Stability Analysis of Physics-Informed Neural Networks for Stiff Linear Differential Equations

G Fabiani, E Bollt, C Siettos… - arXiv preprint arXiv …, 2024 - arxiv.org
… In particular, we prove that multi-collocation random projection PINNs guarantee …
Randonet: Shallow-networks with random projections for learning linear and nonlinear operators

From disorganized data to emergent dynamic models: Questionnaires to partial differential equations

DW Sroczynski, FP Kemeth, AS Georgiou… - PNAS …, 2025 - academic.oup.com
… , we use machine learning (here, neural networks) to approximate the operators governing
the … nonlinear operators via DeepONet based on the universal approximation theorem of …

GRINNs: Godunov-Riemann Informed Neural Networks for Learning Hyperbolic Conservation Laws

DG Patsatzis, M di Bernardo, L Russo… - arXiv preprint arXiv …, 2024 - arxiv.org
… For obtaining the numerical solution of the unknown system, we perform operator splitting
and solve the homogeneous part of the PDEs with high-resolution Godunov-type methods with …

Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiology

M De Florio, Z Zou, DE Schiavazzi, GE Karniadakis - ArXiv, 2024 - pmc.ncbi.nlm.nih.gov
… on biological and physiological models, this study investigates the decomposition of total …
approach for uncertainty quantification based on random projections and Monte-Carlo sampling…