Top AI Repos — open-source AI, indexed and scored
Top AI Repos tracks AI repositories on GitHub and answers two different questions about each one: is it moving right now, and would you bet a product on it.
Top AI Repos tracks AI repositories on GitHub and answers two different questions about each one: is it moving right now, and would you bet a product on it.
Solve forward and inverse problems related to partial differential equations using finite basis physics-informed neural networks (FBPINNs)
| Date | Stars |
|---|---|
| 2026-07-31 | 568 |
| 2026-08-01 | 569 |
| 2026-08-02 | 569 |
| 2026-08-05 | 569 |
| 2026-08-06 | 569 |
Today
— stars today
This week
— stars this week
This month
— stars this month
Momentum
0.0
growth rate 0.00%/day
# Finite basis physics-informed neural networks (FBPINNs)
---
This repository allows you to solve forward and inverse problems related to partial differential equations (PDEs) using **finite basis physics-informed neural networks** (FBPINNs).
> 🔥 MAJOR UPDATE 🔥: we have rewritten the `fbpinns` library in [JAX](https://jax.readthedocs.io/en/latest/index.html): it now runs 10-1000X faster than the original PyTorch code (by parallelising subdomain computations using `jax.vmap`) and scales to 1000s+ subdomains. We have also added extra functionality: you can now solve inverse problems, add arbitrary types of boundary/data constraints, define irregular/multilevel domain decompositions and custom subdomain networks, and the high-level interface is much more flexible and easier to use. See the [Release note](https://github.com/benmoseley/FBPINNs/releases/tag/v0.2.0) for more info.
FBPINNs are described in detail here: *[Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations](https://link.springer.com/article/10.1007/s10444-023-10065-9), B. Moseley, T. Nissen-Meyer and A. Markham, Jul 2023 Advances in Computational Mathematics*. See the slides from our 2023 Maths4DL conference talk [here](https://maths4dl.ac.uk/wp-content/uploads/2023/07/Moseley.pdf).
---
<p align="center">
<img src="images/FBPINN.gif" alt="FBPINN solving the high-frequency 1D harmonic oscillator" width=48%>
<img src="images/PINN.gif" alt="PINN solving the high-frequency 1D harmonic oscillator" width=48%>
</p>
<p align="center">
<img src="images/test-loss.png" alt="Test loss comparison" width=33%>
</p>
<p align="center">
<b>Fig 1: FBPINN vs PINN solving the high-frequency 1D harmonic oscillator</b>
</p>
## Why FBPINNs?
- [Physics-informed neural networks](https://benmoseley.blog/my-research/so-what-is-a-physics-informed-neural-network/) (PINNs) are a popular approach for solving **forward and inverse problems** related to PDEs
- However, PINNs often struggle to solve problems with **high frequencies** and/or **multi-scale solutions**
- This is due to the **spectral bias** of neural networks and the **heavily increasing complexity** of the PINN optimisation problem
- FBPINNs improve the performance of PINNs in this regime by combining them with **domain decomposition**, **individual subdomain normalisation** and **flexible subdomain training schedules**
- Empirically, FBPINNs **significantly outperform** PINNs (in terms of accuracy and computational efficiency) when solving problems with high frequencies and multi-scale solutions (Fig 1 and 2)
<p align="center">
<img src="images/we-multiscale.gif" alt="FBPINN solution of the (2+1)D wave equation with multiscale sources" width=100%>
</p>
<p align="center">
<b>Fig 2: FBPINN solution of the (2+1)D wave equation with multiscale sources</b>
</p>
## How are FBPINNs different to PINNs?
<p align="center">
<img src="images/workflow.png" alt="FBPINN workflow overview" width=100%>
</p>
<p align="center">
<b>Fig 3: FBPINN workflow overview</b>
</p>
To improve the scalability of PINNs to high frequency/ multiscale solutions:
- FBPINNs divide the problem domain into many small, **overlapping subdomains** (Fig 3).
- A neural network is placed within each subdomain, and the solution to the PDE is defined as the **summation over all subdomain networks**.
- Each subdomain network is **locally confined** to its subdomain by multiplying it by a smooth, differentiable window function.
- Finally, the inputs of each network are **individually normalised** over their subdomain.
The hypothesis is that this "divide and conquer" approach significantly reduces the complexity of the PINN optimisation problem. Furthermore, individual subdomain normalisation ensures the "effective" frequency each subdomain network sees is low, reducing the effect of spectral bias.
## Subdomain scheduling
<p align="center">
<img src=Excerpt of 14,210 characters
Read on GitHub
22
Would you bet a product on this? Bounded 0–100 and slow moving.
matched fp:2c73cba315da53e3, topic:jax