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hypino

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

arXiv Paper

GitHub Code

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.

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 $(x, y) \in [-1, 1]^2$.

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:

bash

# 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:

Notebook	Description
`01_visualize_data.ipynb`	Visualizes benchmark PDE inputs and reference solutions. Shows both supervised (MMS-generated) and unsupervised samples.
`02_inference.ipynb`	Explains expected HyPINO inputs, output format, and how to use predictions for downstream tasks.
`03_iterative_refinement.ipynb`	Demonstrates how to build ensembles of PINNs via residual-based iterative refinement and visualize test-time improvements.
`04_pinn_finetuning.ipynb`	Shows how HyPINO-generated PINNs can be used as initialization for PDE-specific fine-tuning.

Citation

If you use this code or model, please cite:

bibtex

@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}
}