196 citations · 2.8k across the 144 of their papers we have counts for
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Variational Boosting for Physics-Informed Neural Networks
Pavlos Protopapas, Kaylee Vo
Physics-Informed Neural Networks (PINNs) solve differential equations by minimizing the residual of a nonlinear operator over a neural parameterization of the solution. However, mo…
Physics-Informed Neural Embeddings of PDE Solution Families
Raul Jimenez, Svitlana Mayboroda, Pavlos Protopapas +3
We introduce a physics-informed framework for learning finite-dimensional embeddings of solution families of partial differential equations. The method uses a multihead Physics-Inf…
Gradient Scaling Effects in Adaptive Spectral PINNs for Stiff Nonlinear ODEs
Isabela M. Yepes, Pavlos Protopapas
Physics-Informed Neural Networks (PINNs) often struggle to train reliably on stiff and oscillatory dynamical systems due to poor optimization conditioning. While prior work has emp…
Chebyshev-Augmented One-Shot Transfer Learning for PINNs on Nonlinear Differential Equations
Yiqi Rao, Pavlos Protopapas
Physics-Informed Neural Networks (PINNs) offer a flexible paradigm for solving differential equations by embedding governing laws into the training objective. A persistent limitati…
PTL-PINNs: Perturbation-Guided Transfer Learning with Physics- Informed Neural Networks for Nonlinear Systems
Duarte Alexandrino, Ben Moseley, Pavlos Protopapas
Accurately and efficiently solving nonlinear differential equations is crucial for modeling dynamic behavior across science and engineering. Physics-Informed Neural Networks (PINNs…
Improved Uncertainty Quantification in Physics-Informed Neural Networks Using Error Bounds and Solution Bundles
Pablo Flores, Olga Graf, Pavlos Protopapas +1
Physics-Informed Neural Networks (PINNs) have been widely used to obtain solutions to various physical phenomena modeled as Differential Equations. As PINNs are not naturally equip…