Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

@article{Raissi2019PhysicsinformedNN,
  title={Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations},
  author={M. Raissi and P. Perdikaris and G. Karniadakis},
  journal={J. Comput. Phys.},
  year={2019},
  volume={378},
  pages={686-707}
}
Abstract We introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations. In this work, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct… Expand
View via Publisher
osti.gov
1,276 Citations
Highly Influential Citations
123
Background Citations
407
Methods Citations
310
Results Citations
14

1,276 Citations

Citation Type

Citation Type

Physics-informed attention-based neural network for solving non-linear partial differential equations
TLDR
PIANNs is a combination of recurrent neural networks and attention mechanisms that finds that PIANNs effectively capture the shock front in a hyperbolic model problem, and are capable of providing high-quality solutions inside and beyond the training set. Expand
Physics-Informed Learning Machines for Partial Differential Equations: Gaussian Processes Versus Neural Networks
We review and compare physics-informed learning models built upon Gaussian processes and deep neural networks for solving forward and inverse problems governed by linear and nonlinear partial… Expand
A Physics Informed Neural Network for Time-Dependent Nonlinear and Higher Order Partial Differential Equations
TLDR
This work proposes a novel PINN scheme that solves the PDE sequentially over successive time segments using a single neural network while satisfying the already obtained solution for all previous time segments, and uses the Cahn Hilliard and Allen Cahn equations to illustrate the advantages. Expand
Variational Physics-Informed Neural Networks For Solving Partial Differential Equations
TLDR
A Petrov-Galerkin version of PINNs based on the nonlinear approximation of deep neural networks (DNNs) by incorporating the variational form of the problem into the loss function of the network and constructing a VPINN, effectively reducing the training cost in VPINNs while increasing their accuracy compared to PINNs that essentially employ delta test functions. Expand
Physics Informed Extreme Learning Machine (PIELM) - A rapid method for the numerical solution of partial differential equations
TLDR
This work develops and demonstrates that PIELM matches or exceeds the accuracy of PINNs on a range of problems, and shows that DPIELM produces excellent results comparable to conventional numerical techniques in the solution of time-dependent problems. Expand
A study on a feedforward neural network to solve partial differential equations in hyperbolic-transport problems
TLDR
A supervised deep neural network is employed that takes into account the equation and initial conditions of the model, providing numerical approximation of entropy solutions with very good precision and consistent to classical as well as to recently novel numerical methods in these particular scenarios. Expand
Deep learning-based method coupled with small sample learning for solving partial differential equations
TLDR
A deep learning-based general numerical method coupled with small sample learning for solving PDEs, which approximate the solution via a deep feedforward neural network, which is trained to satisfy the P DEs with the initial and boundary conditions. Expand
LIMITATIONS OF PHYSICS INFORMED MACHINE LEARNING FOR NONLINEAR TWO-PHASE TRANSPORT IN POROUS MEDIA
Deep learning techniques have recently been applied to a wide range of computational physics problems. In this paper, we focus on developing a physics-based approach that enables the neural network… Expand
Data Driven Solutions and Discoveries in Mechanics Using Physics Informed Neural Network
Deep learning has achieved remarkable success in diverse computer science applications, however, its use in other traditional engineering fields has emerged only recently. In this project, we solved… Expand
Neural Time-Dependent Partial Differential Equation
TLDR
This work proposes a sequence deep learning framework called Neural-PDE, which allows to automatically learn governing rules of any time-dependent PDE system from existing data by using a bidirectional LSTM encoder, and predict the next n time steps data. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 52 REFERENCES
Hidden physics models: Machine learning of nonlinear partial differential equations
Abstract While there is currently a lot of enthusiasm about “big data”, useful data is usually “small” and expensive to acquire. In this paper, we present a new paradigm of learning partial… Expand
Inferring solutions of differential equations using noisy multi-fidelity data
TLDR
This work develops data-driven algorithms for general linear equations using Gaussian process priors tailored to the corresponding integro-differential operators that circumvents the tyranny of numerical discretization as well as the consistency and stability issues of time-integration, and is scalable to high-dimensions. Expand
Solving differential equations with unknown constitutive relations as recurrent neural networks
TLDR
This work extends TensorFlow's recurrent neural network architecture to create a simple but scalable and effective solver for the unknown functions, and applies it to a fedbatch bioreactor simulation problem. Expand
Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations
TLDR
The method circumvents the need for spatial discretization of the differential operators by proper placement of Gaussian process priors and is an attempt to construct structured and data-efficient learning machines, which are explicitly informed by the underlying physics that possibly generated the observed data. Expand
A paradigm for data-driven predictive modeling using field inversion and machine learning
TLDR
In contrast to inferring model parameters, this work uses inverse modeling to obtain corrective, spatially distributed functional terms, offering a route to directly address model-form errors. Expand
Data-driven discovery of partial differential equations
TLDR
The sparse regression method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Expand
Machine learning of linear differential equations using Gaussian processes
TLDR
Gaussian process priors are modified according to the particular form of such operators and are employed to infer parameters of the linear equations from scarce and possibly noisy observations, leading to model discovery from just a handful of noisy measurements. Expand
Artificial neural networks for solving ordinary and partial differential equations
TLDR
This article illustrates the method by solving a variety of model problems and presents comparisons with solutions obtained using the Galekrkin finite element method for several cases of partial differential equations. Expand
Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification
TLDR
This approach achieves state of the art performance in terms of predictive accuracy and uncertainty quantification in comparison to other approaches in Bayesian neural networks as well as techniques that include Gaussian processes and ensemble methods even when the training data size is relatively small. Expand
Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification
TLDR
Deep neural networks (DNN) are used to construct surrogate models for numerical simulators in a manner that lends the DNN surrogate the interpretation of recovering a low-dimensional nonlinear manifold. Expand
...
1
2
3
4
5
...