POSEIDON: Foundation Models for PDEs 🌊🔬

POSEIDON is a foundation model for solving Partial Differential Equations (PDEs) efficiently. Instead of training a separate model for each PDE, POSEIDON learns a general solution operator—allowing it to generalize across different physics with minimal data. Think of it as the GPT4.5 for PDEs, trained on a diverse set of fluid dynamics equations and capable of adapting to new, unseen physical systems.

Dataset Explorer

POSEIDON provides solutions to a variety of fluid dynamics problems. Below are a few datasets you can explore:

CE-RM (Richtmyer-Meshkov)

Based on the compressible Euler equations, this dataset models shock-driven instability at fluid interfaces.
Used in astrophysics, fusion research, and high-speed aerodynamics.

NS-PwC (Navier-Stokes - Piecewise Constant Vorticity)

Based on the incompressible Navier-Stokes equations, modeling turbulence and vortex dynamics.
Applications include climate modeling, aerodynamics, and turbulent flow control.

CE-RPUI (Riemann Problems with Uncertain Interfaces)

Models shock interactions across uncertain boundaries, crucial for hypersonic flows and uncertainty quantification.
Helps in high-speed aerodynamics and robust PDE solvers.

Explore these datasets to visualize fluid behavior and analyze dynamic flow evolution!

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Key Innovations

Multiscale Operator Transformer (scOT)

A hierarchical transformer-based architecture that captures PDE solution dynamics across multiple spatial and temporal scales. It uses shifted-window attention (SwinV2) to efficiently process large solution spaces.

Continuous-in-Time Learning

Instead of learning PDE solutions at discrete time steps, POSEIDON uses time-conditioned layer normalization, enabling predictions at any arbitrary time—like a true continuous function.

All2All Training Strategy

By leveraging the semi-group property of PDEs, POSEIDON scales training data quadratically without additional simulations. Every time step becomes a learning opportunity!

Pretrained on Fluid Dynamics, Generalizes to New Physics

Trained on compressible Euler and Navier-Stokes equations, POSEIDON transfers its knowledge to unseen wave, diffusion, and reaction-diffusion PDEs—a huge step for scientific machine learning!

Outperforms FNO & Neural Operators

POSEIDON achieves the same accuracy as an FNO trained on 1024 samples—using only 20 samples. That's a 50x efficiency boost in sample efficiency.

Why Does This Matter?

Traditional PDE solvers are computationally expensive. POSEIDON is a general-purpose neural PDE solver that:

• Works across multiple physics domains
• Requires fewer training samples
• Enables real-time simulation & forecasting

It's a step towards universal scientific models, just like foundation models transformed NLP and vision.

Try POSEIDON Now!

You can experiment and empower your research with POSEIDON-T (21M parameters), POSEIDON-B (158M parameters), and POSEIDON-L (629M parameters).

• Pretrained models & datasets: Hugging Face Hub
• Code & Paper: GitHub | arXiv
• Join the Discussion: Hugging Face Forums

Let's reshape the future of PDE solving—one foundation model at a time!

If you use POSEIDON in your research, please cite the paper:

@misc{herde2024poseidon,
    title={Poseidon: Efficient Foundation Models for PDEs}, 
    author={Maximilian Herde and Bogdan Raonić and Tobias Rohner and Roger Käppeli and Roberto Molinaro and Emmanuel de Bézenac and Siddhartha Mishra},
    year={2024},
    eprint={2405.19101},
    archivePrefix={arXiv},
    primaryClass={cs.LG}
}