Google Scholar


  1. C. Moya, A. Mollaali, Z. Zhang, L. Lu, & G. Lin. Conformalized-DeepONet: A distribution-free framework for uncertainty quantification in deep operator networks. arXiv preprint arXiv:2402.15406, 2024.
  2. W. Wu, M. Daneker, K. T. Turner, M. A. Jolley, & L. Lu. Identifying heterogeneous micromechanical properties of biological tissues via physics-informed neural networks. arXiv preprint arXiv:2402.10741, 2024.
  3. M. Yin, N. Charon, R. Brody, L. Lu, N. Trayanova, & M. Maggioni. DIMON: Learning solution operators of partial differential equations on a diffeomorphic family of domains. arXiv preprint arXiv:2402.07250, 2024.
  4. Y. Yin, C. Kou, S. Jia, L. Lu, X. Yuan, & Y. Luo. PF-DMD: Physics-fusion dynamic mode decomposition for accurate and robust forecasting of dynamical systems with imperfect data and physics. arXiv preprint arXiv:2311.15604, 2023.
  5. Z. Hao, J. Yao, C. Su, H. Su, Z. Wang, F. Lu, Z. Xia, Y. Zhang, S. Liu, L. Lu, & J. Zhu. PINNacle: A comprehensive benchmark of physics-informed neural networks for solving PDEs. arXiv preprint arXiv:2306.08827, 2023.
  6. B. Fan, E. Qiao, A. Jiao, Z. Gu, W. Li, & L. Lu. Deep learning for solving and estimating dynamic macro-finance models. arXiv preprint arXiv:2305.09783, 2023.
  7. Z. Jiang, M. Zhu, D. Li, Q. Li, Y. O. Yuan, & L. Lu. Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration. arXiv preprint arXiv:2303.04778, 2023.
  8. A. Jiao, H. He, R. Ranade, J. Pathak, & L. Lu. One-shot learning for solution operators of partial differential equations. arXiv preprint arXiv:2104.05512, 2021.

Journal Papers

  1. Z. Zhang, C. Moya, L. Lu, G. Lin, & H. Schaeffer. D2NO: Efficient handling of heterogeneous input function spaces with distributed deep neural operators. Computer Methods in Applied Mechanics and Engineering, 428, 117084, 2024.
  2. J. Hayford, J. Goldman-Wetzler, E. Wang, & L. Lu. Speeding up and reducing memory usage for scientific machine learning via mixed precision. Computer Methods in Applied Mechanics and Engineering, 428, 117093, 2024.
  3. M. Daneker, S. Cai, Y. Qian, E. Myzelev, A. Kumbhat, H. Li, & L. Lu. Transfer learning on physics-informed neural networks for tracking the hemodynamics in the evolving false lumen of dissected aorta. Nexus, 1 (2), 100016, 2024.
  4. Y. Zhang, Y. Qiang, H. Li, G. Li, L. Lu, M. Dao, G. E. Karniadakis, A. S. Popel, & C. Zhao. Signaling-biophysical modeling unravels mechanistic control of red blood cell phagocytosis by macrophages in sickle cell disease. PNAS Nexus, 3 (2), pgae031, 2024.
  5. X. Liu, M. Zhu, L. Lu, H. Sun, & J. Wang. Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics. Communications Physics, 7 (1), 31, 2024.
  6. H. Wang, L. Lu, S. Song, & G. Huang. Learning specialized activation functions for physics-informed neural networks. Communications in Computational Physics, 34 (4), 869–906, 2023.
  7. L. Lu, Y. Qian, Y. Dong, H. Su, Y. Deng, Q. Zeng, & H. Li. A systematic study of the performance of machine learning models on analyzing the association between semen quality and environmental pollutants. Frontiers in Physics, 11, 1259273, 2023.
  8. M. Zhu, S. Feng, Y. Lin, & L. Lu. Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness. Computer Methods in Applied Mechanics and Engineering, 416, 116300, 2023.
  9. W. Wu, M. Daneker, M. A. Jolley, K. T. Turner, & L. Lu. Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics. Applied Mathematics and Mechanics, 44 (7), 1039–1068, 2023.
  10. S. Mao, R. Dong, L. Lu, K. M. Yi, S. Wang, & P. Perdikaris. PPDONet: Deep operator networks for fast prediction of steady-state solutions in disk-planet systems. The Astrophysical Journal Letters, 950 (2), L12, 2023.
  11. M. Zhu, H. Zhang, A. Jiao, G. E. Karniadakis, & L. Lu. Reliable extrapolation of deep neural operators informed by physics or sparse observations. Computer Methods in Applied Mechanics and Engineering, 412, 116064, 2023.
  12. J. Wang, H. Jiang, G. Chen, H. Wang, L. Lu, J. Liu, & L. Xing. Integration of multi-physics and machine learning-based surrogate modelling approaches for multi-objective optimization of deformed GDL of PEM fuel cells. Energy and AI, 14, 100261, 2023.
  13. P. C. Di Leoni, L. Lu, C. Meneveau, G. E. Karniadakis, & T. A. Zaki. Neural operator prediction of linear instability waves in high-speed boundary layers. Journal of Computational Physics, 474, 111793, 2023.
  14. C. Wu, M. Zhu, Q. Tan, Y. Kartha, & L. Lu. A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering, 403, 115671, 2023.
  15. P. Jin, S. Meng, & L. Lu. MIONet: Learning multiple-input operators via tensor product. SIAM Journal on Scientific Computing, 44 (6), A3490–A3514, 2022.
  16. B. Deng, Y. Shin, L. Lu, Z. Zhang, & G. E. Karniadakis. Approximation rates of DeepONets for learning operators arising from advection-diffusion equations. Neural Networks, 153, 411–426, 2022.
  17. L. Lu, R. Pestourie, S. G. Johnson, & G. Romano. Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport. Physical Review Research, 4 (2), 023210, 2022.
  18. J. Yu, L. Lu, X. Meng, & G. E. Karniadakis. Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. Computer Methods in Applied Mechanics and Engineering, 393, 114823, 2022.
  19. L. Lu, X. Meng, S. Cai, Z. Mao, S. Goswami, Z. Zhang, & G. E. Karniadakis. A comprehensive and fair comparison of two neural operators (with practical extensions) based on FAIR data. Computer Methods in Applied Mechanics and Engineering, 393, 114778, 2022.
  20. L. Lu, R. Pestourie, W. Yao, Z. Wang, F. Verdugo, & S. G. Johnson. Physics-informed neural networks with hard constraints for inverse design. SIAM Journal on Scientific Computing, 43 (6), B1105–B1132, 2021.
  21. H. Li, Z. L. Liu, L. Lu, P. Buffet, & G. E. Karniadakis. How the spleen reshapes and retains young and old red blood cells: A computational investigation. PLoS Computational Biology, 17 (11), e1009516, 2021.
  22. Z. Mao, L. Lu, O. Marxen, T. A. Zaki, & G. E. Karniadakis. DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators. Journal of Computational Physics, 447, 110698, 2021.
  23. Y. Deng, L. Lu, L. Aponte, A. M. Angelidi, V. Novak, G. E. Karniadakis, & C. S. Mantzoros. Deep transfer learning and data augmentation improve glucose levels prediction in type 2 diabetes patients. npj Digital Medicine, 4, 109, 2021.
  24. G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, & L. Yang. Physics-informed machine learning. Nature Reviews Physics, 3 (6), 422–440, 2021.
    • > 2,000 Citations
  25. S. Cai, Z. Wang, L. Lu, T. A. Zaki, & G. E. Karniadakis. DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks. Journal of Computational Physics, 436, 110296, 2021.
  26. L. Lu, P. Jin, G. Pang, Z. Zhang, & G. E. Karniadakis. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nature Machine Intelligence, 3 (3), 218–229, 2021.
  27. C. Lin, Z. Li, L. Lu, S. Cai, M. Maxey, & G. E. Karniadakis. Operator learning for predicting multiscale bubble growth dynamics. The Journal of Chemical Physics, 154 (10), 104118, 2021.
  28. L. Lu, X. Meng, Z. Mao, & G. E. Karniadakis. DeepXDE: A deep learning library for solving differential equations. SIAM Review, 63 (1), 208–228, 2021.
    • Most Read article in SIAM Review
    • > 1,000 Citations
  29. A. Yazdani, L. Lu, M. Raissi, & G. E. Karniadakis. Systems biology informed deep learning for inferring parameters and hidden dynamics. PLoS Computational Biology, 16 (11), e1007575, 2020.
  30. L. Lu, Y. Shin, Y. Su, & G. E. Karniadakis. Dying ReLU and initialization: Theory and numerical examples. Communications in Computational Physics, 28 (5), 1671–1706, 2020.
  31. P. Jin, L. Lu, Y. Tang, & G. E. Karniadakis. Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness. Neural Networks, 130, 85–99, 2020.
  32. Y. Chen, L. Lu, G. E. Karniadakis, & L. Dal Negro. Physics-informed neural networks for inverse problems in nano-optics and metamaterials. Optics Express, 28 (8), 11618–11633, 2020.
    • Top-downloaded articles on deep learning in Optics Express, 2020
  33. L. Lu, M. Dao, P. Kumar, U. Ramamurty, G. E. Karniadakis, & S. Suresh. Extraction of mechanical properties of materials through deep learning from instrumented indentation. Proceedings of the National Academy of Sciences, 117 (13), 7052–7062, 2020.
  34. G. Pang, L. Lu, & G. E. Karniadakis. fPINNs: Fractional physics-informed neural networks. SIAM Journal on Scientific Computing, 41 (4), A2603–A2626, 2019.
  35. L. Lu, Z. Li, H. Li, X. Li, P. G. Vekilov, & G. E. Karniadakis. Quantitative prediction of erythrocyte sickling for the development of advanced sickle cell therapies. Science Advances, 5 (8), eaax3905, 2019.
  36. D. Zhang, L. Lu, L. Guo, & G. E. Karniadakis. Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems. Journal of Computational Physics, 397, 108850, 2019.
  37. H. Li, L. Lu, X. Li, P. A. Buffet, M. Dao, G. E. Karniadakis, & S. Suresh. Mechanics of diseased red blood cells in human spleen and consequences for hereditary blood disorders. Proceedings of the National Academy of Sciences, 115 (38), 9574–9579, 2018.
  38. H. Li, D. Papageorgiou, H. Chang, L. Lu, J. Yang, & Y. Deng. Synergistic integration of laboratory and numerical approaches in studies of the biomechanics of diseased red blood cells. Biosensors, 8 (3), 76, 2018.
  39. L. Lu, Y. Deng, X. Li, H. Li, & G. E. Karniadakis. Understanding the twisted structure of amyloid fibrils via molecular simulations. The Journal of Physical Chemistry B, 122 (49), 11302–11310, 2018.
  40. H. Li, J. Yang, T. T. Chu, R. Naidu, L. Lu, R. Chandramohanadas, M. Dao & G. E. Karniadakis. Cytoskeleton remodeling induces membrane stiffness and stability changes of maturing reticulocytes. Biophysical Journal, 114 (8), 2014–2023, 2018.
    • Highlighted on Biophysical Journal homepage
  41. H. Li, H. Chang, J. Yang, L. Lu, Y. Tang, & G. Lykotrafitis. Modeling biomembranes and red blood cells by coarse-grained particle methods. Applied Mathematics and Mechanics, 39 (1), 3–20, 2018.
  42. L. Lu, H. Li, X. Bian, X. Li, & G. E. Karniadakis. Mesoscopic adaptive resolution scheme toward understanding of interactions between sickle cell fibers. Biophysical Journal, 113 (1), 48–59, 2017.
  43. Y. Tang, L. Lu, H. Li, C. Evangelinos, L. Grinberg, V. Sachdeva, & G. E. Karniadakis. OpenRBC: A fast simulator of red blood cells at protein resolution. Biophysical Journal, 112 (10), 2030–2037, 2017.
    • Highlighted on Biophysical Journal homepage
  44. L. Lu, X. Li, P. G. Vekilov, & G. E. Karniadakis. Probing the twisted structure of sickle hemoglobin fibers via particle simulations. Biophysical Journal, 110 (9), 2085–2093, 2016.
    • Highlighted on Biophysical Journal homepage
  45. L. Lu, X. Zhang, Y. Yan, J. Li, & X. Zhao. Theoretical analysis of natural-gas leakage in urban medium-pressure pipelines. Journal of Environment and Human, 1 (2), 71–86, 2014.

Conference Papers

  1. P. Rathore, W. Lei, Z. Frangella, L. Lu, & M. Udell. Challenges in training PINNs: A loss landscape perspective. International Conference on Machine Learning, 2024.
    • Oral Presentation
  2. A. W. C. do Lago, L. C. Sousa, D. H. B. de Sousa, L. Lu, & H. V. H. Ayala. Pose estimation of robotic manipulators using deep transfer learning towards video-based system identification. Brazilian Symposium on Intelligent Automation, 2023.

Book Chapters

  1. M. Daneker, Z. Zhang, G. E. Karniadakis, & L. Lu. Systems biology: Identifiability analysis and parameter identification via systems-biology-informed neural networks. Computational Modeling of Signaling Networks, Springer, 87–105, 2023.


  1. G. E. Karniadakis, & L. Lu. Deep operator network. U.S. Application No. 63/145,783, International Application No. PCT/US2022/015340, filed on February 4, 2021.
  2. L. Lu, M. Dao, S. Suresh, & G. E. Karniadakis. Machine learning techniques for estimating mechanical properties of materials. U.S. Patent No. 11,461,519, filed on June 24, 2019, and issued on June 30, 2022.
  3. X. Dong, J. M. Li, Y. Yan, H. Zhang, L. Lu, J. Wang, & H. Xiao. A test device and method for simulating natural gas leakage in soil. China Invention Patent CN103712755A, filed on June 14, 2013, and issued on April 9, 2014.