# PinnDE: Physics-Informed Neural Networks for Solving Differential Equations

arXiv: https://arxiv.org/abs/2408.10011 · HTML: https://mlsanity.com/paper/2408.10011/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 53 references that are in the map.
- First posted on arXiv 19 Aug 2024.

## Builds on (most cited first, 21 of 21)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems](https://mlsanity.com/paper/2111.02801/) (2021)
- [Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations](https://mlsanity.com/paper/1811.02033/) (2018)
- [Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks](https://mlsanity.com/paper/2007.04542/) (2020)
- [Efficient training of physics-informed neural networks via importance sampling](https://mlsanity.com/paper/2104.12325/) (2021)
- [Long-time integration of parametric evolution equations with physics-informed DeepONets](https://mlsanity.com/paper/2106.05384/) (2021)
- [NOMAD: Nonlinear Manifold Decoders for Operator Learning](https://mlsanity.com/paper/2206.03551/) (2022)
- [Meta-learning PINN loss functions](https://mlsanity.com/paper/2107.05544/) (2021)
- [A novel meta-learning initialization method for physics-informed neural networks](https://mlsanity.com/paper/2107.10991/) (2021)
- [Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models](https://mlsanity.com/paper/2108.12956/) (2021)
- [SVD Perspectives for Augmenting DeepONet Flexibility and Interpretability](https://mlsanity.com/paper/2204.12670/) (2022)
- [Physics-informed neural networks for the shallow-water equations on the sphere](https://mlsanity.com/paper/2104.00615/) (2021)
- [Adaptive deep density approximation for Fokker-Planck equations](https://mlsanity.com/paper/2103.11181/) (2021)
- [HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork](https://mlsanity.com/paper/2312.15949/) (2023)
- [Improving physics-informed neural networks with meta-learned optimization](https://mlsanity.com/paper/2303.07127/) (2023)
- [Exactly conservative physics-informed neural networks and deep operator networks for dynamical systems](https://mlsanity.com/paper/2311.14131/) (2023)
- [Improving physics-informed DeepONets with hard constraints](https://mlsanity.com/paper/2309.07899/) (2023)

## Built on by (most cited first, 1 of 1)

- [RINN: One Sample Radio Frequency Imaging based on Physics Informed Neural Network](https://mlsanity.com/paper/2504.15311/) (2025)

## Abstract (arXiv)

In recent years the study of deep learning for solving differential equations has grown substantially. The use of physics-informed neural networks (PINNs) and deep operator networks (DeepONets) have emerged as two of the most useful approaches in approximating differential equation solutions using machine learning. Here, we introduce PinnDE, an open-source Python library for solving differential equations with both PINNs and DeepONets. We give a brief review of both PINNs and DeepONets, introduce PinnDE along with the structure and usage of the package, and present worked examples to show PinnDE's effectiveness in approximating solutions of systems of differential equations with both PINNs and DeepONets.