A discontinuity-capturing PINN for parabolic interface problems

A physics-informed neural network has been proposed to solve parabolic interface problems. The error bounds for neural network approximating the solution to the parabolic interface problem have been derived. Due to the discontinuous nature of the solution to the interface problem, a discontinuity-capturing shallow neural network as a surrogate model has been introduced. Further, extreme-learning machine approach has been incorporated as an innovative strategy for efficient training. Theoretical results are validated through numerical examples, demonstrating the effectiveness of the proposed approach. To further illustrate the capability of the proposed discontinuity-capturing shallow neural network for high-dimensional applications, we conclude with the solution of a six-dimensional problem.