# 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

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#### References

SHOWING 1-10 OF 19 REFERENCES

Hamiltonian Neural Networks for solving differential equations

- Computer Science, Physics
- ArXiv
- 2020

Artificial neural networks for solving ordinary and partial differential equations

- Mathematics, Physics
- IEEE Trans. Neural Networks
- 1998

NeuroDiffEq: A Python package for solving differential equations with neural networks

- Computer Science
- J. Open Source Softw.
- 2020

PyDEns: a Python Framework for Solving Differential Equations with Neural Networks

- Computer Science, Mathematics
- ArXiv
- 2019

Neural-network methods for boundary value problems with irregular boundaries

- Mathematics, Computer Science
- IEEE Trans. Neural Networks Learn. Syst.
- 2000

DGM: A deep learning algorithm for solving partial differential equations

- Mathematics, Economics
- 2018

Artificial Neural Network Method for Solution of Boundary Value Problems With Exact Satisfaction of Arbitrary Boundary Conditions

- Mathematics, Computer Science
- IEEE Transactions on Neural Networks
- 2009

DeepXDE: A Deep Learning Library for Solving Differential Equations

- Computer Science, Physics
- AAAI Spring Symposium: MLPS
- 2020