Adaptive Error-Bounded Hierarchical Matrices for Efficient Neural Network Compression

TL;DR

This paper presents a dynamic, error-bounded hierarchical matrix compression technique for Physics-Informed Neural Networks that improves efficiency, accuracy, and real-time inference capabilities in large-scale scientific models.

Contribution

It introduces an adaptive hierarchical matrix method that reduces computational costs while maintaining model accuracy, outperforming traditional compression techniques.

Findings

Outperforms SVD, pruning, and quantization in accuracy.

Reduces computational complexity and memory usage.

Enhances inference speed for real-time applications.

Abstract

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.