Reproduce “An efficient wavelet-based physics-informed neural network for multiscale problems” on OpenResearch

About this paper

Himanshu Pandey, Anshima Singh, Ratikanta Behera

A Wavelet-based Physics-Informed Neural Network (W-PINN) is introduced, reformulating the learning task to predict wavelet coefficients, which enables analytical derivative computation and eliminates the reliance on automatic differentiation. The method demonstrates enhanced accuracy and significantly reduced training time when solving complex multiscale differential equations compared to conventional PINNs and other approaches.

Key insights

• Reformulating the learning problem in the wavelet domain effectively smooths out abrupt features in the physical space, leading to a better-conditioned optimization problem and more robust convergence.
• The analytical computation of derivatives through pre-computed wavelet basis functions drastically reduces computational complexity and training time compared to AD-based methods.
• Neural Tangent Kernel (NTK) analysis shows that W-PINN exhibits a flatter spectral profile of eigenvalues, indicating an improved ability to learn and capture high-frequency and multiscale components more efficiently.

Summary by alphaXiv.