Adaptive Error-Bounded Hierarchical Matrices for Efficient Neural Network Compression
This provides a scalable and efficient solution for deploying PINNs in complex scientific and engineering domains, though it appears incremental as an adaptation of hierarchical matrices to a specific neural network type.
The paper tackles the computational complexity and memory demands of Physics-Informed Neural Networks (PINNs) by introducing a dynamic, error-bounded hierarchical matrix compression method, which outperforms traditional compression techniques like SVD, pruning, and quantization while maintaining high accuracy and improving generalization.
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.