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

arXiv: https://arxiv.org/abs/1909.11544 · HTML: https://mlsanity.com/paper/1909.11544/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2019.

## Built on by (most cited first, 14 of 14)

- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations](https://mlsanity.com/paper/2107.07871/) (2021)
- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators](https://mlsanity.com/paper/2208.11866/) (2022)
- [Conditional physics informed neural networks](https://mlsanity.com/paper/2104.02741/) (2021)
- [Learning Density Distribution of Reachable States for Autonomous Systems](https://mlsanity.com/paper/2109.06728/) (2021)
- [IDRLnet: A Physics-Informed Neural Network Library](https://mlsanity.com/paper/2107.04320/) (2021)
- [Physics-informed neural networks for solving parametric magnetostatic problems](https://mlsanity.com/paper/2202.04041/) (2022)
- [Gravitational Duals from Equations of State](https://mlsanity.com/paper/2403.14763/) (2024)
- [PDE-Agent: A toolchain-augmented multi-agent framework for PDE solving](https://mlsanity.com/paper/2512.16214/) (2025)
- [dNNsolve: an efficient NN-based PDE solver](https://mlsanity.com/paper/2103.08662/) (2021)
- [Stable Weight Updating: A Key to Reliable PDE Solutions Using Deep Learning](https://mlsanity.com/paper/2407.07375/) (2024)
- [Qade: Solving Differential Equations on Quantum Annealers](https://mlsanity.com/paper/2204.03657/) (2022)
- [Learning Biomolecular Motion: The Physics-Informed Machine Learning Paradigm](https://mlsanity.com/paper/2511.06585/) (2025)

## Abstract (arXiv)

Recently, a lot of papers proposed to use neural networks to approximately solve partial differential equations (PDEs). Yet, there has been a lack of flexible framework for convenient experimentation. In an attempt to fill the gap, we introduce a PyDEns-module open-sourced on GitHub. Coupled with capabilities of BatchFlow, open-source framework for convenient and reproducible deep learning, PyDEns-module allows to 1) solve partial differential equations from a large family, including heat equation and wave equation 2) easily search for the best neural-network architecture among the zoo, that includes ResNet and DenseNet 3) fully control the process of model-training by testing different point-sampling schemes. With that in mind, our main contribution goes as follows: implementation of a ready-to-use and open-source numerical solver of PDEs of a novel format, based on neural networks.