A physics-informed operator regression framework for extracting data-driven continuum models

Abstract

The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate and robust. We present here a framework for discovering continuum models from high fidelity molecular simulation data. Our approach applies a neural network parameterization of governing physics in modal space, allowing a characterization of differential operators while providing structure which may be used to impose biases related to symmetry, isotropy, and conservation form. We demonstrate the effectiveness of our framework for a variety of physics, including local and nonlocal diffusion processes and single and multiphase flows. For the flow physics we demonstrate this approach leads to a learned operator that generalizes to system characteristics not included in the training sets, such as variable particle sizes, densities, and concentration.

37 pages, 15 figures

References in corpus (20)

• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• The Effectiveness of Data Augmentation in Image Classification using Deep Learning
• A Performance and Cost Assessment of Machine Learning Interatomic Potentials
• Rotation-invariant convolutional neural networks for galaxy morphology prediction
• PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network
• Learning data driven discretizations for partial differential equations
• Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
• A Comprehensive Physics-Informed Machine Learning Framework for Predictive Turbulence Modeling
• Physics-Informed Machine Learning Approach for Augmenting Turbulence Models: A Comprehensive Framework
• From Diffusion to Anomalous Diffusion: A Century after Einstein's Brownian Motion
• Data Augmentation by Pairing Samples for Images Classification
• Data Driven Governing Equations Approximation Using Deep Neural Networks
• Interaction potentials for soft and hard ellipsoids
• Data-Driven Deep Learning of Partial Differential Equations in Modal Space
• Numerical Aspects for Approximating Governing Equations Using Data
• What Is the Fractional Laplacian?
• PiNet: A Permutation Invariant Graph Neural Network for Graph Classification
• Stochastic Solution of Elliptic and Parabolic Boundary Value Problems for the Spectral Fractional Laplacian

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