The MST for ROM modeling of PDEs
Presented at the 2021 April Meeting of the American Physical Society (18 April 2021) by Francis Ogoke from Carnegie Mellon University
SAND2021-4708 C, and SAND2021-4773 V
PDF of viewgraphs can be found at:
http://tiny.cc/fo_aps_21_presentation
The development of data-driven models to describe physical phenomenon requires frameworks that are physically principled and generalizable. We present a data-driven framework for reduced order modeling of continuum physics by harnessing the Mallat Scattering Transform (MST). The MST acts as an analogue to the traditional Convolutional Neural Network framework with predefined, physics-informed weights to aggregate information in a scale-dependent manner while preserving conservation properties. The transform provides a state based represen- tation of the physics and time-independent rate coefficients describing their evolution, which can be determined using a modified version of the Generalized Master Equation. This framework reduces the amount of parameters that must be independently optimized compared to sim- ilar data-driven models, while enforcing the necessary conditions like diffeomorphic continuity. The framework also produces descriptors of the dynamics that are translatable to the underlying physical principles governing the behavior of the PDE. We demonstrate the efficacy of the framework by surrogating the behavior of one-dimensional linear and non-linear Partial Differential Equations, such as Burgers Equation. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.