# Publications

- Google Scholar
^{*}Contributed equally

## Preprints

- 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.*arXiv preprint arXiv:2009.12935*, 2020.

## Journal Papers

**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*, to appear.- G. E. Karniadakis, Y. Kevrekidis,
**L. Lu**, P. Perdikaris, S. Wang, & L. Yang. A perspective on physics-informed machine learning.*Nature Reviews Physics*, to appear, invited. **L. Lu**^{*}, Y. Shin^{*}, Y. Su, & G. E. Karniadakis. Dying ReLU and initialization: Theory and numerical examples.*Communications in Computational Physics*, to appear.- A. Yazdani
^{*},**L. Lu**^{*}, M. Raissi, & G. E. Karniadakis. Systems biology informed deep learning for inferring parameters and hidden dynamics.*PLoS Computational Biology*, to appear. **L. Lu**, X. Meng, Z. Mao, & G. E. Karniadakis. DeepXDE: A deep learning library for solving differential equations.*SIAM Review*, to appear.- 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. - 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. **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)- G. Pang
^{*},**L. Lu**^{*}, & G. E. Karniadakis. fPINNs: Fractional physics-informed neural networks.*SIAM Journal on Scientific Computing*, 41(4), A2603–A2626, 2019. **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**, eHealthNews.eu, Brown News, Brown Daily Herald)*Science Advances*homepage- 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. - 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. - 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. **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.- 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 - 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. **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)- 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 **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**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.

## Workshop Papers

**L. Lu**, X. Meng, Z. Mao, & G. E. Karniadakis. DeepXDE: A deep learning library for solving differential equations.*AAAI Spring Symposium on Combining Artificial Intelligence and Machine Learning with Physical Sciences*, 2020.**L. Lu**, X. Meng, Z. Mao, & G. E. Karniadakis. DeepXDE: A deep learning library for solving differential equations.*Conference on Neural Information Processing Systems Workshop on Machine Learning and the Physical Sciences*, 2019.