Cautious Conflict-Free Inverse Gradient Methods

arXiv:2610.31855v1 Announce Type: new Abstract: Partial differential equations (PDEs) are indispensable tools for modeling complex phenomena in physics and engineering. Physics-Informed Neural Networks (PINNs) have emerged as a powerful alternative to traditional numerical solvers by directly incorporating physical constraints into neural network loss functions. Despite their advantages, PINN training requires multi-objective optimization, which often leads to significant gradient conflicts among boundary, initial, and residual loss terms.