B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

(2020) Liu Yang et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Bayesian deep learning with hierarchical prior: Predictions from limited and noisy data

(2020) Xihaier Luo et al.   STRUCTURAL SAFETY

Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems

(2019) Liang Yan et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Neural-net-induced Gaussian process regression for function approximation and PDE solution

(2019) Guofei Pang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Data-driven discovery of PDEs in complex datasets

(2019) Jens Berg et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

(2019) Dongkun Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems

(2019) Xuhui Meng et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Machine learning of linear differential equations using Gaussian processes

(2017) Maziar Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Inferring solutions of differential equations using noisy multi-fidelity data

(2017) Maziar Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Data-driven discovery of partial differential equations

(2017) Samuel H. Rudy et al.   Science Advances

Deep learning

(2015) Yann LeCun et al.   NATURE

Adaptive Construction of Surrogates for the Bayesian Solution of Inverse Problems

(2014) Jinglai Li et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING