Machine Learning
- 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.
- X. Menga, Z. Li, D. Zhang, G. E. Karniadakis, PPINN: Parareal physics-informed neural network for time-dependent PDEs, Computer Methods in Applied Mechanics and Engineering, Volume 370, https://doi.org/10.1016/j.cma.2020.113250, October 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.
- Q. Zheng, L. Zeng, G. E. Karniadakis, Physics-informed semantic inpainting: Application to geostatistical modeling, Journal of Computational Physics, https://doi.org/10.1016/j.jcp.2020.109676, June 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.
- M. Alber, A. B. Tepole, W. R. Cannon, S. De, S. Dura-Bernal, K. Garikipati, G. Karniadakis, W. W. Lytton, P. Perdikaris, L. Petzold, E. Kuhl, “Integrating machine learning and multiscale modeling— perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences.” npj Digital Medicine 2:115 ; https://doi.org/10.1038/s41746-019-0193-y, 2019.
- M. Raissi, P. Perikaris, G.E. Karniadakis, “Physics-informed neutral networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.” Journal of Computational Physics 378, 686-707, 2019.
- D. Zhang, L. Lu, L. Guo, G.E. Karniadakis, “Quantifying total uncertainty in physics-informed neutral networks for solving forward and inverse stochastic problems”, Journal of computational Physics, 2019.
- G. Pang, L. Lu, G.E. Karniadakis, “fPINNS: Fractional physics-informed neutral networks”, SIAM Journal on Scientific Computing 41 (4), A2603-A2626, 2019.
- M. Raissi, H. Babee, G.E. Karniadakis, “Parametric Gaussian process regression for big data”, Compuational Mechanics 64 (2), 409-41, 2019.
- M. Gulian, M.Raissi, P. Perdikaris, G.E. Karniadakis, “Machine learning of space-fractional differential equations”, SIAM Journal on Scientific Computing 14 (4), A2485-A2509, 2019.
- A.L. Blumers, Z. Li, G.E. Karniadakis, “Supervised parallel-in-time algorithm for long-time Lagrangian simulations of stochastic dynamics: Application to hydrodynamics.” Journal of Comp. Physics 393, 214-228, 2019
- G. Pang, L Yang, G.E. Karniadakis, “Neural-net-induced Gaussian process regression for function approximation and PDE solution.” Journal of Computational Physics 384, 270-288, 2019.
- S. Lee, F. Dietrich, G.E Karniadakis, I.G. Kevrekidis, “Linking Gaussian process regression with data-driven manifold embeddings for nonlinear data fusion.” Interface focus 9 (3), 20180083, 2019.
- M. Rassi, Z. Wang, M.S. Triantafyllou, G.E. Karniadakis, “Deep Learning of vortex-induced vibrations.” Journal of Fluid Mechanics 861, 119-137, 2019.
- Z. Wang, , M. Triantafyllou, Y. Constantinides, G. E. Karniadakis, "An entropy-viscosity large eddy simulation study of turbulent flow in a flexible pipe." J. Fluid Mech.,859, 691-730, 2019.
- N. Perakakis, A. Yazdani, G. E. Karniadakis, C. Mantzoros, “Omics, big data and machine learning as tools to propel understanding of biological mechanisms and to discover novel diagnostics and therapeutics.” Metabolism, 87:A1-A9, 2018.
- L. Bonfiglio, P. Perdikaris, J. del Aguila, G. E. Karniadakis, "Aprobabilistic framework for multidisciplinary design: Application to the hydrostructural optimization of supercavitating hydrofoils." Int. J. Numer Methods Eng. 116:246-269, 2018.
- D. Zhang, H. Babaee, G. E. Karniadakis, "Stochastic domain decompostition via moment minimization." SIAM J. Sci. Comput. 40(4), A2152-A2173, 2018.
- M. Raissi, P. Perdikaris, G. E. Karniadakis, "Numerical Gaussian processes for time-dependent and non-linear partial differential equations." SIAM J. Sci. Comput. 40(1), A172-182, 2018.
- M. Raissi, G. E. Karniadakis, “Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations.” J. Comp. Phys. 357(15), 125-141, 2018.
- Y. H. Tang, D. Zhang, G. E. Karniadakis, "An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Field." J. Chem. Phys. 148, 034101, 2018.
- L. Zhao, Z. Li, B. Caswell, J. Ouyang, G. E. Karniadakis, "Active learning of constitutive relation from mesoscopic dynamics for macroscopic modeling of non-Newtonian flows." J Comp. Phys. 363, 116-127, 2018.
- L. Bonfiglio, P. Perdikaris, S. Brizzolara, G. E. Karniadakis, "Multi-fidelity optimization of super-cavitating hydrofoils." Comput. Methods Appl. Mech. Engrg. 332, 63-85, 2018.
- M. Raissi, P. Perdikaris, G. E. Karniadakis, "Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations." arXiv:1711.10561v1.
- M. Raissi, P. Perdikaris, G. E. Karniadakis, "Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations." arXiv:1711.10566v1.
- M. Xu, D. P. Papageorgiou, S. Z. Abidi, M. Dao, H. Zhao, G. E. Karniadakis, "A deep convolutional neural network for classification of red blood cells in sickle cell anemia." PLOS Comput. Biol. 13(10):e1005746, 2017.
- G. Pang, P. Perdikaris, W. Cai, G. E. Karniadakis, "Discovering variable fractional orders of advection–dispersion equations from field data using multi-fidelity Bayesian optimization." J. Comput. Phys. 348:694-714, 2017.
- P. Perdikaris, M. Raissi, A. Damianou, N. D. Lawrence, G. E. Karniadakis, "Nonlinear information fusion algorithms for data-efficient multi-fidelity modeling." P. R. Soc. A. 473(2198), 2017.
- M. Raissi, P. Perdikaris, G. E. Karniadakis, “Inferring solutions of differential equations using noisy multi-fidelity data.” J. Comput. Phys. 335, 736-746, 2017.
- M. Raissi, P. Perdikaris, G. E. Karniadakis, “Machine learning of linear differential equations using Gaussian processes.” J. Comput. Phys. 348, 683-693, 2017.
- L. Bonfiglio, P. Perdikaris, S. Brizzolara, G. E. Karniadakis, “A multi-fidelity framework for investigating the performance of super-cavitating hydrofoils under uncertain flow conditions.” 19th AIAA Non-Deterministic Approaches Conference 1328, 2017.
- P. Prempraneerach, P. Perdikaris, G. E. Karniadakis, C. Chryssostomidis, “Sea Surface Temperature estimation from satellite observations and in-situ measurements using multifidelity Gaussian Process regression.” In Digital Arts, Media and Technology (ICDAMT), International Conference on (pp. 28-33). IEEE, 2017,
- S. Lee, I. G. Kevrekidis, G. E. Karniadakis, “A resilient and efficient CFD framework: Statistical learning tools for multi-fidelity and heterogeneous information fusion.” J. Comput. Phys. 344, 516-533, 2017.
- S. Lee, I. G. Kevrekidis, G. E. Karniadakis, “A general CFD framework for fault-resilient simulations based on multi-resolution information fusion." J. Comput. Phys. 347, 290-304, 2017.
- L. Parussini, D. Venturi, P. Perdikaris, G. E. Karniadakis, “Multi-fidelity Gaussian process regression for prediction of random fields.” J. Comput. Phys. 336, 36-50, 2017.
- H. Babaee, P. Perdikaris, C. Chryssostomidis, G. E. Karniadakis, "Multi-fidelity modelling of mixed convection based on experimental correlations and numerical simulations." J. Fluid Mech. 809:895-917, 2016.
- M. Raissi, G. E. Karniadakis, "Deep Multi-Fidelity Gaussian Processes." arXicv preprint arXiv:1604.07484, 2016.
- P. Perdikaris, D. Venturi, G. E. Karniadakis, “Multifidelity information fusion algorithms for high-dimensional systems and massive data sets.” SIAM J. Sci. Comput, 38(4), B521-B538, 2016.
- P. Perdikaris, G. E. Karniadakis, “Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond.” J. Royal Soc. Interface. 13(118), 20151107, 2016.
- P. Perdikaris, D. Venturi, J.O Royset, G. E. Karniadakis, "Multi-fidelity modeling via recursive co-kringing and Gaussian Markov random fields." P. R. Soc. A. 471, 20150018, 2015.
- S. Lee, I. G., Kevrekidis, G. E. Karniadakis, “Resilient algorithms for reconstructing and simulating gappy flow fields in CFD." Fluid Dynamics Research, 47(5), 051402, 2015.
- A. Yakhot, T. Anor, G. E. Karniadakis, "A reconstruction method for gappy and noisy arterial flow data." IEEE Transactions on Medical Imaging. 26(12):1681-97, 2007.
- H. Gunes, S. Sirisup, G. E. Karniadakis, "Gappy data: To Krig or not to Krig?" J. Comput. Phys. 212(1):358-82, 2006.