Corpus ID: 220056028

Solving Differential Equations Using Neural Network Solution Bundles

@article{Flamant2020SolvingDE,
  title={Solving Differential Equations Using Neural Network Solution Bundles},
  author={Cedric Wen Flamant and P. Protopapas and David Sondak},
  journal={ArXiv},
  year={2020},
  volume={abs/2006.14372}
}
The time evolution of dynamical systems is frequently described by ordinary differential equations (ODEs), which must be solved for given initial conditions. Most standard approaches numerically integrate ODEs producing a single solution whose values are computed at discrete times. When many varied solutions with different initial conditions to the ODE are required, the computational cost can become significant. We propose that a neural network be used as a solution bundle, a collection of… Expand
A Maxwell's Equations Based Deep Learning Method for Time Domain Electromagnetic Simulations
Semi-supervised Neural Networks solve an inverse problem for modeling Covid-19 spread
A Maxwell's Equations Based Deep Learning Method for Time Domain Electromagnetic Simulations
Unsupervised Neural Networks for Quantum Eigenvalue Problems
A Swarm Variant for the Schr\"odinger Solver
Collocation Polynomial Neural Forms and Domain Fragmentation for Initial Value Problems

References

SHOWING 1-10 OF 19 REFERENCES
Hamiltonian Neural Networks for solving differential equations
Artificial neural networks for solving ordinary and partial differential equations
NeuroDiffEq: A Python package for solving differential equations with neural networks
PyDEns: a Python Framework for Solving Differential Equations with Neural Networks
Neural-network-based approximations for solving partial differential equations
Neural-network methods for boundary value problems with irregular boundaries
DGM: A deep learning algorithm for solving partial differential equations
Artificial Neural Network Method for Solution of Boundary Value Problems With Exact Satisfaction of Arbitrary Boundary Conditions
DeepXDE: A Deep Learning Library for Solving Differential Equations
Artificial Neural Networks Approach for Solving Stokes Problem
...
1
2
...