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.

翻译：神经代理模型在模拟动力学系统方面展现出巨大潜力，同时具备实时计算能力。我们提出神经孪生作为神经代理模型的进阶形态，旨在创建真实系统的数字副本。神经孪生在测试阶段通过吸收测量数据来更新其状态，从而实现特定情境下的决策制定。我们认为，神经孪生的关键特性在于其保持轨迹跟踪的能力，即随时间推移始终接近真实系统状态。本文提出并行时间神经孪生（PAINT）——一种与架构无关的动力学系统测量建模方法体系。PAINT通过训练生成式神经网络来并行建模状态随时间演化的分布。在测试阶段，系统状态通过滑动窗口方式从测量数据中预测得出。理论分析表明PAINT具有轨迹跟踪特性，而自回归模型通常不具备该特性。我们在具有挑战性的二维湍流流体动力学问题上进行了实证评估。结果表明PAINT能够保持轨迹跟踪，并能从稀疏测量数据中以高保真度预测系统状态。这些发现凸显了PAINT在开发具有轨迹跟踪能力的神经孪生方面的潜力，为实现更精确的状态估计和决策制定提供了可能。