4 papers
PINN Balls: Scaling Second-Order Methods for PINNs with Domain Decomposition and Adaptive Sampling
Andrea Bonfanti, Ismael Medina, Roman List +3
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 alt…
A Mesh Is Worth 512 Numbers: Spectral-domain Diffusion Modeling for High-dimension Shape Generation
Jiajie Fan, Amal Trigui, Andrea Bonfanti +3
Recent advancements in learning latent codes derived from high-dimensional shapes have demonstrated impressive outcomes in 3D generative modeling. Traditionally, these approaches e…
The Challenges of the Nonlinear Regime for Physics-Informed Neural Networks
Andrea Bonfanti, Giuseppe Bruno, Cristina Cipriani
The Neural Tangent Kernel (NTK) viewpoint is widely employed to analyze the training dynamics of overparameterized Physics-Informed Neural Networks (PINNs). However, unlike the cas…
Hammering at the entropy: A GENERIC-guided approach to learning polymeric rheological constitutive equations using PINNs
David Nieto Simavilla, Andrea Bonfanti, Imanol GarcÃa de Beristain +2
We present a versatile framework that employs Physics-Informed Neural Networks (PINNs) to discover the entropic contribution that leads to the constitutive equation for the extra-s…