Uncertainty quantification for noisy inputs–outputs in physics-informed neural networks and neural operators

Z Zou, X Meng, GE Karniadakis - Computer Methods in Applied Mechanics …, 2025 - Elsevier
Uncertainty quantification (UQ) in scientific machine learning (SciML) becomes increasingly
critical as neural networks (NNs) are being widely adopted in addressing complex problems …

A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks

K Shukla, JD Toscano, Z Wang, Z Zou… - arxiv preprint arxiv …, 2024 - arxiv.org
Kolmogorov-Arnold Networks (KANs) were recently introduced as an alternative
representation model to MLP. Herein, we employ KANs to construct physics-informed …

Convergence framework of deep learning-based hybrid iterative methods and the application to designing a fourier neural solver for parametric pdes

C Cui, K Jiang, Y Liu, S Shu - arxiv preprint arxiv:2408.08540, 2024 - arxiv.org
Recently, deep learning-based hybrid iterative methods (DL-HIM) have emerged as a
promising approach for designing fast neural solvers to tackle large-scale sparse linear …