## Publications

### Preprints

- 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. - M. Zhu, H. Zhang, A. Jiao, G. E. Karniadakis, & L. Lu. Reliable extrapolation of deep neural operators informed by physics or sparse observations.
*arXiv preprint arXiv:2212.06347*, 2022. - 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.
*arXiv preprint arXiv:2211.15423*, 2022. - X. Liu, H. Sun, M. Zhu, L. Lu, & J. Wang. Predicting parametric spatiotemporal dynamics by multi-resolution PDE structure-preserved deep learning.
*arXiv preprint arXiv:2205.03990*, 2022. - M. Daneker, Z. Zhang, G. E. Karniadakis, & L. Lu. Systems biology: Identifiability analysis and parameter identification via systems-biology informed neural networks.
*arXiv preprint arXiv:2202.01723*, 2022. - 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

- P. Clark 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. - 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. - P. Jin, S. Meng, & L. Lu. MIONet: Learning multiple-input operators via tensor product.
*SIAM Journal on Scientific Computing*, 44(6), A3490–A3514, 2022. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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

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- 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. - 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. - 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

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- 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. - 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.- Top-downloaded articles on deep learning in
*Optics Express*, 2020

- Top-downloaded articles on deep learning in
- 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. - 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
*Science Advances*homepage, SIAM News, eHealthNews.eu, Brown News, Brown Daily Herald

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- 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

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- 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, DOE Science News Source, OLCF News, Brown News, Brown Daily Herald, Brown Graduate School 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

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- 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

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- 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

### Patents

- 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. - 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. - 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.