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Andrea Bonfanti

2 accepted papers

2025

PINN Balls: Scaling Second-Order Methods for PINNs with Domain Decomposition and Adaptive Sampling

NeurIPS 2025poster

Recent advances in Scientific Machine Learning have shown that second-order methods can enhance the training of Physics-Informed Neural Networks (PINNs), making them a suitable alternative to traditional numerical methods for Partial Differential Equations (PDEs). However, second-order methods induc…

Cited by 0SourceScholar
2024

The Challenges of the Nonlinear Regime for Physics-Informed Neural Networks

NeurIPS 2024poster

The Neural Tangent Kernel (NTK) viewpoint is widely employed to analyze the training dynamics of overparameterized Physics-Informed Neural Networks (PINNs). However, unlike the case of linear Partial Differential Equations (PDEs), we show how the NTK perspective falls short in the nonlinear scenario…

Cited by 12SourcePDFScholar