Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systems. - Kevin Linka; Amelie Schäfer; Xuhui Meng; Zongren Zou; George Em Karniadakis; Ellen Kuhl (CoRR, 2022)

L-HYDRA: Multi-Head Physics-Informed Neural Networks. - Zongren Zou; George Em Karniadakis (CoRR, 2023)

Leveraging Multi-time Hamilton-Jacobi PDEs for Certain Scientific Machine Learning Problems. - Paula X. Chen; Tingwei Meng; Zongren Zou; Jérôme Darbon; George Em Karniadakis (CoRR, 2023)

A Generative Modeling Framework for Inferring Families of Biomechanical Constitutive Laws in Data-Sparse Regimes. - Minglang Yin; Zongren Zou; Enrui Zhang; Cristina Cavinato; Jay D. Humphrey; George Em Karniadakis (CoRR, 2023)

Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regression. - Zhen Zhang 029; Zongren Zou; Ellen Kuhl; George Em Karniadakis (CoRR, 2023)

Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators. - Zongren Zou; Xuhui Meng; George Em Karniadakis (CoRR, 2023)

Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons. - Apostolos F. Psaros; Xuhui Meng; Zongren Zou; Ling Guo; George Em Karniadakis (J. Comput. Phys., 2023)

Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learning. - Paula X. Chen; Tingwei Meng; Zongren Zou; Jérôme Darbon; George Em Karniadakis (L4DC, 2024)

Large scale scattering using fast solvers based on neural operators. - Zongren Zou; Adar Kahana; Enrui Zhang; Eli Turkel; Rishikesh Ranade; Jay Pathak; George Em Karniadakis (CoRR, 2024)

A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks. - Khemraj Shukla; Juan Diego Toscano; Zhicheng Wang; Zongren Zou; George Em Karniadakis (CoRR, 2024)

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements. - Khemraj Shukla; Zongren Zou; Chi Hin Chan; Additi Pandey; Zhicheng Wang; George Em Karniadakis (CoRR, 2024)

Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiology. - Mario De Florio; Zongren Zou; Daniele E. Schiavazzi; George Em Karniadakis (CoRR, 2024)

HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative models. - Tingwei Meng; Zongren Zou; Jérôme Darbon; George Em Karniadakis (CoRR, 2024)

From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning. - Juan Diego Toscano; Vivek Oommen; Alan John Varghese; Zongren Zou; Nazanin Ahmadi Daryakenari; Chenxi Wu; George Em Karniadakis (CoRR, 2024)

Correcting model misspecification in physics-informed neural networks (PINNs). - Zongren Zou; Xuhui Meng; George Em Karniadakis (J. Comput. Phys., 2024)

Leveraging Viscous Hamilton-Jacobi PDEs for Uncertainty Quantification in Scientific Machine Learning. - Zongren Zou; Tingwei Meng; Paula X. Chen; Jérôme Darbon; George Em Karniadakis (SIAM/ASA J. Uncertain. Quantification, 2024)

Leveraging Multitime Hamilton-Jacobi PDEs for Certain Scientific Machine Learning Problems. - Paula X. Chen; Tingwei Meng; Zongren Zou; Jérôme Darbon; George Em Karniadakis (SIAM J. Sci. Comput., 2024)

NeuralUQ: A Comprehensive Library for Uncertainty Quantification in Neural Differential Equations and Operators. - Zongren Zou; Xuhui Meng; Apostolos F. Psaros; George E. Karniadakis (SIAM Rev., 2024)

Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification. - Zongren Zou; George Em Karniadakis (J. Comput. Phys., 2025)

Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble. - Zongren Zou; Zhicheng Wang; George Em Karniadakis (CoRR, 2025)

Bilevel optimization for learning hyperparameters: Application to solving PDEs and inverse problems with Gaussian processes. - Nicholas H. Nelsen; Houman Owhadi; Andrew M. Stuart; Xianjin Yang; Zongren Zou (CoRR, 2025)