Physics-informed deep learning and compressive collocation for high-dimensional diffusion-reaction equations: practical existence theory and numerics

The emergence of Deep Learning (DL) as a powerful tool for solving Partial Differential Equations (PDEs) marks a significant advancement in scientific computing. This paper highlights the application of DL in addressing the curse of dimensionality, which complicates the sample complexity in high-dimensional spaces. By leveraging recent advancements in function approximation, the authors propose a new high-dimensional PDE solver that not only demonstrates theoretical efficiency but also competes effectively with established methods like the compressive spectral collocation. This work underscores the growing importance of DL in enhancing numerical analysis, stability, and accuracy in solving complex equations, paving the way for further innovations in the field.