Author: Eduard Duta Costache

Poster by E. A. Duta Costache at the Protein Folding in Real Time conference, Stockholm, 11 March 2026

Pointwise absolute error plots for the heat equation tested across five architectures. The plots show the mean absolute error achieved by each architecture on a periodic-mode initial condition. Errors are shown on a logarithmic scale. Blue colors indicate smaller errors. (Image by E. A. Duta Costache.)
The optimization autopsy of PINNs
Eduard Duta Costache, Benjamin Girault
Date: 11 March 2026
Time: 18:00-20:00
Place: Aula Medica, Karolinska Institute, Solna
Conference Protein Folding in Real Time, 11-13 March 2026, Stockholm, Sweden

Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving Partial Differential Equations (PDEs) by combining data-driven learning with physical laws. However, the spectral bias and optimization challenges limit their efficacy. This work investigates these issues and whether the advantages of classical spectral methods translate to the non-convex neural network optimization landscape. We show that gradient imbalance greatly affect learning and we study the Hessian conditioning under different settings. Our results indicate that spectral priors stabilize training, reduce error, and improve parameter efficiency. We also identify that learnable-basis models act as implicit regularizers under sparse sampling.