标题： 神经动态模式：从稀疏观测中计算动态系统的成像 显示英文标题

标题： Neural Dynamic Modes: Computational Imaging of Dynamical Systems from Sparse Observations

摘要： 动力系统在科学和工程中无处不在，从飞机机翼上的湍流到蛋白质的结构变化。 尽管一些系统已经被很好地理解和模拟，但科学成像经常面临通过间接、噪声和高度稀疏的测量所观察到的前所未有的动态。 我们提出了NeuralDMD，这是一种模型无关的框架，将神经隐式表示与动态模式分解（DMD）相结合，以从这些测量中重建连续的时空动态。 神经表示的表达能力能够捕捉复杂的空间结构，而DMD的线性动态模式引入了归纳偏差，指导训练并支持稳定、低维的表示和预测。 我们在两个现实世界的问题上验证了NeuralDMD：从稀疏的站点观测中重建北美近地表风速场，以及恢复银河系中心黑洞Sgr A*附近的等离子体演化。 在这两种情况下，NeuralDMD都优于现有的基线方法，证明了它作为跨地球科学、天文学等领域的动态系统成像通用工具的潜力。 显示英文摘要

摘要： Dynamical systems are ubiquitous within science and engineering, from turbulent flow across aircraft wings to structural variability of proteins. Although some systems are well understood and simulated, scientific imaging often confronts never-before-seen dynamics observed through indirect, noisy, and highly sparse measurements. We present NeuralDMD, a model-free framework that combines neural implicit representations with Dynamic Mode Decomposition (DMD) to reconstruct continuous spatio-temporal dynamics from such measurements. The expressiveness of neural representations enables capturing complex spatial structures, while the linear dynamical modes of DMD introduce an inductive bias that guides training and supports stable, low-dimensional representations and forecasting. We validate NeuralDMD on two real-world problems: reconstructing near-surface wind-speed fields over North America from sparse station observations, and recovering the evolution of plasma near the Galactic-center black hole, Sgr A*. In both cases, NeuralDMD outperforms established baselines, demonstrating its potential as a general tool for imaging dynamical systems across geoscience, astronomy, and beyond.