PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics

📰 ArXiv cs.AI

Learn to efficiently reconstruct and quantify uncertainty in spatiotemporal dynamics using PerFlow, a physics-embedded rectified flow model

advanced Published 6 May 2026

Action Steps

Implement PerFlow using PyTorch or TensorFlow to reconstruct PDE-governed fields from sparse measurements
Use PerFlow to quantify uncertainty in spatiotemporal dynamics by sampling from the learned distribution
Compare the performance of PerFlow with existing generative models and deterministic surrogates on benchmark datasets
Apply PerFlow to real-world problems, such as weather forecasting or fluid dynamics, to demonstrate its effectiveness
Evaluate the impact of PerFlow on uncertainty quantification and reconstruction accuracy in various applications

Who Needs to Know This

Researchers and engineers working on spatiotemporal dynamics reconstruction and uncertainty quantification can benefit from this model, as it provides a more efficient and accurate approach to handling sparse and irregular measurements

Key Insight

💡 PerFlow combines the strengths of generative models and physics-embedded approaches to provide a more accurate and efficient method for reconstructing and quantifying uncertainty in spatiotemporal dynamics

Key Takeaways

Learn to efficiently reconstruct and quantify uncertainty in spatiotemporal dynamics using PerFlow, a physics-embedded rectified flow model

Full Article

Title: PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics

Abstract:
arXiv:2605.03548v1 Announce Type: cross Abstract: Reconstructing PDE-governed fields from sparse and irregular measurements is challenging due to their ill-posed nature. Deterministic surrogates are trained on dense fields that struggle with limited measurements and uncertainty quantification. Generative models, by learning distributions over spatiotemporal fields, can better handle sparsity and uncertainty. However, existing generative approaches enforce data consistency and PDE constraints sim

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