用物理规律指导神经网络，实现多时序的精准概率预测。
Spatio-temporal probabilistic forecast using MMAF-guided learning
- 基于奥尔斯坦-乌伦贝克过程约束网络结构与训练
- 多时间步预测均保持校准，且性能优于卷积/扩散模型
- 适合需要可靠置信度的气象、交通等时空预测任务
我们提出一种理论引导的广义贝叶斯方法，用于时空栅格数据建模，通过在数据嵌入设计和优化过程中引入时空奥尔斯坦-乌伦贝克过程的依赖与因果结构约束，训练一组具有高斯权重的随机前馈神经网络。推理阶段，通过在不同预测时程施加不同初始条件，生成具有因果关系的集合预测。该流程称为MMAF引导学习。在合成数据和真实数据上的实验表明，我们的预测在多个时间步上始终保持校准。此外，结果表明，在此类数据上，浅层前馈网络的性能可媲美甚至优于用于概率预测任务的卷积或扩散深度学习架构。
原文摘要 · Abstract (English)
We present a theory-guided generalized Bayesian methodology for spatio-temporal raster data, which we use to train an ensemble of stochastic feed-forward neural networks with Gaussian-distributed weights. The methodology incorporates the dependence and causal structure of a spatio-temporal Ornstein-Uhlenbeck process into training and inference by enforcing constraints on the design of the data embedding and the related optimization routine. In inference mode, the networks are employed to generate causal ensemble forecasts by applying different initial conditions at different horizons. We call this workflow MMAF-guided learning. Experiments conducted on both synthetic and real data demonstrate that our forecasts remain calibrated across multiple time horizons. Moreover, we show that on such data, shallow feed-forward architectures can achieve performance comparable to, and in some cases better than, convolutional or diffusion deep learning architectures used in probabilistic forecasting tasks.
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