Elvet -- a neural network-based differential equation and variational problem solver
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Abstract (arXiv)
We present Elvet, a Python package for solving differential equations and variational problems using machine learning methods. Elvet can deal with any system of coupled ordinary or partial differential equations with arbitrary initial and boundary conditions. It can also minimize any functional that depends on a collection of functions of several variables while imposing constraints on them. The solution to any of these problems is represented as a neural network trained to produce the desired function.
Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 10 of its 39 references that are in the map. First posted on arXiv 26 Mar 2021.
Builds on
10 of 39 references.
References · 10
- 2014Adam: A Method for Stochastic Optimizationcited by 37,240
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
- 2017DGM: A deep learning algorithm for solving partial differential equationscited by 678
- 2017Solving high-dimensional partial differential equations using deep learningcited by 556
- 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 373
- 2017The Expressive Power of Neural Networks: A View from the Widthcited by 320
- 2017Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equationscited by 161
- 2018Neural Networks Trained to Solve Differential Equations Learn General Representationscited by 16
- 2019A Discussion on Solving Partial Differential Equations using Neural Networkscited by 13
- 2021dNNsolve: an efficient NN-based PDE solvercited by 4
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Citing papers per year: 2021: 2; 2022: 2; 2023: 0; 2024: 2; 2025: 1.
7 papers.
- 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 608
- 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
- 2021IDRLnet: A Physics-Informed Neural Network Librarycited by 10
- 2021Quantum Optimisation of Complex Systems with a Quantum Annealercited by 7
- 2022Qade: Solving Differential Equations on Quantum Annealerscited by 1
- 2024jinns: a JAX Library for Physics-Informed Neural Networkscited by 0
- 2025Learning Biomolecular Motion: The Physics-Informed Machine Learning Paradigmcited by 0
- 2025Learning Biomolecular Motion: The Physics-Informed Machine Learning Paradigm10 Nov 2025
- 2024jinns: a JAX Library for Physics-Informed Neural Networks18 Dec 2024
- 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning17 Oct 2024
- 2022Qade: Solving Differential Equations on Quantum Annealers7 Apr 2022
- 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next14 Jan 2022
- 2021IDRLnet: A Physics-Informed Neural Network Library9 Jul 2021
- 2021Quantum Optimisation of Complex Systems with a Quantum Annealer28 May 2021