P. Jin, Z. Zhang, A. Zhu, Y. Tang, G. E. Karniadakis, SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems, Natural Networks, Volume 132, https://doi.org/10.1016/j.neunet.2020.08.017, 2020.
G. Pang, M. D'Elia, M. Parks, G. E. Karniadakis, nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications, Journal of Computational Physics Volume 422, https://doi.org/10.1016/j.jcp.2020.109760, December 2020.
K. Shukla, P. C. Di Leoni, J. Blackshire, D. Sparkman, G. E. Karniadakis, Physics-Informed Neural Network for Ultrasound Nondestructive Quantification of Surface Breaking Cracks, Journal of Nondestructive Evaluation, Article number: 61, August 2020.
A. D. Jagtap, K. Kawaguchi, G. E. Karniadakis, Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks, Proceedings of the Royal Socierty, https://doi.org/10.1098/rspa.2020.0334, July 2020.
Y. Chen, L. Lu, G. E. Karniadakis, and L. D. Negro, Physics-informed neural networks for inverse problems in nano-optics and metamaterials, Optics Express, Vol. 28, Issue 8, pp. 11618-11633, https://doi.org/10.1364/OE.384875, 2020.
P.Jin, L. Lu, Y. Tanga, G. E. Karniadakis, Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness, Neural Networks, https://doi.org/10.1016/j.neunet.2020.06.024, July 2020.
Q Zheng, L Zeng, GE Karniadakis, Physics-informed semantic inpainting: Application to geostatistical modeling, Journal of Computational Physics, 109676, 2020.
AD Jagtap, E Kharazmi, GE Karniadakis, Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems ,Computer Methods in Applied Mechanics and Engineering 365, 113028, 2020.
L Lu, M Dao, P Kumar, U Ramamurty, GE Karniadakis, S Suresh, Extraction of mechanical properties of materials through deep learning from instrumented indentation, Proceedings of the National Academy of Sciences, March 16, 2020.
Z Mao, AD Jagtap, GE Karniadakis, Physics-informed neural networks for high-speed flows, Computer Methods in Applied Mechanics and Engineering 360, 112789, 2020.
AD Jagtap, K Kawaguchi, GE Karniadakis, Adaptive activation functions accelerate convergence in deep and physics-informed neural networks, Journal of Computational Physics 404, 109136, 2020.
M Raissi, A Yazdani, GE Karniadakis, Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations, Science 367 (6481), 1026-1030, 2020.
GCY Peng, M Alber, AB Tepole, WR Cannon, S De, .., GE Karniadakis, E. Kuhl, Multiscale Modeling Meets Machine Learning: What Can We Learn?, Archives of Computational Methods in Engineering, 1-2, 2020.
X Meng, GE Karniadakis, A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems, Journal of Computational Physics 401, 109020, 2020.
L Yang, D Zhang, GE Karniadakis, Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations, SIAM Journal on Scientific Computing 42 (1), A292-A317, 2020.
D Zhang, L Guo, GE Karniadakis, Learning in modal space: Solving time-dependent stochastic PDEs using physics-informed neural networks, SIAM Journal on Scientific Computing 42 (2), A639-A665, 2020.
PP Mehta, G Pang, F Song, GE Karniadakis, Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network, Fractional Calculus and Applied Analysis 22 (6), 1675-1688, 2019.
Z Mao, Z Li, GE Karniadakis, Nonlocal flocking dynamics: Learning the fractional order of PDEs from particle simulations, Communications on Applied Mathematics and Computation 1 (4), 597-619, 2019.
D Fan, G Jodin, TR Consi, L Bonfiglio, Y Ma, LR Keyes, GE Karniadakis, ...,MS Triantafyllou, A robotic Intelligent Towing Tank for learning complex fluid-structure dynamics, Science Robotics 4 (36), 2019.