Publications

2022

1. Efficient Physics Informed Neural Networks Coupled with Domain Decomposition Methods for Solving Coupled Multi-physics Problems Nguyen, Long, Raissi, Maziar, and Seshaiyer, Padmanabhan 2022 [URL]
2. Modeling, Analysis and Physics Informed Neural Network approaches for studying the dynamics of COVID-19 involving human-human and human-pathogen interaction Nguyen, Long, Raissi, Maziar, and Seshaiyer, Padmanabhan Computational and Mathematical Biophysics 2022 [URL]
3. Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next Cuomo, Salvatore, Di Cola, Vincenzo Schiano, Giampaolo, Fabio, Rozza, Gianluigi, Raissi, Maziar, and Piccialli, Francesco Journal of Scientific Computing 2022 [Abs] [URL]

   Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional equations, integral-differential equations, and stochastic PDEs. This novel methodology has arisen as a multi-task learning framework in which a NN must fit observed data while reducing a PDE residual. This article provides a comprehensive review of the literature on PINNs: while the primary goal of the study was to characterize these networks and their related advantages and disadvantages. The review also attempts to incorporate publications on a broader range of collocation-based physics informed neural networks, which stars form the vanilla PINN, as well as many other variants, such as physics-constrained neural networks (PCNN), variational hp-VPINN, and conservative PINN (CPINN). The study indicates that most research has focused on customizing the PINN through different activation functions, gradient optimization techniques, neural network structures, and loss function structures. Despite the wide range of applications for which PINNs have been used, by demonstrating their ability to be more feasible in some contexts than classical numerical techniques like Finite Element Method (FEM), advancements are still possible, most notably theoretical issues that remain unresolved.

4. Data-driven approaches for predicting spread of infectious diseases through DINNs: Disease Informed Neural Networks Shaier, Sagi, Raissi, Maziar, and Seshaiyer, Padmanabhan Letters in Biomathematics 2022 [URL]
5. ViscoelasticNet: A physics informed neural network framework for stress discovery and model selection Thakur, Sukirt, Raissi, Maziar, and Ardekani, Arezoo M arXiv preprint arXiv:2209.06972 2022 [URL]

2021

1. A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics Haghighat, Ehsan, Raissi, Maziar, Moure, Adrian, Gomez, Hector, and Juanes, Ruben Computer Methods in Applied Mechanics and Engineering 2021 [URL]
2. Physics informed learning machine Raissi, Maziar, Perdikaris, Paris, and Karniadakis, George E 2021 [URL]

2020

1. Hidden Fluid Mechanics: Learning Velocity and Pressure Fields from Flow Visualizations Raissi, Maziar, Yazdani, Alireza, and Karniadakis, George Em Science 2020 [URL]
2. Systems biology informed deep learning for inferring parameters and hidden dynamics Yazdani, Alireza, Lu, Lu, Raissi, Maziar, and Karniadakis, George Em PLoS computational biology 2020 [URL]

2019

1. Parametric Gaussian Process Regression for Big Data Raissi, Maziar, Babaee, Hessam, and Karniadakis, George Em Computational Mechanics 2019 [URL]
2. Machine Learning of Space-fractional Differential Equations Gulian, Mamikon, Raissi, Maziar, Perdikaris, Paris, and Karniadakis, George SIAM Journal on Scientific Computing 2019 [URL]
3. Deep Learning of Turbulent Scalar Mixing Raissi, Maziar, Babaee, Hessam, and Givi, Peyman Phys. Rev. Fluids 2019 [URL]
4. On Parameter Estimation Approaches for Predicting Disease Transmission through Optimization, Deep Learning and Statistical Inference Methods Raissi, Maziar, Ramezani, Niloofar, and Seshaiyer, Padmanabhan Letters in Biomathematics 2019 [URL]
5. 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 E Journal of Computational Physics 2019 [URL]
6. Deep Learning of Vortex-induced Vibrations Raissi, Maziar, Wang, Zhicheng, Triantafyllou, Michael S, and Karniadakis, George Em Journal of Fluid Mechanics 2019 [URL]

2018

1. Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations Raissi, Maziar arXiv preprint arXiv:1804.07010 2018 [URL]
2. 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]
3. Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations Raissi, Maziar Journal of Machine Learning Research 2018 [URL]
4. Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations Raissi, Maziar, and Karniadakis, George Em Journal of Computational Physics 2018 [URL]
5. 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]
6. 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]

2017

1. Machine Learning of Linear Differential Equations using Gaussian Processes Raissi, Maziar, Perdikaris, Paris, and Karniadakis, George Em Journal of Computational Physics 2017 [URL]
2. Inferring Solutions of Differential Equations using Noisy Multi-fidelity Data Raissi, Maziar, Perdikaris, Paris, and Karniadakis, George Em Journal of Computational Physics 2017 [URL]
3. 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]