PINN Failure Remedies Require Joint Evaluation, Not Single Fixes

Physics-Informed Neural Networks (PINNs) often struggle with challenging Partial Differential Equations (PDEs), particularly those that are stiff or advection-dominated. Two prominent proposed solutions are using higher floating-point precision (FP64 instead of FP32) to mitigate L-BFGS stopping artifacts, or replacing the standard Multi-Layer Perceptron (MLP) backbone with a State-Space Model (SSM) combined with subsequence alignment to address architectural biases. A rigorous, pre-registered study involving 144 runs across convection, reaction, and wave PDEs, along with an independent 85-run study, investigated these remedies under matched, seed-paired controls. The findings indicate that neither precision nor architecture alone is a universal fix; instead, they address disjoint sets of problems and seeds. For instance, on hard convection problems, alignment was key to recovery, regardless of precision, while the SSM backbone alone showed limited improvement. The study emphasizes that success is highly seed-specific, meaning the same intervention can yield opposite results for different random initializations. Tightening L-BFGS tolerance, while reducing median error, did not significantly increase success rates. This highlights the necessity of jointly evaluating precision, stopping criteria, network backbone, and alignment, and reporting results per seed to accurately understand and improve PINN performance.