2.5k citations · 6.9k across the 23 of their papers we have counts for
11 papers · 1 filter
Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators
Zongren Zou, Xuhui Meng, George Em Karniadakis
Uncertainty quantification (UQ) in scientific machine learning (SciML) becomes increasingly critical as neural networks (NNs) are being widely adopted in addressing complex problem…
Correcting model misspecification in physics-informed neural networks (PINNs)
Zongren Zou, Xuhui Meng, George Em Karniadakis
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 theoreti…
Physics-informed neural networks for predicting gas flow dynamics and unknown parameters in diesel engines
Kamaljyoti Nath, Xuhui Meng, Daniel J Smith +1
This paper presents a physics-informed neural network (PINN) approach for monitoring the health of diesel engines. The aim is to evaluate the engine dynamics, identify unknown para…
Deep neural operator for learning transient response of interpenetrating phase composites subject to dynamic loading
Minglei Lu, Ali Mohammadi, Zhaoxu Meng +3
Additive manufacturing has been recognized as an industrial technological revolution for manufacturing, which allows fabrication of materials with complex three-dimensional (3D) st…
NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators
Zongren Zou, Xuhui Meng, Apostolos F Psaros +1
Uncertainty quantification (UQ) in machine learning is currently drawing increasing research interest, driven by the rapid deployment of deep neural networks across different field…
Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systems
Kevin Linka, Amelie Schafer, Xuhui Meng +3
Understanding real-world dynamical phenomena remains a challenging task. Across various scientific disciplines, machine learning has advanced as the go-to technology to analyze non…
Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons
Apostolos F Psaros, Xuhui Meng, Zongren Zou +2
Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challen…
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
Jeremy Yu, Lu Lu, Xuhui Meng +1
Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual…
Learning Functional Priors and Posteriors from Data and Physics
Xuhui Meng, Liu Yang, Zhiping Mao +2
We develop a new Bayesian framework based on deep neural networks to be able to extrapolate in space-time using historical data and to quantify uncertainties arising from both nois…
Multi-fidelity Bayesian Neural Networks: Algorithms and Applications
Xuhui Meng, Hessam Babaee, George Em Karniadakis
We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as t…
DeepXDE: A deep learning library for solving differential equations
Lu Lu, Xuhui Meng, Zhiping Mao +1
Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present…