用并行时间神经孪生模型，从稀疏观测中高保真重建动态系统状态。
PAINT: Parallel-in-time Neural Twins for Dynamical System Reconstruction
- 并行建模多时序状态分布，测试时滑动窗口预测
- 在二维湍流问题上保持轨迹稳定，稀疏测量下误差低
- 适合需要实时精准状态估计的物理系统建模
神经代理在模拟动态系统方面展现出巨大潜力，具备实时能力。我们设想神经孪生是神经代理的演进，旨在创建真实系统的数字副本。神经孪生在测试时接收测量值以更新状态，从而实现情境化决策。我们认为，神经孪生的关键特性是其保持在轨性，即随时间保持贴近真实系统状态。本文提出并行时间神经孪生（PAINT），一种与架构无关的动态系统建模方法。PAINT训练生成神经网络以并行方式建模多时序状态分布。测试时，基于滑动窗口的测量值预测状态。理论分析表明，PAINT具有在轨性，而自回归模型通常不具备。我们在一个具有挑战性的二维湍流流体动力学问题上评估该方法。结果表明，PAINT保持在轨性，并能从稀疏测量中高保真预测系统状态。这些发现突显了PAINT在构建保持在轨性的神经孪生方面的潜力，有助于提升状态估计精度和决策能力。
原文摘要 · Abstract (English)
Neural surrogates have shown great potential in simulating dynamical systems, while offering real-time capabilities. We envision Neural Twins as a progression of neural surrogates, aiming to create digital replicas of real systems. A neural twin consumes measurements at test time to update its state, thereby enabling context-specific decision-making. We argue, that a critical property of neural twins is their ability to remain on-trajectory, i.e., to stay close to the true system state over time. We introduce Parallel-in-time Neural Twins (PAINT), an architecture-agnostic family of methods for modeling dynamical systems from measurements. PAINT trains a generative neural network to model the distribution of states in parallel over time. At test time, states are predicted from measurements in a sliding window fashion. Our theoretical analysis shows that PAINT is on-trajectory, whereas autoregressive models generally are not. Empirically, we evaluate our method on a challenging two-dimensional turbulent fluid dynamics problem. The results demonstrate that PAINT stays on-trajectory and predicts system states from sparse measurements with high fidelity. These findings underscore PAINT's potential for developing neural twins that stay on-trajectory, enabling more accurate state estimation and decision-making.
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