AI 中文总结
该研究提出无标签框架TraCTra，仅用部分观测序列和可微正向模型训练，可在四类流体系统中实现高精度流场重建，性能优于相关方法，还具备良好泛化能力，确立轨迹一致性为通用监督原则。
AI 中文摘要
实验科学中的一个核心反问题是从稀疏或间接测量中推断隐藏的动力学状态，深度学习方法在此具有天然优势，但机器学习的重建方法通常需要完整状态数据进行训练。我们提出轨迹一致网络训练（TraCTra），这是一种无标签框架，仅使用部分观测序列和可微正向模型训练重建网络。TraCTra要求网络重建结果与动力学演化相互一致：网络预测的状态随时间推进以匹配后续观测，并在全状态空间中与后续时刻的独立重建结果一致。在四个流体系统中，该目标函数可从粗粒度场重建三维湍流、从密度波动观测重建速度、从投影的二维阴影图序列重建三维密度和速度，还可从局限于小空间窗口的观测中恢复全局涡量。TraCTra的性能优于仅同化方法和物理信息神经网络方法，能保留动力学重要的多尺度结构，且在优化窗口之外仍保持准确；在三维阴影图问题中可泛化到未见过的时刻，在跨轨迹训练时，在二维问题中可泛化到未见过的流场。这些结果确立了轨迹一致性作为无需完整状态训练目标即可重建隐藏动力学状态的通用监督原则。
英文摘要
A core inverse problem in the experimental sciences is the inference of a hidden dynamical state from sparse or indirect measurements. There is a natural opportunity for deep learning methods here, but machine-learnt reconstruction methods typically require full state data for training. We present Trajectory-Consistent Network Training (TraCTra), a label-free framework that trains reconstruction networks using only partial observation sequences and a differentiable forward model. TraCTra requires the network reconstruction and dynamical evolution to be mutually consistent: network-predicted states are marched forward in time to match subsequent observations and to agree in the full state space with independent reconstructions at later times. Across four fluid systems, the same objective reconstructs three-dimensional turbulence from coarse-grained fields, velocity from observations of density fluctuations, and three-dimensional density and velocity from sequences of projected two-dimensional shadowgraphs, while also recovering global vorticity from observations confined to a small spatial window. TraCTra outperforms assimilation-only and physics-informed neural approaches, preserves dynamically important multiscale structure, and remains accurate beyond the optimisation window. It transfers to held-out times in the three-dimensional shadowgraph problem and, when trained across trajectories, generalises to unseen flows in the two-dimensional problem. The results establish trajectory consistency as a general supervision principle for reconstructing hidden dynamical states without full state training targets.
