Predicting rare events using neural networks and short-trajectory data
Predicting rare events using neural networks and short-trajectory data
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DOI：
10.1016/j.jcp.2023.112152
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发表时间：
2022-08
影响因子：
4.1
通讯作者：
J. Strahan;J. Finkel;A. Dinner;J. Weare
中科院分区：
文献类型：
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作者：
J. Strahan;J. Finkel;A. Dinner;J. Weare
估计事件的可能性、时间和性质是随机动力系统建模的主要目标。当与解决元素动力学所需的模拟和/或测量的时间尺度相比，该事件很少见时，直接观察的准确预测就变得具有挑战性。在这种情况下，更有效的方法是将感兴趣的统计数据转换为 Feynman-Kac 方程（偏微分方程）的解。在这里，我们开发了一种通过短轨迹数据训练神经网络来求解 Feynman-Kac 方程的方法。我们的方法基于马尔可夫近似，但避免了对基础模型和动态的假设。这使得它适用于处理复杂的计算模型和观测数据。我们使用有助于可视化的低维模型来说明我们的方法的优点，并且这种分析激发了自适应采样策略，该策略允许动态识别数据并将其添加到对于预测感兴趣的统计数据很重要的区域。最后，我们证明我们可以为平流层突然变暖的 75 维模型计算准确的统计数据。该系统为我们的方法提供了严格的测试平台。
Estimating the likelihood, timing, and nature of events is a major goal of modeling stochastic dynamical systems. When the event is rare in comparison with the timescales of simulation and/or measurement needed to resolve the elemental dynamics, accurate prediction from direct observations becomes challenging. In such cases a more effective approach is to cast statistics of interest as solutions to Feynman-Kac equations (partial differential equations). Here, we develop an approach to solve Feynman-Kac equations by training neural networks on short-trajectory data. Our approach is based on a Markov approximation but otherwise avoids assumptions about the underlying model and dynamics. This makes it applicable to treating complex computational models and observational data. We illustrate the advantages of our method using a low-dimensional model that facilitates visualization, and this analysis motivates an adaptive sampling strategy that allows on-the-fly identification of and addition of data to regions important for predicting the statistics of interest. Finally, we demonstrate that we can compute accurate statistics for a 75-dimensional model of sudden stratospheric warming. This system provides a stringent test bed for our method.