# Physics-informed neural networks for high-speed flows

@article{Mao2020PhysicsinformedNN, title={Physics-informed neural networks for high-speed flows}, author={Zhiping Mao and Ameya Dilip Jagtap and George Em Karniadakis}, journal={Computer Methods in Applied Mechanics and Engineering}, year={2020}, volume={360}, pages={112789} }

## 177 Citations

Physics-informed neural networks for inverse problems in supersonic flows

- MathematicsArXiv
- 2022

Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles. In particular, we consider the problem where we have data…

Inferring incompressible two-phase flow fields from the interface motion using physics-informed neural networks

- MathematicsMachine Learning with Applications
- 2021

Application of mixed-variable physics-informed neural networks to solve normalised momentum and energy transport equations for 2D internal convective flow

- Physics
- 2021

The prohibitive cost and low fidelity of experimental data in industry-scale thermofluid systems limit the usefulness of pure data-driven machine learning methods. Physics-informed neural networks…

A hybrid physics-informed neural network for nonlinear partial differential equation

- Computer ScienceArXiv
- 2021

This paper focuses on the discrete time physics-informed neural network (PINN), and proposes a hybrid PINN scheme for the nonlinear PDEs, which has a better performance in approximating the discontinuous solution even at a relatively larger time step.

Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems

- Computer Science
- 2020

Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation

- PhysicsJ. Comput. Phys.
- 2021

Physics-Informed Neural Networks for Heat Transfer Problems

- Physics
- 2021

Physics-informed neural networks (PINNs) have gained popularity across different engineering fields due to their effectiveness in solving realistic problems with noisy data and often partially…

Physics-informed neural networks (PINNs) for fluid mechanics: A review

- Computer ScienceActa Mechanica Sinica
- 2022

The effectiveness of physics-informed neural networks (PINNs) for inverse problems related to three-dimensional wake flows, supersonic flows, and biomedical flows is demonstrated.

Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential training

- Computer ScienceArXiv
- 2021

This work presents a PINN approach to solving the equations of coupled flow and deformation in porous media for both single-phase and multiphase flow, and proposes a sequential training approach based on the stress-split algorithms of poromechanics.

Physics-Informed PointNet: A Deep Learning Solver for Steady-State Incompressible Flows and Thermal Fields on Multiple Sets of Irregular Geometries

- Computer Science
- 2020

, We present a novel physics-informed deep learning framework for solving steady-state incompressible flow on multiple sets of irregular geometries by incorporating two main elements: using a…

## References

SHOWING 1-10 OF 39 REFERENCES

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

- Computer ScienceJ. Comput. Phys.
- 2019

Adaptive activation functions accelerate convergence in deep and physics-informed neural networks

- Computer ScienceJ. Comput. Phys.
- 2020

fPINNs: Fractional Physics-Informed Neural Networks

- MathematicsSIAM J. Sci. Comput.
- 2019

This work extends PINNs to fractional PINNs (fPINNs) to solve space-time fractional advection-diffusion equations (fractional ADEs), and demonstrates their accuracy and effectiveness in solving multi-dimensional forward and inverse problems with forcing terms whose values are only known at randomly scattered spatio-temporal coordinates (black-box forcing terms).

The solution of the compressible Euler equations at low Mach numbers using a stabilized finite element algorithm

- Computer Science, Mathematics
- 2001

Numerical Methods for High-Speed Flows

- Physics
- 2011

We review numerical methods for direct numerical simulation (DNS) and large-eddy simulation (LES) of turbulent compressible flow in the presence of shock waves. Ideal numerical methods should be…

A discontinuous Galerkin method for the Navier-Stokes equations

- Computer Science
- 1999

The foundations of a new discontinuous Galerkin method for simulating compressible viscous flows with shocks on standard unstructured grids are presented and monotonicity is enforced by appropriately lowering the basis order and performing h-refinement around discontinuities.

High-order methods for the Euler and Navier–Stokes equations on unstructured grids

- Computer Science
- 2007

A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems

- Computer ScienceJ. Comput. Phys.
- 2020

Positivity preserving finite volume Roe: schemes for transport-diffusion equations

- Computer Science
- 1999