Learning Low Rank Neural Representations of Hyperbolic Wave Dynamics from Data
This work addresses dimensionality reduction for physics-based wave data, offering potential efficiency gains for deployment in performance-critical applications, though it appears incremental as it builds on existing neural and hypernetwork frameworks.
The authors tackled the problem of representing hyperbolic wave propagation data by developing a low rank neural representation (LRNR) method, which learns efficient low-dimensional representations from data and reveals interpretable physical features through decomposition.
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.