| Physics-informed machine learning GE Karniadakis, IG Kevrekidis, L Lu, P Perdikaris, S Wang, L Yang Nature Reviews Physics 3 (6), 422-440, 2021 | 8059 | 2021 |
| Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators L Lu, P Jin, G Pang, Z Zhang, GE Karniadakis Nature Machine Intelligence 3 (3), 218-229, 2021 | 4572* | 2021 |
| DeepXDE: A deep learning library for solving differential equations L Lu, X Meng, Z Mao, GE Karniadakis SIAM Review 63 (1), 208-228, 2021 | 2844 | 2021 |
| fPINNs: Fractional physics-informed neural networks G Pang, L Lu, GE Karniadakis SIAM Journal on Scientific Computing 41 (4), A2603-A2626, 2019 | 1188 | 2019 |
| Physics-informed neural networks with hard constraints for inverse design L Lu, R Pestourie, W Yao, Z Wang, F Verdugo, SG Johnson SIAM Journal on Scientific Computing 43 (6), B1105-B1132, 2021 | 948 | 2021 |
| Dying ReLU and Initialization: Theory and Numerical Examples L Lu, Y Shin, Y Su, GE Karniadakis COMMUNICATIONS IN COMPUTATIONAL PHYSICS 28 (5), 1671-1706, 2020 | 847 | 2020 |
| Physics-informed neural networks for inverse problems in nano-optics and metamaterials Y Chen, L Lu, GE Karniadakis, L Dal Negro Optics Express 28 (8), 11618-11633, 2020 | 834 | 2020 |
| Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems J Yu, L Lu, X Meng, GE Karniadakis Computer Methods in Applied Mechanics and Engineering 393, 114823, 2022 | 767 | 2022 |
| A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks C Wu, M Zhu, Q Tan, Y Kartha, L Lu Computer Methods in Applied Mechanics and Engineering 403, 115671, 2023 | 711 | 2023 |
| A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data L Lu, X Meng, S Cai, Z Mao, S Goswami, Z Zhang, GE Karniadakis Computer Methods in Applied Mechanics and Engineering 393, 114778, 2022 | 676 | 2022 |
| Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems D Zhang, L Lu, L Guo, GE Karniadakis Journal of Computational Physics 397, 108850, 2019 | 636 | 2019 |
| Systems biology informed deep learning for inferring parameters and hidden dynamics A Yazdani, L Lu, M Raissi, GE Karniadakis PLOS Computational Biology 16 (11), e1007575, 2020 | 397 | 2020 |
| Extraction of mechanical properties of materials through deep learning from instrumented indentation L Lu, M Dao, P Kumar, U Ramamurty, GE Karniadakis, S Suresh Proceedings of the National Academy of Sciences 117 (13), 7052-7062, 2020 | 383 | 2020 |
| DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks S Cai, Z Wang, L Lu, TA Zaki, GE Karniadakis Journal of Computational Physics 436, 110296, 2021 | 329 | 2021 |
| MIONet: Learning Multiple-Input Operators via Tensor Product P Jin, S Meng, L Lu SIAM Journal on Scientific Computing 44 (6), A3490-A3514, 2022 | 291 | 2022 |
| DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators Z Mao, L Lu, O Marxen, TA Zaki, GE Karniadakis Journal of Computational Physics 447, 110698, 2021 | 212 | 2021 |
| Operator learning for predicting multiscale bubble growth dynamics C Lin, Z Li, L Lu, S Cai, M Maxey, GE Karniadakis The Journal of Chemical Physics 154 (10), 104118, 2021 | 210 | 2021 |
| Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport L Lu, R Pestourie, SG Johnson, G Romano Physical Review Research 4 (2), 023210, 2022 | 195 | 2022 |
| Challenges in Training PINNs: A Loss Landscape Perspective P Rathore, W Lei, Z Frangella, L Lu, M Udell International Conference on Machine Learning, 2024 | 172 | 2024 |
| Deep transfer learning and data augmentation improve glucose levels prediction in type 2 diabetes patients Y Deng, L Lu, L Aponte, AM Angelidi, V Novak, GE Karniadakis, ... NPJ Digital Medicine 4 (1), 109, 2021 | 157 | 2021 |
George Em KarniadakisThe Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics and EngineeringVerified email at brown.edu
