Bi-fidelity modeling of uncertain and partially unknown systems using DeepONets

Physics-informed neural networks (PINNs) for fluid mechanics: a review

(2022) Shengze Cai et al.   ACTA MECHANICA SINICA

Neural Network Training Using ℓ1-Regularization and Bi-fidelity Data

(2022) Subhayan De et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data

(2022) Lu Lu et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials

(2022) Somdatta Goswami et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Approximation rates of DeepONets for learning operators arising from advection–diffusion equations

(2022) Beichuan Deng et al.   NEURAL NETWORKS

A Survey of Bayesian Calibration and Physics-informed Neural Networks in Scientific Modeling

(2021) Felipe A. C. Viana et al.   ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING

Uncertainty Quantification of Locally Nonlinear Dynamical Systems Using Neural Networks

(2021) Subhayan De   JOURNAL OF COMPUTING IN CIVIL ENGINEERING

Deep neural network enabled corrective source term approach to hybrid analysis and modeling

(2021) Sindre Stenen Blakseth et al.   NEURAL NETWORKS

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

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

Bi-fidelity stochastic gradient descent for structural optimization under uncertainty

(2020) Subhayan De et al.   COMPUTATIONAL MECHANICS

Topology optimization under uncertainty using a stochastic gradient-based approach

(2020) Subhayan De et al.   STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION

ConvPDE-UQ: Convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains

(2019) Nick Winovich et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data

(2019) Yinhao Zhu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Adversarial uncertainty quantification in physics-informed neural networks

(2019) Yibo Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Deep Learning for Computer Vision: A Brief Review

(2018) Athanasios Voulodimos et al.   Computational Intelligence and Neuroscience

Turbulence Modeling in the Age of Data

(2018) Karthik Duraisamy et al.   Annual Review of Fluid Mechanics

Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification

(2018) Rohit K. Tripathy 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

Error bounds for approximations with deep ReLU networks

(2017) Dmitry Yarotsky   NEURAL NETWORKS

A paradigm for data-driven predictive modeling using field inversion and machine learning

(2016) Eric J. Parish et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Response surface methodology with prediction uncertainty: A multi-objective optimisation approach

(2011) Guoyi Chi et al.   CHEMICAL ENGINEERING RESEARCH & DESIGN

A non-adapted sparse approximation of PDEs with stochastic inputs

(2011) Alireza Doostan et al.   JOURNAL OF COMPUTATIONAL PHYSICS