Physics-Informed Temporal U-Net for High-Fidelity Fluid Interpolation

TL;DR

This paper introduces a Physics-Informed Temporal U-Net that improves high-fidelity fluid interpolation from sparse data by ensuring smooth transitions and preserving turbulent details, outperforming standard models.

Contribution

The authors propose a novel Temporal U-Net architecture with physics-informed constraints and perceptual loss to enhance fluid data interpolation accuracy.

Findings

Achieves a Mean Absolute Error of 0.015, significantly better than the baseline 0.085.

Retains high-frequency turbulent details in fluid reconstructions.

Outperforms standard models in structural fidelity and texture preservation.

Abstract

Reconstructing high-fidelity fluid dynamics from sparse temporal observations is quite challenging, mainly due to the chaotic and non-linear nature of fluid transport. Standard deep learning-based interpolation methods often tend to regress to the mean, which results in spatial blurring and temporal strobing, especially noticeable around the observed anchor frames where transitions become discontinuous. In this work, we propose a novel Temporal U-Net architecture that integrates a VGG-based perceptual loss along with a Physics-Informed Bridge to overcome these issues. By introducing time-weighted feature blending and enforcing a parabolic boundary condition defined by t(1 - t), the model ensures smooth transitions while also maintaining perfect consistency at the endpoints. Experimental results on multi-channel RGB fluid data show that our method clearly outperforms standard models, both in terms of structural fidelity and texture preservation. In particular, the model achieves a Mean Absolute Error of 0.015, compared to 0.085 for a standard L1 baseline. Further Spatial Power Spectral Density (PSD) analysis reveals that the model is able to retain high-frequency turbulent details that are usually lost in deterministic reconstructions.