动态误差可控的矩阵压缩，让物理神经网络更省算力、更快推理。
Adaptive Error-Bounded Hierarchical Matrices for Efficient Neural Network Compression
- 基于局部误差自适应调整分层矩阵近似，实现动态压缩。
- 相比SVD、剪枝、量化等方法，保持更高精度与泛化能力。
- 适合需要实时推理的科学计算与工程建模场景。
本文提出一种针对物理信息神经网络（PINNs）的动态、误差有界分层矩阵（H-matrix）压缩方法。该方法在降低大规模物理模型计算复杂度和内存需求的同时，保留了神经切线核（NTK）的关键性质。通过根据局部误差估计自适应地细化分层矩阵近似，确保训练效率与模型鲁棒性。实验表明，该技术在保持高精度的同时，显著优于传统的奇异值分解（SVD）、剪枝和量化方法，提升泛化能力并加快推理速度，适用于实时应用。该方案为在复杂科学与工程领域部署PINNs提供了可扩展且高效的解决方案。
原文摘要 · Abstract (English)
This paper introduces a dynamic, error-bounded hierarchical matrix (H-matrix) compression method tailored for Physics-Informed Neural Networks (PINNs). The proposed approach reduces the computational complexity and memory demands of large-scale physics-based models while preserving the essential properties of the Neural Tangent Kernel (NTK). By adaptively refining hierarchical matrix approximations based on local error estimates, our method ensures efficient training and robust model performance. Empirical results demonstrate that this technique outperforms traditional compression methods, such as Singular Value Decomposition (SVD), pruning, and quantization, by maintaining high accuracy and improving generalization capabilities. Additionally, the dynamic H-matrix method enhances inference speed, making it suitable for real-time applications. This approach offers a scalable and efficient solution for deploying PINNs in complex scientific and engineering domains, bridging the gap between computational feasibility and real-world applicability.
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