to appear


  1. Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations Raissi, Maziar, Perdikaris, Paris, and Karniadakis, George Em Journal of Computational Physics to appear
  2. Deep Learning of Vortex Induced Vibrations Raissi, Maziar, Wang, Zhicheng, Triantafyllou, Michael S, and Karniadakis, George Em Journal of Fluid Mechanics to appear [URL]

2018


  1. Application of Local Improvements to Reduced-order Models to Sampling Methods for Nonlinear PDEs with Noise Raissi, Maziar, and Seshaiyer, Padmanabhan International Journal of Computer Mathematics 2018 [URL]
  2. Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations Raissi, Maziar arXiv preprint arXiv:1804.07010 2018 [URL]
  3. Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems Raissi, Maziar, Perdikaris, Paris, and Karniadakis, George Em arXiv preprint arXiv:1801.01236 2018 [URL]
  4. Machine Learning of Space-Fractional Differential Equations Gulian, Mamikon, Raissi, Maziar, Perdikaris, Paris, and Karniadakis, George arXiv preprint arXiv:1808.00931 2018 [URL]
  5. Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations Raissi, Maziar Journal of Machine Learning Research 2018 [URL]
  6. Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations Raissi, Maziar, and Karniadakis, George Em Journal of Computational Physics 2018 [URL]
  7. Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations Raissi, Maziar, Perdikaris, Paris, and Karniadakis, George Em SIAM Journal on Scientific Computing 2018 [URL]
  8. Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data Raissi, Maziar, Yazdani, Alireza, and Karniadakis, George Em arXiv preprint arXiv:1808.04327 2018 [URL]

2017


  1. Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations Raissi, Maziar, Perdikaris, Paris, and Karniadakis, George Em arXiv preprint arXiv:1711.10561 2017 [URL]
  2. Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations Raissi, Maziar, Perdikaris, Paris, and Karniadakis, George Em arXiv preprint arXiv:1711.10566 2017 [URL]
  3. Parametric Gaussian Process Regression for Big Data Raissi, Maziar arXiv preprint arXiv:1704.03144 2017 [URL]
  4. Machine Learning of Linear Differential Equations using Gaussian Processes Raissi, Maziar, Perdikaris, Paris, and Karniadakis, George Em Journal of Computational Physics 2017 [URL]
  5. Inferring Solutions of Differential Equations using Noisy Multi-fidelity Data Raissi, Maziar, Perdikaris, Paris, and Karniadakis, George Em Journal of Computational Physics 2017 [URL]
  6. Nonlinear Information Fusion Algorithms for Data-efficient Multi-fidelity Modelling Perdikaris, Paris, Raissi, Maziar, Damianou, Andreas, Lawrence, Neil D., and Karniadakis, George Em Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 2017 [URL]

2016


  1. Conic Economics Raissi, Maziar 2016 [URL]
  2. Deep Multi-fidelity Gaussian Processes Raissi, Maziar, and Karniadakis, George arXiv preprint arXiv:1604.07484 2016 [URL]

2014


  1. The Differential Effects of Oil Demand and Supply Shocks on the Global Economy Cashin, Paul, Mohaddes, Kamiar, Raissi, Maziar, Raissi, Mehdi Energy Economics 2014 [URL]
  2. A Multi-fidelity Stochastic Collocation Method for Parabolic Partial Differential Equations with Random Input Data Raissi, Maziar, and Seshaiyer, Padmanabhan International Journal for Uncertainty Quantification 2014 [URL]

2013


  1. Multi-fidelity Stochastic Collocation Raissi, Maziar 2013 [URL]