Learning Low Rank Neural Representations of Hyperbolic Wave Dynamics from Data

TL;DR

This paper introduces a neural network-based method for data-driven, low-dimensional representation of hyperbolic wave dynamics, enabling efficient inference and revealing interpretable physical features.

Contribution

It proposes a novel low rank neural representation architecture within a hypernetwork framework, supported by theoretical proofs of efficient wave representations.

Findings

Low rank tensor representations naturally emerge in trained models

The method reveals interpretable physical features of wave propagation

Enables efficient inference through a compression scheme

Abstract

We present a data-driven dimensionality reduction method that is well-suited for physics-based data representing hyperbolic wave propagation. The method utilizes a specialized neural network architecture called low rank neural representation (LRNR) inside a hypernetwork framework. The architecture is motivated by theoretical results that rigorously prove the existence of efficient representations for this wave class. We illustrate through archetypal examples that such an efficient low-dimensional representation of propagating waves can be learned directly from data through a combination of deep learning techniques. We observe that a low rank tensor representation arises naturally in the trained LRNRs, and that this reveals a new decomposition of wave propagation where each decomposed mode corresponds to interpretable physical features. Furthermore, we demonstrate that the LRNR architecture enables efficient inference via a compression scheme, which is a potentially important feature when deploying LRNRs in demanding performance regimes.