Learning Low Rank Neural Representations of Hyperbolic Wave Dynamics from Data

📝 Original Info

• Title: Learning Low Rank Neural Representations of Hyperbolic Wave Dynamics from Data
• ArXiv ID: 2510.25123
• Date: 2025-10-29
• Authors: ** 논문에 명시된 저자 정보가 제공되지 않았습니다. (가능하면 원문에서 확인 필요) **

📝 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.

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