Uncertainty quantification for noisy inputs–outputs in physics-informed neural networks and neural operators
Uncertainty quantification (UQ) in scientific machine learning (SciML) becomes increasingly
critical as neural networks (NNs) are being widely adopted in addressing complex problems …
critical as neural networks (NNs) are being widely adopted in addressing complex problems …
Correcting model misspecification in physics-informed neural networks (PINNs)
Data-driven discovery of governing equations in computational science has emerged as a
new paradigm for obtaining accurate physical models and as a possible alternative to …
new paradigm for obtaining accurate physical models and as a possible alternative to …
Leveraging viscous Hamilton–Jacobi PDEs for uncertainty quantification in scientific machine learning
Uncertainty quantification (UQ) in scientific machine learning (SciML) combines the powerful
predictive power of SciML with methods for quantifying the reliability of the learned models …
predictive power of SciML with methods for quantifying the reliability of the learned models …
NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements
Multiphysics problems that are characterized by complex interactions among fluid dynamics,
heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to …
heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to …
A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks
Kolmogorov-Arnold Networks (KANs) were recently introduced as an alternative
representation model to MLP. Herein, we employ KANs to construct physics-informed …
representation model to MLP. Herein, we employ KANs to construct physics-informed …
Large scale scattering using fast solvers based on neural operators
We extend a recently proposed machine-learning-based iterative solver, ie the hybrid
iterative transferable solver (HINTS), to solve the scattering problem described by the …
iterative transferable solver (HINTS), to solve the scattering problem described by the …
HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative models
The interplay between stochastic processes and optimal control has been extensively
explored in the literature. With the recent surge in the use of diffusion models, stochastic …
explored in the literature. With the recent surge in the use of diffusion models, stochastic …