Differentiable Hash Encoding for Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have received considerable attention in the field of scientific computing. Enhancing their performance to fully realize their potential is a key concern in related fields. Recent studies have shown that multiresolution hash encoding can significantly improve the training performance of neural networks, which has been well-documented in various neural representation tasks. However, the global non-differentiable nature of widely used linear interpolation hash encoding makes it unsuitable for direct combination with automatic differentiation (AD) based PINNs. This work introduces and analyzes two differentiable hash encoding methods and studies their performance through numerical experiments. The proposed encoding methods are combined directly with AD-based PINNs, which, to the best of our knowledge, has not been done before.