limitations in the length and time scales it can address. To combine the strengths of both methods and to obtain a coarse-grained, homogenized continuum model that efficiently and accurately captures materials' behavior, we propose a learning framework to extract, from MD data, an optimal Linear Peridynamic Solid (LPS) model as a surrogate for MD displacements. To maximize the accuracy of the learnt model we allow the peridynamic influence function to be partially negative, while preserving the well-posedness of the resulting model. To achieve this, we provide sufficient well-posedness conditions for discretized LPS models with sign-changing influence functions and develop a constrained optimization algorithm that minimizes the equation residual while enforcing such solvability conditions. This framework guarantees that the resulting model is mathematically well-posed, physically consistent, and that it generalizes well to settings that are different from the ones used during training. We illustrate the efficacy of the proposed approach with several numerical tests for single layer graphene. Our two-dimensional tests show the robustness of the proposed algorithm on validation data sets that include thermal noise, different domain shapes and external loadings, and discretizations substantially different from the ones used for training.

Related papers

• Hybrid data-driven and physics-informed regularized learning of cyclic plasticity with Neural Networks [0.0]
  The proposed model architecture is simpler and more efficient compared to existing solutions from the literature. The validation of the approach is carried out by means of surrogate data obtained with the Armstrong-Frederick kinematic hardening model.
  arXiv  Detail & Related papers  (2024-03-04T07:09:54Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Score-based Diffusion Models in Function Space [140.792362459734]
  Diffusion models have recently emerged as a powerful framework for generative modeling. We introduce a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space. We show that the corresponding discretized algorithm generates accurate samples at a fixed cost independent of the data resolution.
  arXiv  Detail & Related papers  (2023-02-14T23:50:53Z)
• Generalized Neural Closure Models with Interpretability [28.269731698116257]
  We develop a novel and versatile methodology of unified neural partial delay differential equations. We augment existing/low-fidelity dynamical models directly in their partial differential equation (PDE) forms with both Markovian and non-Markovian neural network (NN) closure parameterizations. We demonstrate the new generalized neural closure models (gnCMs) framework using four sets of experiments based on advecting nonlinear waves, shocks, and ocean acidification models.
  arXiv  Detail & Related papers  (2023-01-15T21:57:43Z)
• Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures [6.478834929962051]
  We propose a learning framework to extract a peridynamic model as a mesoscale continuum surrogate from MD simulated material fracture datasets. Our peridynamics surrogate model can be employed in further prediction tasks with different grid resolutions from training.
  arXiv  Detail & Related papers  (2023-01-11T16:07:17Z)
• Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling [3.9181541460605116]
  We propose to use data-driven modeling to predict a material's response without using conventional models. The material response is modeled by learning the implicit mappings between loading conditions and the resultant displacement and/or damage fields. We demonstrate the performance of our proposed method for a number of examples, including hyperelastic, anisotropic and brittle materials.
  arXiv  Detail & Related papers  (2022-03-15T19:08:13Z)
• Extension of Dynamic Mode Decomposition for dynamic systems with incomplete information based on t-model of optimal prediction [69.81996031777717]
  The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. The application of this approach becomes problematic if the available data is incomplete because some dimensions of smaller scale either missing or unmeasured. We consider a first-order approximation of the Mori-Zwanzig decomposition, state the corresponding optimization problem and solve it with the gradient-based optimization method.
  arXiv  Detail & Related papers  (2022-02-23T11:23:59Z)
• Learning continuous models for continuous physics [94.42705784823997]
  We develop a test based on numerical analysis theory to validate machine learning models for science and engineering applications. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.
  arXiv  Detail & Related papers  (2022-02-17T07:56:46Z)
• Goal-directed Generation of Discrete Structures with Conditional Generative Models [85.51463588099556]
  We introduce a novel approach to directly optimize a reinforcement learning objective, maximizing an expected reward. We test our methodology on two tasks: generating molecules with user-defined properties and identifying short python expressions which evaluate to a given target value.
  arXiv  Detail & Related papers  (2020-10-05T20:03:13Z)
• Automatic Differentiation and Continuous Sensitivity Analysis of Rigid Body Dynamics [15.565726546970678]
  We introduce a differentiable physics simulator for rigid body dynamics. In the context of trajectory optimization, we introduce a closed-loop model-predictive control algorithm.
  arXiv  Detail & Related papers  (2020-01-22T03:54:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.