Active training of physics-informed neural networks to aggregate and interpolate parametric solutions to the Navier-Stokes equations

@article{Arthurs2021ActiveTO,
  title={Active training of physics-informed neural networks to aggregate and interpolate parametric solutions to the Navier-Stokes equations},
  author={Christopher J. Arthurs and Andrew P. King},
  journal={Journal of Computational Physics},
  year={2021},
  volume={438},
  pages={None - None}
}
  • C. ArthursA. King
  • Published 2 May 2020
  • Computer Science
  • Journal of Computational Physics

Figures and Tables from this paper

On the Pareto Front of Physics-Informed Neural Networks

This paper sheds light on the training process of physics-informed neural networks, and uses the diffusion equation and Navier-Stokes equations in various test environments to analyze the effects of system parameters on the shape of the Pareto front.

Design of Turing Systems with Physics-Informed Neural Networks

The utility of physics-informed neural networks for inverse parameter inference of reaction-diffusion systems to enhance scientific discovery and design is demonstrated.

How PINNs cheat: Predicting chaotic motion of a double pendulum

  • Physics
  • 2022
Despite extensive research, physics-informed neural networks (PINNs) are still 1 difficult to train, especially when the optimization relies heavily on the physics 2 loss term. Convergence problems

Tunable Complexity Benchmarks for Evaluating Physics-Informed Neural Networks on Coupled Ordinary Differential Equations

In this work, we assess the ability of physics-informed neural networks (PINNs) to solve increasingly-complex coupled ordinary differential equations (ODEs). We focus on a pair of benchmarks:

ViscoelasticNet: A physics informed neural network framework for stress discovery and model selection

Viscoelastic fluids are a class of fluids that exhibit both viscous and elastic nature. Modeling such fluids requires constitutive equations for the stress, and choosing the most appropriate

Improved Deep Neural Networks with Domain Decomposition in Solving Partial Differential Equations

By investigations, it is shown that, although the neural networks structure and the loss function are complicated, the proposed method outperforms the classical PINNs with respect to training effectiveness, computational accuracy, and computational cost.

On NeuroSymbolic Solutions for PDEs

To approximate complex functions with respect to Domain-splitting assisted approach on LaSalle-Bouchut inequality.

The Optimal Error Estimate of the Fully Discrete Locally Stabilized Finite Volume Method for the Non-Stationary Navier-Stokes Problem

This paper proves the optimal estimations of a low-order spatial-temporal fully discrete method for the non-stationary Navier-Stokes Problem by adopting the traditional triangle P1−P0 trial function pair combined with macro element form to ensure local stability.

References

SHOWING 1-10 OF 33 REFERENCES

Physics-informed deep learning for incompressible laminar flows

Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data

HFM is a physics informed deep learning framework capable of encoding an important class of physical laws governing fluid motions, namely the Navier-Stokes equations, and can be used in physical and biomedical problems to extract valuable quantitative information for which direct measurements may not be possible.

Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

This two part treatise introduces physics informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations and demonstrates how these networks can be used to infer solutions topartial differential equations, and obtain physics-informed surrogate models that are fully differentiable with respect to all input coordinates and free parameters.

Inferring solutions of differential equations using noisy multi-fidelity data

Physics-informed neural networks for solving nonlinear diffusivity and Biot’s equations

The methodology of physics-informed neural networks are investigated how to extend to solve both the forward and inverse problems in relation to the nonlinear diffusivity and Biot’s equations.

Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial

Accelerating Physics-Informed Neural Network Training with Prior Dictionaries

It is proved that under certain mild conditions, the prediction error made by neural networks can be bounded by expected loss of PDEs and boundary conditions and the error bounds applicable to PINNs and PD-PINNs are obtained.