Learning Low Rank Neural Representations of Hyperbolic Wave Dynamics from Data

2025-10-28

AI Summary

Efficiently modeling hyperbolic wave dynamics remains challenging due to the high dimensionality and physical complexity of wavefield data. Method: This paper proposes Low-Rank Neural Representation (LRNR), a learnable neural architecture built upon a hypernetwork framework that induces a physically consistent, low-dimensional representation directly from wavefield data in an end-to-end manner. Unlike conventional dimensionality reduction, LRNR spontaneously discovers interpretable low-rank tensor decompositions during training, revealing intrinsic modal structures underlying wave propagation. Contribution/Results: LRNR enables both model compression and accelerated inference while preserving physical fidelity. Experiments on canonical hyperbolic wave problems demonstrate that LRNR achieves high-fidelity reconstruction and strong generalization with significantly fewer parameters than baseline methods. It establishes a new paradigm for physics-informed deep learning—unifying interpretability, parameter efficiency, and computational tractability.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Low Level & Physics-based Vision
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• Learning low-rank neural representations of hyperbolic wave dynamics
• Developing data-driven dimensionality reduction for wave propagation
• Discovering interpretable physical feature decomposition in wave propagation

Innovation

• Low rank neural network for hyperbolic waves
• Hypernetwork framework learns from data directly
• Tensor decomposition reveals interpretable physical modes