• Corpus ID: 237940588

Using neural networks to solve the 2D Poisson equation for electric field computation in plasma fluid simulations

@article{Cheng2021UsingNN,
  title={Using neural networks to solve the 2D Poisson equation for electric field computation in plasma fluid simulations},
  author={Li Mei Cheng and Ekhi Ajuria Illarramendi and Guillaume Bogopolsky and Micha{\"e}l Bauerheim and B{\'e}n{\'e}dicte Cuenot},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.13076}
}
The Poisson equation is critical to get a self-consistent solution in plasma fluid simulations used for Hall effect thrusters and streamers discharges. Solving the 2D Poisson equation with zero Dirichlet boundary conditions using a deep neural network is investigated using multiple-scale architectures, defined in terms of number of branches, depth and receptive field 1. The latter is found critical to correctly capture large topological structures of the field. The investigation of multiple… 
[PDF] Semantic Reader
9 Citations
Highly Influential Citations
1
Background Citations
5
Methods Citations
3
Results Citations
2

9 Citations

PlasmaNet: a framework to study and solve elliptic differential equations using neural networks in plasma fluid simulations

Elliptic partial differential equations are common in many areas of physics, from the Poisson equation in plasmas and incompressible flows to the Helmholtz equation in electromagnetism but their numerical solution requires to solve a linear system efficiently requires preconditioning the system.

Performance and accuracy assessments of an incompressible fluid solver coupled with a deep convolutional neural network

A hybrid strategy is developed, which couples a CNN with a traditional iterative solver to ensure a user-defined accuracy level, and improves both the accuracy and the inference performance compared with feedforward CNN architectures.

An Implicit GNN Solver for Poisson-like problems

To the best of the knowledge, $\Psi$-GNN is the first physics-informed GNN-based method that can handle various unstructured domains, boundary conditions and initial solutions while also providing convergence guarantees.

Deep-Learning Architecture-Based Approach for 2-D-Simulation of Microwave Plasma Interaction

The DL technique proposed in this work is significantly fast when compared to the existing computational techniques and can be used as a new, prospective, and alternative computational approach for investigating microwave–plasma interaction in a real-time scenario.

Calculation of Photoionization Rates During Streamer Discharge Using Neural Networks

A novel method for calculating the photoionization rate using neural networks (NNs) is proposed and the effects of hyperparameters and attention mechanisms are evaluated, laying the groundwork for the application of NNs in practical streamer models.

Embedding temporal error propagation on CNN for unsteady flow simulations

This work investigates the interaction of a CNN-based Poisson solver with an incompressible fluid solver for unsteady flow simulations, finding a partial implementation without differentiable solver is found accurate, robust and less costly than full implementation.

Accelerating numerical methods by gradient-based meta-solving

This paper formulates a general framework to describe these problems, and proposes a gradient-based algorithm to solve them in a unified way, and demonstrates the performance and versatility of this method through theoretical analysis and numerical experiments.

Foundations of machine learning for low-temperature plasmas: methods and case studies

A tutorial overview of some of the widely-used ML methods that can be useful, amongst others, for discovering and correlating patterns in the data that may be otherwise impractical to decipher by human intuition alone.

Principled Acceleration of Iterative Numerical Methods Using Machine Learning

,

References

SHOWING 1-10 OF 39 REFERENCES

Poisson CNN: Convolutional neural networks for the solution of the Poisson equation on a Cartesian mesh

A novel fully convolutional neural network architecture to infer the solution of the Poisson equation on a 2D Cartesian grid with different resolutions given the right-hand side term, arbitrary boundary conditions, and grid parameters, which provides unprecedented versatility for a CNN approach dealing with partial differential equations.

Towards an hybrid computational strategy based on Deep Learning for incompressible flows

The capability of the hybrid approach to tackle new flow physics, unseen during the network training, is demonstrated, by maintaining the desired accuracy whatever the flow condition, makes the code stable and reliable even at large Richardson numbers for which the network was not trained for.

Study on a Fast Solver for Poisson’s Equation Based on Deep Learning Technique

It is shown that deep neural networks have a good learning capacity for numerical simulations, which could help to build some fast solvers for some computational electromagnetic problems.

Accelerating Eulerian Fluid Simulation With Convolutional Networks

This work proposes a data-driven approach that leverages the approximation power of deep-learning with the precision of standard solvers to obtain fast and highly realistic simulations of the Navier-Stokes equations.

Unsupervised Deep Learning of Incompressible Fluid Dynamics

This work proposes an unsupervised framework that allows powerful deep neural networks to learn the dynamics of incompressible fluids end to end on a grid-based representation and introduces a loss function that penalizes residuals of the incompressable Navier Stokes equations.

Fourier Neural Operator for Parametric Partial Differential Equations

This work forms a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture and shows state-of-the-art performance compared to existing neural network methodologies.

Performance and accuracy assessments of an incompressible fluid solver coupled with a deep convolutional neural network

A hybrid strategy is developed, which couples a CNN with a traditional iterative solver to ensure a user-defined accuracy level, and improves both the accuracy and the inference performance compared with feedforward CNN architectures.

Predicting the Propagation of Acoustic Waves using Deep Convolutional Neural Networks

A novel approach for numerically propagating acoustic waves in two-dimensional quiescent media has been developed through a fully convolutional multi-scale neural network, resulting in an improved prediction accuracy when adding the spatial gradient difference error to the traditional mean squared error loss function.

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.

Data‐driven projection method in fluid simulation

A novel data‐driven projection method using an artificial neural network to avoid iterative computation is proposed, which could obtain projection results in relatively constant time per grid cell, which is independent of scene complexity.