FDN: Interpretable Spatiotemporal Forecasting with Future Decomposition Networks

Abstract: Spatiotemporal systems comprise a collection of spatially distributed yet interdependent entities each generating unique dynamic signals. Highly sophisticated methods have been proposed in recent years delivering state-of-the-art (SOTA) forecasts but few have focused on interpretability. To address this, we propose the Future Decomposition Network (FDN), a novel forecast model capable of (a) providing interpretable predictions through classification (b) revealing latent activity patterns in the target time-series and (c) delivering forecasts competitive with SOTA methods at a fraction of their memory and runtime cost. We conduct comprehensive analyses on FDN for multiple datasets from hydrologic, traffic, and energy systems, demonstrating its improved accuracy and interpretability.

• The paper introduces a future decomposition layer that models forecasts as convex combinations of learned spatiotemporal patterns for direct interpretability.
• It employs a classifier-interpolator pipeline with localized attention and graph-based encoding to achieve high accuracy with reduced computational overhead.
• Experimental results show significant error metric improvements on benchmark datasets, highlighting efficiency and robustness in high-variance scenarios.

Interpretable Spatiotemporal Forecasting with Future Decomposition Networks

Introduction and Motivations

Spatiotemporal forecasting remains a central research area in machine learning, particularly due to the complexity and interconnectedness of real-world systems such as hydrological basins, traffic networks, and energy grids. Traditional approaches leveraging RNNs, CNNs, GNNs, and Transformer-based architectures have advanced SOTA accuracy, yet most of them fail to provide interpretability, especially concerning the underlying generative factors of the system's future evolution. "FDN: Interpretable Spatiotemporal Forecasting with Future Decomposition Networks" (2606.25201) introduces a structural breakthrough by directly modeling system dynamics as a finite set of fundamental patterns, enabling direct interpretability and competitive or superior forecast accuracy with substantially lower computational overhead.

Model Architecture

FDN builds on the hypothesis that a system's future can be largely decomposed into a set of recurring spatiotemporal patterns. The core innovation—Future Decomposition (FD) layer—is a new forecast operator distinct from prior reliance on FC, convolution, AR, or attention mechanisms. The FDN architecture incorporates:

• Classifier-Interpolator Pipeline: Past signals are projected via a soft classifier into a K-dimensional probability simplex, each dimension corresponding to a learned future pattern. Forecasts are synthesized as a convex combination of these patterns weighted by classifier confidences. This directly links each forecast to interpretable, discovered system modes.
• Pattern Discovery by Learning: Pattern bases are not derived analytically (e.g., via SVD) but learned end-to-end via SGD to optimize forecast performance. This both avoids expensive pre-processing and maximizes data-driven adaptation.
• Localized Dynamic Attention (LDA): Feature relevance is dynamically and node-locally adapted, supporting robust multivariate processing by tuning attention with learned node embeddings.
• Graph-based Dependency Encoding: Chebyshev GCNs parameterize spatial coupling, with the underlying graph structure either given (as in traffic and hydrology) or learned implicitly, thereby capturing non-local interactions.
• Conditioning via Embeddings: Both spatial and temporal conditioning is performed via learned node and periodic embeddings, enabling precise adaptation to heterogeneous node behaviors and periodic rhythms.

Experimental Results

Experiments span three canonical benchmarks: Wabash River (hydrology), E-PEMS-BAY (traffic), and Solar-Energy (energy), each with multi-variate and multi-node time-series. All comparison models represent SOTA in various operator classes (Graph Attention, CNNs, RNNs, Transformers, SCINet, etc). FDN achieves:

• Consistent SOTA or Near-SOTA Accuracy: On the longest horizons, FDN delivers the lowest MAE/MAPE/RMSE across all datasets. For E-PEMS-BAY, FDN achieves a 9.1% reduction in MAPE and a 2.5% reduction in RMSE over the next-best competitor. MAPE reductions of 6.3% (Wabash River) and 1% (Solar-Energy) are observed.
• Superior Forecasting in High-Variance Nodes: Node-level analysis indicates FDN's advantage is pronounced in cases with high signal variability—critical for rare event detection or operational responsiveness.

Efficiency is significant: FDN typically utilizes $1/12$ to $1/2$ the parameters of strong baselines (e.g., AGCRN, MTGNN or SCINet) and executes with $2.4\times$ speed-up on real-world-scale graph-structured datasets.

Interpretability and Model Introspection

A primary outcome is FDN's model-intrinsic interpretability, which is visualized and analyzed extensively. For any forecast, the model provides:

• Pattern Attribution: Each prediction is explicitly tied to a probabilistic mixture of K learned dynamics patterns. These patterns often correspond to observable macroscopic states (e.g., flood onsets, rush hour traffic collapse, or solar output drop at sunset).
• Mechanistic Transparency: The forecast process—preamble classification, selection of pattern basis, and probabilistic interpolation—is fully accessible. Model ablations (including no-attention, no-GCN, random embeddings, etc.) show the necessity and benefit of each component for both accuracy and interpretability.

The learned patterns themselves become a catalog of system "motifs," affording practical value for domain experts to diagnose, audit, and plan responsive interventions.

Theoretical and Practical Implications

FDN's formalization of spatiotemporal forecasting as classification-plus-interpolation over a learned pattern space breaks from the classical generative protocol of sequence-to-sequence models. Most notably:

• Direct Interpretability: The approach moves interpretable forecasting beyond attention heatmaps into explicit, decomposable representations.
• Parameter and Computational Efficiency: The architecture's expressiveness per parameter is high due to shared pattern structure and the avoidance of over-parameterized fully-connected or attention layers.
• Generalization and Robustness: Empirical results suggest that learning a compact basis of fundamental patterns enhances generalization, especially for high-variance and long-horizon forecasting settings.

Potential extensions include conditional pattern spaces for regime-switching systems, hierarchical decompositions for multi-scale signals, and further integration with error-corrective or domain-instructed regularization objectives.

Conclusion

FDN establishes a new paradigm for interpretable spatiotemporal sequence modeling by synthesizing predictions as soft interpolations over learned future patterns, with strong empirical evidence of accuracy, transparency, and efficiency (2606.25201). The classifier-interpolator decomposition, enriched with graph, attention, and embedding mechanisms, demonstrates that competitive forecasting need not come at the expense of interpretability. This approach is broadly applicable across domains where understanding, diagnosis, and trust in the model's decisions are as important as raw predictive performance. Future research can exploit FDN's design for adaptive, modular, and expert-integrated time series analysis in complex structured environments.