Loss Jump During Loss Switch in Solving PDEs with Neural Networks

arXiv:2405.03095v1 Announce Type: new
Abstract: Using neural networks to solve partial differential equations (PDEs) is gaining popularity as an alternative approach in the scientific computing community. Neural networks can integrate different types of information into the loss function. These include observation data, governing equations, and variational forms, etc. These loss functions can be broadly categorized into two types: observation data loss directly constrains and measures the model output, while other loss functions indirectly model the performance of the network, which …

abstract alternative arxiv community computing cs.lg data differential etc forms function information loss math.mp math-ph networks neural networks observation scientific solve type types