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app.py
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with gr.Blocks(css=css) as demo:
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gr.Markdown(
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"""
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#
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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 **GPT-4 for PDEs**, trained on a diverse set of **fluid dynamics equations** and capable of adapting to **new, unseen physical systems**.
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# **Dataset Explorer**
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POSEIDON provides solutions to a variety of fluid dynamics problems. Below are a few datasets you can explore:
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- Models shock interactions across uncertain boundaries, crucial for hypersonic flows and uncertainty quantification.
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- Helps in high-speed aerodynamics and robust PDE solvers.
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Explore these datasets to visualize fluid behavior and analyze dynamic flow evolution!
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"""
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)
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gr.Markdown(
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"""
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##
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###
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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.
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###
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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**.
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###
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By leveraging the semi-group property of PDEs, POSEIDON scales training data quadratically without additional simulations. Every time step becomes a learning opportunity!
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###
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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!
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###
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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.
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---
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##
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Traditional PDE solvers are computationally expensive
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It's a step towards universal scientific models, just like foundation models transformed NLP and vision.
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---
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##
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You can experiment and empower your research with POSEIDON-T (21M parameters), POSEIDON-B (158M parameters), and POSEIDON-L (629M parameters).
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Let's reshape the future of PDE solving—one foundation model at a time!
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---
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primaryClass={cs.LG}
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}
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```
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"""
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with gr.Blocks(css=css) as demo:
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gr.Markdown(
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"""
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# POSEIDON: Foundation Models for PDEs 🌊🔬
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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 **GPT-4 for PDEs**, trained on a diverse set of **fluid dynamics equations** and capable of adapting to **new, unseen physical systems**.
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# **Dataset Explorer**
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POSEIDON provides solutions to a variety of fluid dynamics problems. Below are a few datasets you can explore:
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- Models shock interactions across uncertain boundaries, crucial for hypersonic flows and uncertainty quantification.
|
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- Helps in high-speed aerodynamics and robust PDE solvers.
|
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Explore these datasets to visualize fluid behavior and analyze dynamic flow evolution!
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"""
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)
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gr.Markdown(
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"""
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## Key Innovations
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### • **Multiscale Operator Transformer (scOT)**
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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.
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### • **Continuous-in-Time Learning**
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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**.
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### • **All2All Training Strategy**
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By leveraging the semi-group property of PDEs, POSEIDON scales training data quadratically without additional simulations. Every time step becomes a learning opportunity!
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### • **Pretrained on Fluid Dynamics, Generalizes to New Physics**
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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!
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### • **Outperforms FNO & Neural Operators**
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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.
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---
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## Why Does This Matter?
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Traditional PDE solvers are computationally expensive. POSEIDON is a general-purpose neural PDE solver that:
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• Works across multiple physics domains
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• Requires fewer training samples
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• Enables real-time simulation & forecasting
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It's a step towards universal scientific models, just like foundation models transformed NLP and vision.
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---
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## Try POSEIDON Now!
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You can experiment and empower your research with POSEIDON-T (21M parameters), POSEIDON-B (158M parameters), and POSEIDON-L (629M parameters).
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• **Pretrained models & datasets**: [Hugging Face Hub](https://huggingface.co/camlab-ethz)
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• **Code & Paper**: [GitHub](https://github.com/camlab-ethz/poseidon) | [arXiv](https://arxiv.org/abs/2405.19101)
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• **Join the Discussion**: [Hugging Face Forums](https://discuss.huggingface.co/)
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Let's reshape the future of PDE solving—one foundation model at a time!
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---
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primaryClass={cs.LG}
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}
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```
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"""
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