用物理约束的U-Net模型，让流体插值更清晰连贯。
Physics-Informed Temporal U-Net for High-Fidelity Fluid Interpolation
- 设计时间U-Net，融合感知损失与物理桥接机制。
- 误差仅0.015，远低于标准L1基线的0.085。
- 适合需要高保真流体模拟的研究者或动画师。
从稀疏时间观测中重建高保真流体动力学极具挑战，主要源于流体传输的混沌与非线性特性。基于深度学习的标准插值方法常趋向均值，导致空间模糊和时间闪烁，尤其在观测锚点帧附近过渡不连续。本文提出一种新型时空U-Net架构，结合基于VGG的感知损失与物理信息桥接机制。通过引入时间加权特征融合，并施加由t(1 - t)定义的抛物线边界条件，模型确保过渡平滑且端点完全一致。在多通道RGB流体数据上的实验表明，该方法在结构保真度和纹理保留方面显著优于标准模型。尤其，模型实现均方绝对误差0.015，相较标准L1基线的0.085大幅降低。进一步的空间功率谱密度（PSD）分析显示，模型能有效保留通常在确定性重建中丢失的高频湍流细节。
原文摘要 · Abstract (English)
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.
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