基于时空相关性的数据驱动方法,可高精度预测复杂流场演化。
Data-Driven Forecasting of High-Dimensional Transient and Stationary Processes via Space-Time Projection
- 通过扩展时空模态提取数据内在结构,利用正交性和相关性进行预报
- 在超新星爆炸与高超音速湍流实验中,预测误差低于LSTM基准模型
- 仅需调整截断秩,无需调参,适合需要可解释性的科研场景
提出一种数据驱动的时空投影(STP)方法,用于高维时序数据的预报。该方法从覆盖预测时长(含历史回溯与未来预测区间)的训练数据中计算扩展时空本征模态,通过将历史部分模态投影至新数据,同时利用其正交性与对未来延伸部分的最佳相关性生成预报。方法基于本征正交分解(POD)理论,内在包含降维与时间延迟嵌入。对于给定集合和固定预测时长,唯一可调参数为截断秩,无额外超参数。历史预报精度可作为短期预测准确性的可靠指标,并确立预报误差下限。在两类数据集上验证:星际介质中湍流环境下的超新星爆炸瞬态模拟,以及高超音速工程湍流速度场实验。与标准长短期记忆(LSTM)神经网络相比,尽管其他架构或训练策略可能表现不同,该方法始终提供更优预测精度。因其简洁性与稳健性能,STP为高维瞬态混沌过程的预报提供了可解释且具有竞争力的基准,仅依赖时空相关性信息。
原文摘要 · Abstract (English)
Space-Time Projection (STP) is introduced as a data-driven forecasting approach for high-dimensional and time-resolved data. The method computes extended space-time proper orthogonal modes from training data spanning a prediction horizon comprising both hindcast and forecast intervals. Forecasts are then generated by projecting the hindcast portion of these modes onto new data, simultaneously leveraging their orthogonality and optimal correlation with the forecast extension. Rooted in Proper Orthogonal Decomposition (POD) theory, dimensionality reduction and time-delay embedding are intrinsic to the approach. For a given ensemble and fixed prediction horizon, the only tunable parameter is the truncation rank--no additional hyperparameters are required. The hindcast accuracy serves as a reliable indicator for short-term forecast accuracy and establishes a lower bound on forecast errors. The efficacy of the method is demonstrated using two datasets: transient, highly anisotropic simulations of supernova explosions in a turbulent interstellar medium, and experimental velocity fields of a turbulent high-subsonic engineering flow. In a comparative study with standard Long Short-Term Memory (LSTM) neural networks--acknowledging that alternative architectures or training strategies may yield different outcomes--the method consistently provided more accurate forecasts. Considering its simplicity and robust performance, STP offers an interpretable and competitive benchmark for forecasting high-dimensional transient and chaotic processes, relying purely on spatiotemporal correlation information.
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