hypino

HyPINO: Multi-Physics Neural Operators via HyperPINNs and the Method of Manufactured Solutions

<p> <a href="https://arxiv.org/abs/2509.05117" target="_blank"> <img src="https://img.shields.io/badge/arXiv-2509.05117-b31b1b.svg" alt="arXiv Paper"/> </a> <a href="https://github.com/rbischof/hypino" target="_blank"> <img src="https://img.shields.io/badge/Code-GitHub-181717?logo=github" alt="GitHub Code"/> </a> <a href="https://rbischof.github.io/hypino_web/" target="_blank"> <img src="https://img.shields.io/badge/Web_Demo-Launch-2ea44f" alt="Web Demo"/> </a> </p>

This repository contains the model files for the paper HyPINO: Multi-Physics Neural Operators via HyperPINNs and the Method of Manufactured Solutions.

HyPINO is a multi-physics neural operator framework that generalizes across diverse linear, 2D, second-order PDEs in a zero-shot manner.
It uses a Swin Transformer–based hypernetwork to generate Physics-Informed Neural Networks (PINNs) conditioned on PDE specifications, trained entirely using the Method of Manufactured Solutions (MMS). This repository contains the official implementation of the paper.

Features

• Zero-shot generalization across linear, 2D, second-order PDE families (elliptic, parabolic, hyperbolic)
• Mixed boundary condition support: Dirichlet, Neumann, and interior boundaries
• Swin Transformer hypernetwork that generates task-specific PINNs
• Residual-based iterative refinement for test-time accuracy improvement
• PINN initialization for faster convergence and improved fine-tuning performance

Framework Overview

As an example, consider the Poisson equation $-\Delta u(x, y) = 0,$ defined on a square domain with circular inner boundaries. The image below shows the input fields expected by HyPINO and their corresponding reference solutions.

<p align="center"> <img src="https://github.com/rbischof/hypino/raw/main/assets/poisson_C/grids.png" width="85%"> </p>

Given a PDE specification, HyPINO’s Swin Transformer hypernetwork generates the weights of a target PINN, which can be evaluated continuously over the spatial domain $(x, y) \in [-1, 1]^2$.

<p align="center"> <img src="https://github.com/rbischof/hypino/raw/main/assets/hypino_framework.png" width="85%"> </p>

Installation

HyPINO was tested with Python 3.12.1.

Install dependencies:

pip install -r requirements.txt

Model Weights

HyPINO pretrained model

Download the pretrained HyPINO model directly from Hugging Face:

# Option 1: Using the Hugging Face CLI
hf download rabischof/hypino hypino.safetensors --local-dir models/

# Option 2: Using wget
wget -O models/hypino.safetensors https://huggingface.co/rabischof/hypino/resolve/main/hypino.safetensors

Training

To train the model:

python train.py

Logs, checkpoints, and plots are saved under:

runs/

Evaluation

Evaluate a trained model:

python evaluate.py --model hypino --weights models/hypino.safetensors

Example Notebooks

The notebooks/ directory in the GitHub Repository contains guided examples for exploring and extending HyPINO:

Citation

If you use this code or model, please cite:

@article{bischof2025hypino,
  title={HyPINO: Multi-Physics Neural Operators via HyperPINNs and the Method of Manufactured Solutions},
  author={Bischof, Rafael and Bickel, Bernd},
  journal={arXiv preprint arXiv:2509.05117},
  year={2025}
}