An Importance Sampling Method for Generating Optimal Interpolation Points in Training Physics-Informed Neural Networks

The application of machine learning and artificial intelligence to solve scientific challenges has significantly increased in recent years. A remarkable development is the use of Physics-Informed Neural Networks (PINNs) to solve Partial Differential Equations (PDEs) numerically. However, current PINN techniques often face problems with accuracy and slow convergence. To address these problems, we propose an importance sampling method to generate optimal interpolation points during training. Experimental results demonstrate that our method achieves a 43% reduction in root mean square error compared to state-of-the-art methods when applied to the one-dimensional Korteweg–De Vries equation.