Reconstructing spatiotemporal dynamics with sparse sensor measurement is a challenging task that is encountered in a wide spectrum of scientific and engineering applications. The problem is particularly challenging when the number or types of sensors (for example, randomly placed) are extremely sparse. Existing end-to-end learning models ordinarily do not generalize well to unseen full-field reconstruction of spatiotemporal dynamics, especially in sparse data regimes typically seen in real-world applications. To address this challenge, here we propose a sparse-sensor-assisted score-based generative model (S³GM) to reconstruct and predict full-field spatiotemporal dynamics on the basis of sparse measurements. Instead of learning directly the mapping between input and output pairs, an unconditioned generative model is first pretrained, capturing the joint distribution of a vast group of pretraining data in a self-supervised manner, followed by a sampling process conditioned on unseen sparse measurement. The efficacy of S³GM has been verified on multiple dynamical systems with various synthetic, real-world and laboratory-test datasets (ranging from turbulent flow modelling to weather/climate forecasting). The results demonstrate the sound performance of S³GM in zero-shot reconstruction and prediction of spatiotemporal dynamics even with high levels of data sparsity and noise. We find that S³GM exhibits high accuracy, generalizability and robustness when handling different reconstruction tasks.

使用稀疏传感器测量重建时空动力学是一项具有挑战性的任务，在广泛的科学和工程应用中会遇到。当传感器的数量或类型（例如，随机放置）非常稀疏时，这个问题尤其具有挑战性。现有的端到端学习模型通常不能很好地推广到看不见的时空动态全场重建，尤其是在实际应用中常见的稀疏数据范围内。为了应对这一挑战，我们在这里提出了一种稀疏传感器辅助的基于分数的生成模型 （S³GM），以在稀疏测量的基础上重建和预测全场时空动力学。首先预训练无条件生成模型，而不是直接学习输入和输出对之间的映射，以自我监督的方式捕获大量预训练数据的联合分布，然后是以看不见的稀疏测量为条件的采样过程。S³GM 的功效已在具有各种合成、真实世界和实验室测试数据集（从湍流建模到天气/气候预报）的多个动力系统上得到验证。结果表明，即使在高水平的数据稀疏性和噪声的情况下，S³GM 在零镜头重建和时空动力学预测方面也具有良好的性能。我们发现 S³GM 在处理不同的重建任务时表现出高精度、泛化性和稳健性。