A physics-informed operator regression framework for extracting data-driven continuum models
This work addresses the challenge of data-driven model discovery in physics and engineering, offering a method to extract continuum models with improved generalization, though it appears incremental as it builds on existing deep learning and physics-informed approaches.
The authors tackled the problem of discovering accurate and robust continuum models from molecular simulation data by introducing a physics-informed operator regression framework that parameterizes governing physics in modal space with neural networks, and demonstrated its effectiveness for various physics including diffusion processes and flows, achieving generalization to unseen system characteristics like variable particle sizes and densities.
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.