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Updated: May 11, 2025

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Towards a foundation model for partial differential equations: Multioperator learning and extrapolation.

Jingmin Sun1, Yuxuan Liu2, Zecheng Zhang3

  • 1Carnegie Mellon University, Department of Mathematical Sciences, Pittsburgh, Pennsylvania 15213, USA.

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Summary
This summary is machine-generated.

This study introduces PROSE-PDE, a multimodal foundation model for scientific problems. It predicts future states of spatiotemporal systems and learns governing equations, demonstrating strong generalization capabilities.

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Area of Science:

  • Multimodal foundation models
  • Scientific machine learning
  • Partial Differential Equations (PDEs)

Background:

  • Foundation models excel in language and image tasks.
  • Predicting spatiotemporal systems and learning governing equations are key scientific challenges.

Purpose of the Study:

  • Introduce PROSE-PDE, a multimodal foundation model for scientific problems.
  • Enable bimodality to bimodality learning for spatiotemporal systems.
  • Predict future states and learn underlying physical equations.

Main Methods:

  • Multi-operator learning approach.
  • Training on one-dimensional time-dependent nonlinear constant coefficient PDEs.
  • Extrapolation studies to assess generalization.

Main Results:

  • PROSE-PDE generalizes physical features through robust multi-operator training.
  • The model extrapolates to predict PDE solutions for unseen models or data.
  • Symbolic modality resolves well-posedness issues and enhances predictive capabilities.

Conclusions:

  • PROSE-PDE offers a novel approach to scientific foundation modeling.
  • The model demonstrates significant potential for applications in physics, geology, and biology.
  • Multimodal learning enhances the prediction of complex spatiotemporal systems.