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Preprints
H. Wang, L. Lu, S. Song, & G. Huang. Learning specialized activation functions for physics-informed neural networks . arXiv preprint arXiv:2308.04073 , 2023.
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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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.
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.
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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.
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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
Book Chapters
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.
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.