PinnDE: Physics-Informed Neural Networks for Solving Differential Equations
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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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 21 of its 53 references that are in the map. First posted on arXiv 19 Aug 2024.
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References · 21
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- 2021Meta-learning PINN loss functionscited by 51
9 more
- 2021A novel meta-learning initialization method for physics-informed neural networkscited by 35
- 2022SVD Perspectives for Augmenting DeepONet Flexibility and Interpretabilitycited by 35
- 2021Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow modelscited by 34
- 2021Physics-informed neural networks for the shallow-water equations on the spherecited by 32
- 2021Adaptive deep density approximation for Fokker-Planck equationscited by 28
- 2023HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetworkcited by 25
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- 2023Exactly conservative physics-informed neural networks and deep operator networks for dynamical systemscited by 13
- 2023Improving physics-informed DeepONets with hard constraintscited by 9
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