mlsanityData to 14 Oct 2026

Enhancing Neural Network Differential Equation Solvers

arXiv 2301.13146 ↗First posted 28 Dec 2022math.NA cs.LG cs.NAcited by 1

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Abstract (arXiv)

We motivate the use of neural networks for the construction of numerical solutions to differential equations. We prove that there exists a feed-forward neural network that can arbitrarily minimise an objective function that is zero at the solution of Poisson's equation, allowing us to guarantee that neural network solution estimates can get arbitrarily close to the exact solutions. We also show how these estimates can be appreciably enhanced through various strategies, in particular through the construction of error correction networks, for which we propose a general method. We conclude by providing numerical experiments that attest to the validity of all such strategies for variants of Poisson's equation.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 15 of its 27 references that are in the map. First posted on arXiv 28 Dec 2022.

Builds on

15 of 27 references.

References · 15

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3 more
  1. 2020Hamiltonian neural networks for solving equations of motioncited by 33
  2. 2020Optimizing Neural Networks via Koopman Operator Theorycited by 33
  3. 2020Error Estimation and Correction from within Neural Network Differential Equation Solverscited by 1

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Citing papers per year: 2025: 1.

1 paper.

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