1. P. Clark Di Leoni, L. Lu, C. Meneveau, G. E. Karniadakis, & T. A. Zaki. DeepONet prediction of linear instability waves in high-speed boundary layers. arXiv preprint arXiv:2105.08697, 2021.
  2. B. Deng, Y. Shin, L. Lu, Z. Zhang, & G. E. Karniadakis. Convergence rate of DeepONets for learning operators arising from advection-diffusion equations. arXiv preprint arXiv:2102.10621, 2021.
  3. L. Lu, R. Pestourie, W. Yao, Z. Wang, F. Verdugo, & S. G. Johnson. Physics-informed neural networks with hard constraints for inverse design. arXiv preprint arXiv:2102.04626, 2021.

Journal Papers

  1. 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, 110698, 2021.
  2. 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.
  3. 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.
  4. 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.
  5. 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, 218–229, 2021. (Highlighted on Nature Machine Intelligence, 3, 192–193, 2021, Tech Xplore, Quanta Magazine)
  6. 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.
  7. 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.
  8. 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. (Highlighted on Nature Computational Science, 1, 16, 2021)
  9. 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.
  10. 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.
  11. Y. Chen, L. Lu, G. E. Karniadakis, & L. D. Negro. Physics-informed neural networks for inverse problems in nano-optics and metamaterials. Optics Express, 28(8), 11618–11633, 2020.
  12. 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. (MIT News, Brown News, NTU News)
  13. G. Pang*, L. Lu*, & G. E. Karniadakis. fPINNs: Fractional physics-informed neural networks. SIAM Journal on Scientific Computing, 41(4), A2603–A2626, 2019.
  14. 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. (Highlighted on Science Advances homepage, SIAM News,, Brown News, Brown Daily Herald)
  15. 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.
  16. 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.
  17. H. Li, D. Papageorgiou, H. Y. 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.
  18. 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.
  19. 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)
  20. H. Li, H. Y. Chang, J. Yang, L. Lu, Y. H. Tang, & G. Lykotrafitis. Modeling biomembranes and red blood cells by coarse-grained particle methods. Applied Mathematics and Mechanics, 39(1), 3–20, 2018.
  21. 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. (Cover Article, Brown Daily Herald, Brown Graduate School News, Brown News, DOE Science News Source, OLCF News)
  22. Y. H. 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)
  23. 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)
  24. L. Lu, X. Zhang, Y. Yan, J. M. 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. L. Lu, H. He, P. Kasimbeg, R. Ranade, & J. Pathak. One-shot learning for solution operators of partial differential equations. ICLR Workshop on Deep Learning for Simulation, 2021.