从数据中学习双曲波传播的低秩神经表征，实现高效压缩与物理可解释性。
Learning Low Rank Neural Representations of Hyperbolic Wave Dynamics from Data
- 基于超网络框架设计低秩神经表征架构，利用深度学习直接从数据中学习波传播规律。
- 训练后自然出现低秩张量结构，分解出对应物理特性的可解释模式。
- 支持高效推理压缩，适合高要求性能场景部署，兼具精度与速度优势。
我们提出一种适用于描述双曲波传播的物理数据的数据驱动降维方法。该方法在超网络框架内采用一种称为低秩神经表征（LRNR）的专用神经网络架构，其设计基于严格理论证明：此类波类存在高效表示。通过典型例子表明，借助深度学习技术可直接从数据中学习到这种高效的低维表示。训练后的LRNR自然呈现出低秩张量结构，揭示了一种新的波传播分解方式，其中每个分解模态对应可解释的物理特征。此外，我们证明了LRNR架构可通过压缩方案实现高效推理，这在部署于高性能需求场景时具有潜在重要价值。
原文摘要 · Abstract (English)
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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