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.

翻译：我们提出了一种面向时空栅格数据的理论引导广义贝叶斯方法，该方法通过训练具有高斯分布权重的随机前馈神经网络集成实现预测。该方法通过约束数据嵌入设计和相关优化流程，将时空Ornstein-Uhlenbeck过程的依赖与因果结构融入训练与推理过程。在推理模式下，通过在不同时间跨度施加不同初始条件，该网络可用于生成因果集成预报。我们将此工作流称为MMAF引导学习。在合成数据与真实数据上的实验表明，我们的预报在多个时间跨度上均保持校准特性。此外，我们证明在此类数据上，浅层前馈架构在概率预报任务中可达到与卷积或扩散深度学习架构相当甚至更优的性能。