*Contributed equally


  1. Lu, L., Jin, P., & Karniadakis, G. E. (2019). DeepONet: Learning Nonlinear Operators for Identifying Differential Equations based on the Universal Approximation Theorem of Operators. arXiv preprint arXiv:1910.03193.
  2. Lu, L., Meng, X., Mao, Z., & Karniadakis, G. E. (2019). DeepXDE: A Deep Learning Library for Solving Differential Equations. arXiv preprint arXiv:1907.04502.
  3. Jin, P.*, Lu, L.*, Tang, Y., & Karniadakis, G. E. (2019). Quantifying the Generalization Error in Deep Learning in terms of Data Distribution and Neural Network Smoothness. arXiv preprint arXiv:1905.11427.
  4. Lu, L.*, Shin, Y.*, Su, Y., & Karniadakis, G. E. (2019). Dying ReLU and Initialization: Theory and Numerical Examples. arXiv preprint arXiv:1903.06733.
  5. Lu, L., Su, Y., & Karniadakis, G. E. (2018). Collapse of Deep and Narrow Neural Nets. arXiv preprint arXiv:1808.04947.

Journal Papers

  1. Pang, G.*, Lu, L.*, & Karniadakis, G. E. (2019). fPINNs: Fractional Physics-Informed Neural Networks. SIAM Journal on Scientific Computing, 41(4), A2603-A2626.
  2. Lu, L.*, Li, Z.*, Li, H.*, Li, X., Vekilov, P. G., & Karniadakis, G. E. (2019). Quantitative Prediction of Erythrocyte Sickling for the Development of Advanced Sickle Cell Therapies. Science Advances, 5(8), eaax3905. (Highlighted on Science Advances homepage,, Brown News)
  3. Zhang, D., Lu, L., Guo, L., & Karniadakis, G. E. (2019). Quantifying Total Uncertainty in Physics-informed Neural Networks for Solving Forward and Inverse Stochastic Problems. Journal of Computational Physics, 397, 108850.
  4. Li, H.*, Lu, L.*, Li, X., Buffet, P. A., Dao, M., Karniadakis, G. E., & Suresh, S. (2018). 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.
  5. Li, H., Papageorgiou, D., Chang, H. Y., Lu, L., Yang, J., & Deng, Y. (2018). Synergistic Integration of Laboratory and Numerical Approaches in Studies of the Biomechanics of Diseased Red Blood Cells. Biosensors, 8(3), 76.
  6. Lu, L.*, Deng, Y.*, Li, X., Li, H., & Karniadakis, G. E. (2018). Understanding the Twisted Structure of Amyloid Fibrils via Molecular Simulations. The Journal of Physical Chemistry B, 122(49), 11302-11310.
  7. Li, H., Yang, J., Chu, T. T., Naidu, R., Lu, L., Chandramohanadas, R., … & Karniadakis, G. E. (2018). Cytoskeleton Remodeling Induces Membrane Stiffness and Stability Changes of Maturing Reticulocytes. Biophysical Journal, 114(8), 2014–2023. (Highlighted on Biophysical Journal homepage)
  8. Li, H., Chang, H. Y., Yang, J., Lu, L., Tang, Y. H., & Lykotrafitis, G. (2018). Modeling Biomembranes and Red Blood Cells by Coarse-grained Particle Methods. Applied Mathematics and Mechanics, 39(1), 3–20.
  9. Lu, L., Li, H., Bian, X., Li, X., & Karniadakis, G. E. (2017). Mesoscopic Adaptive Resolution Scheme toward Understanding of Interactions between Sickle Cell Fibers. Biophysical Journal, 113(1), 48–59. (Cover Article, Brown Daily Herald, Brown Graduate School News, Brown News, DOE Science News Source, OLCF News)
  10. Tang, Y. H.*, Lu, L.*, Li, H., Evangelinos, C., Grinberg, L., Sachdeva, V., & Karniadakis, G. E. (2017). OpenRBC: A Fast Simulator of Red Blood Cells at Protein Resolution. Biophysical Journal, 112(10), 2030–2037. (Highlighted on Biophysical Journal homepage)
  11. Lu, L., Li, X., Vekilov, P. G., & Karniadakis, G. E. (2016). Probing the Twisted Structure of Sickle Hemoglobin Fibers via Particle Simulations. Biophysical Journal, 110(9), 2085–2093. (Highlighted on Biophysical Journal homepage)
  12. Lu, L., Zhang, X., Yan, Y., Li, J. M., & Zhao, X. (2014). Theoretical Analysis of Natural-Gas Leakage in Urban Medium-pressure Pipelines. Journal of Environment and Human, 1(2), 71–86.