Developing robust and accurate data-based models for dynamical systems originating from plasma physics and hydrodynamics is of paramount importance. These applications pose several challenges, including the presence of multiple scales in time and space and a limited number of data, which is often noisy or inconsistent. The aim of structure-preserving ML is to strongly enforce physics-based constraints to improve quantitative performance of the model. In this talk, two applications of structure-preserving ML are demonstrated. First, a network architecture that parameterizes singularly perturbed dynamical systems, commonly known as fast-slow systems, via the Fenichel normal form is presented. The architecture enforces the existence of a trainable, attracting invariant slow manifold as a hard constraint which enables efficient integration on the slow time scale and significantly improved prediction accuracy. The network is demonstrated on several examples that exhibit multiple timescales. In the second part of the talk, an attention-based neural network for density reconstruction and parameter estimation of a hydrodynamics problem is discussed. The trained network can robustly recover equation of state parameters, initial condition parameters, and the complex topologies given by the Richtmyer-Meshkoff instability from a sequence of hydrodynamic features derived from radiographic images corrupted with blur, scatter, and noise. The key component of this network is a transformer encoder that acts to learn temporal dependencies in features extracted from noisy radiographs.

Zoom Link:  https://ncsu.zoom.us/j/97638681103?pwd=dDJrRkE3d3NQZEhrRlhOMDc4T0pRUT09