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.

翻译：我们提出了一种适用于表示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了一种称为低秩神经表示（LRNR）的专用神经网络架构。该架构的理论基础源于严格证明此类波存在高效表示的理论结果。通过典型示例，我们阐明这种传播波的高效低维表示可以通过深度学习技术的结合直接从数据中学习。我们观察到，在训练后的LRNR中自然涌现出低秩张量表示，这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LRNR架构通过压缩方案实现了高效推理，这在性能要求严苛的场景中部署LRNR时可能具有重要意义。