Bi-directional coupling between a PDE-domain and an adjacent Data-domain equipped with multi-fidelity sensors. - Dongkun Zhang; Liu Yang 027; George E. Karniadakis (J. Comput. Phys., 2018)

Highly-Ccalable, Physics-Informed GANs for Learning Solutions of Stochastic PDEs. - Liu Yang 027; Prabhat; George E. Karniadakis; Sean Treichler; Thorsten Kurth; Keno Fischer; David A. Barajas-Solano; Joshua Romero; Valentin Churavy; Alexandre M. Tartakovsky; Michael Houston (DLS@SC, 2019)

Potential Flow Generator with $L_2$ Optimal Transport Regularity for Generative Models. - Liu Yang 027; George E. Karniadakis (CoRR, 2019)

Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEs. - Liu Yang 027; Sean Treichler; Thorsten Kurth; Keno Fischer; David A. Barajas-Solano; Joshua Romero; Valentin Churavy; Alexandre M. Tartakovsky; Michael Houston; Prabhat; George E. Karniadakis (CoRR, 2019)

Neural-net-induced Gaussian process regression for function approximation and PDE solution. - Guofei Pang; Liu Yang 027; George E. Karniadakis (J. Comput. Phys., 2019)

Reinforcement Learning for Active Flow Control in Experiments. - Dixia Fan; Liu Yang 027; Michael S. Triantafyllou; George Em Karniadakis (CoRR, 2020)

Generative Ensemble-Regression: Learning Stochastic Dynamics from Discrete Particle Ensemble Observations. - Liu Yang 027; Constantinos Daskalakis; George Em Karniadakis (CoRR, 2020)

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations. - Liu Yang 027; Dongkun Zhang; George Em Karniadakis (SIAM J. Sci. Comput., 2020)

Measure-conditional Discriminator with Stationary Optimum for GANs and Statistical Distance Surrogates. - Liu Yang 027; Tingwei Meng; George Em Karniadakis (CoRR, 2021)

B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data. - Liu Yang 027; Xuhui Meng; George Em Karniadakis (J. Comput. Phys., 2021)

Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-Informed Neural Networks. - Xiaoli Chen; Liu Yang 027; Jinqiao Duan; George Em Karniadakis (SIAM J. Sci. Comput., 2021)

Learning functional priors and posteriors from data and physics. - Xuhui Meng; Liu Yang 027; Zhiping Mao; José del Águila Ferrandis; George Em Karniadakis (J. Comput. Phys., 2022)

Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-informed Deep Generative Models. - Liu Yang 027; Constantinos Daskalakis; George E. Karniadakis (SIAM J. Sci. Comput., 2022)

Potential Flow Generator With L2 Optimal Transport Regularity for Generative Models. - Liu Yang 027; George Em Karniadakis (IEEE Trans. Neural Networks Learn. Syst., 2022)

In-Context Operator Learning for Differential Equation Problems. - Liu Yang 027; Siting Liu 003; Tingwei Meng; Stanley J. Osher (CoRR, 2023)

Prompting In-Context Operator Learning with Sensor Data, Equations, and Natural Language. - Liu Yang 027; Tingwei Meng; Siting Liu 003; Stanley J. Osher (CoRR, 2023)

VICON: Vision In-Context Operator Networks for Multi-Physics Fluid Dynamics Prediction. - Yadi Cao; Yuxuan Liu; Liu Yang 027; Rose Yu; Hayden Schaeffer; Stanley J. Osher (CoRR, 2024)

PDE generalization of in-context operator networks: A study on 1D scalar nonlinear conservation laws. - Liu Yang 027; Stanley J. Osher (J. Comput. Phys., 2024)

Fine-tune language models as multi-modal differential equation solvers. - Liu Yang 027; Siting Liu 003; Stanley J. Osher (Neural Networks, 2025)

A Multimodal PDE Foundation Model for Prediction and Scientific Text Descriptions. - Elisa Negrini; Yuxuan Liu; Liu Yang 027; Stanley J. Osher; Hayden Schaeffer (CoRR, 2025)