OpenRBC: A Fast Simulator of Red Blood Cells at Protein Resolution. - Yu-Hang Tang; Lu Lu 010; He Li; Constantinos Evangelinos; Leopold Grinberg; Vipin Sachdeva; George E. Karniadakis (CoRR, 2017)

Collapse of Deep and Narrow Neural Nets. - Lu Lu 010; Yanhui Su; George E. Karniadakis (CoRR, 2018)

Dying ReLU and Initialization: Theory and Numerical Examples. - Lu Lu 010; Yeonjong Shin; Yanhui Su; George E. Karniadakis (CoRR, 2019)

DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators. - Lu Lu 010; Pengzhan Jin; George Em Karniadakis (CoRR, 2019)

Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems. - Dongkun Zhang; Lu Lu 010; Ling Guo; George Em Karniadakis (J. Comput. Phys., 2019)

fPINNs: Fractional Physics-Informed Neural Networks. - Guofei Pang; Lu Lu 010; George Em Karniadakis (SIAM J. Sci. Comput., 2019)

Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness. - Pengzhan Jin; Lu Lu 010; Yifa Tang; George Em Karniadakis (Neural Networks, 2020)

Systems biology informed deep learning for inferring parameters and hidden dynamics. - Alireza Yazdani 001; Lu Lu 010; Maziar Raissi; George Em Karniadakis (PLoS Comput. Biol., 2020)

Convergence rate of DeepONets for learning operators arising from advection-diffusion equations. - Beichuan Deng; Yeonjong Shin; Lu Lu 010; Zhongqiang Zhang; George Em Karniadakis (CoRR, 2021)

Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. - Jeremy Yu; Lu Lu 010; Xuhui Meng; George Em Karniadakis (CoRR, 2021)

DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks. - Shengze Cai; Zhicheng Wang; Lu Lu 010; Tamer A. Zaki; George Em Karniadakis (J. Comput. Phys., 2021)

DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators. - Zhiping Mao; Lu Lu 010; Olaf Marxen; Tamer A. Zaki; George Em Karniadakis (J. Comput. Phys., 2021)

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. - Lu Lu 010; Pengzhan Jin; Guofei Pang; Zhongqiang Zhang; George Em Karniadakis (Nat. Mach. Intell., 2021)

Deep transfer learning and data augmentation improve glucose levels prediction in type 2 diabetes patients. - Yixiang Deng; Lu Lu 010; Laura Aponte; Angeliki M. Angelidi; Vera Novak; George Em Karniadakis; Christos S. Mantzoros (npj Digit. Medicine, 2021)

How the spleen reshapes and retains young and old red blood cells: A computational investigation. - He Li; Zixiang Leonardo Liu; Lu Lu 010; Pierre Buffet; George Em Karniadakis (PLoS Comput. Biol., 2021)

DeepXDE: A Deep Learning Library for Solving Differential Equations. - Lu Lu 010; Xuhui Meng; Zhiping Mao; George Em Karniadakis (SIAM Rev., 2021)

Physics-Informed Neural Networks with Hard Constraints for Inverse Design. - Lu Lu 010; Raphaël Pestourie; Wenjie Yao; Zhicheng Wang; Francesc Verdugo; Steven G. Johnson (SIAM J. Sci. Comput., 2021)

Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networks. - Mitchell Daneker; Zhen Zhang 029; George Em Karniadakis; Lu Lu 010 (CoRR, 2022)

Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport. - Lu Lu 010; Raphaël Pestourie; Steven G. Johnson; Giuseppe Romano (CoRR, 2022)

Effective Data Sampling Strategies and Boundary Condition Constraints of Physics-Informed Neural Networks for Identifying Material Properties in Solid Mechanics. - Wensi Wu; Mitchell Daneker; Matthew A. Jolley; Kevin T. Turner; Lu Lu 010 (CoRR, 2022)

Reliable extrapolation of deep neural operators informed by physics or sparse observations. - Min Zhu; Handi Zhang; Anran Jiao; George Em Karniadakis; Lu Lu 010 (CoRR, 2022)

Approximation rates of DeepONets for learning operators arising from advection-diffusion equations. - Beichuan Deng; Yeonjong Shin; Lu Lu 010; Zhongqiang Zhang; George Em Karniadakis (Neural Networks, 2022)

MIONet: Learning Multiple-Input Operators via Tensor Product. - Pengzhan Jin; Shuai Meng; Lu Lu 010 (SIAM J. Sci. Comput., 2022)

Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration. - Zhongyi Jiang; Min Zhu; Dongzhuo Li; Qiuzi Li; Yanhua O. Yuan; Lu Lu 010 (CoRR, 2023)

Deep Learning for Solving and Estimating Dynamic Macro-Finance Models. - Benjamin Fan; Edward Qiao; Anran Jiao; Zhouzhou Gu; Wenhao Li; Lu Lu 010 (CoRR, 2023)

Neural operator prediction of linear instability waves in high-speed boundary layers. - Patricio Clark Di Leoni; Lu Lu 010; Charles Meneveau; George Em Karniadakis; Tamer A. Zaki (J. Comput. Phys., 2023)

DIMON: Learning Solution Operators of Partial Differential Equations on a Diffeomorphic Family of Domains. - Minglang Yin; Nicolas Charon; Ryan Brody; Lu Lu 010; Natalia A. Trayanova; Mauro Maggioni (CoRR, 2024)

Identifying heterogeneous micromechanical properties of biological tissues via physics-informed neural networks. - Wensi Wu; Mitchell Daneker; Kevin T. Turner; Matthew A. Jolley; Lu Lu 010 (CoRR, 2024)

Solving forward and inverse PDE problems on unknown manifolds via physics-informed neural operators. - Anran Jiao; Qile Yan; John Harlim; Lu Lu 010 (CoRR, 2024)

ADEPT: A Noninvasive Method for Determining Elastic Parameters of Valve Tissue. - Wensi Wu; Mitchell Daneker; Christian Herz; Hannah Dewey; Jeffrey A. Weiss; Alison M. Pouch; Lu Lu 010; Matthew A. Jolley (CoRR, 2024)

PCDMD: Physics-constrained dynamic mode decomposition for accurate and robust forecasting of dynamical systems with imperfect data and physics. - Yuhui Yin; Chenhui Kou; Shengkun Jia; Lu Lu 010; Xigang Yuan; Yiqing Luo (Comput. Phys. Commun., 2024)

Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration. - Zhongyi Jiang; Min Zhu; Lu Lu 010 (Reliab. Eng. Syst. Saf., 2024)

A scalable framework for learning the geometry-dependent solution operators of partial differential equations. - Minglang Yin; Nicolas Charon; Ryan Brody; Lu Lu 010; Natalia A. Trayanova; Mauro Maggioni (Nat. Comput. Sci., 2024)

Quantum DeepONet: Neural operators accelerated by quantum computing. - Pengpeng Xiao; Muqing Zheng; Anran Jiao; Xiu Yang; Lu Lu 010 (Quantum, 2025)

Active operator learning with predictive uncertainty quantification for partial differential equations. - Nick Winovich; Mitchell Daneker; Lu Lu 010; Guang Lin (CoRR, 2025)