Application of physics-informed neural network on multidimensional quantum tunneling

Abstract Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving high-dimensional partial differential equations, demonstrating promising results across various fields of physics and engineering. In this study, we present the first application of PINNs to quantum scattering problems, specifically focusing on quantum tunneling in heavy-ion fusion reactions. By incorporating the physical laws directly into the neural network's loss function, PINNs enable the accurate solution of the multidimensional Schrödinger equation. The calculated quantum tunneling probabilities exhibit well agreement with those obtained using the finite element method at the near barrier energy region. Furthermore, we demonstrate a significant advantage of the PINN approach to save and fine-tune pre-trained neural networks for related tunneling calculations, thereby enhancing computational efficiency and adaptability.