FlowMixer: A Constrained Neural Architecture for Interpretable Spatiotemporal Forecasting

2025-05-22

AI Summary

This work addresses key challenges in spatiotemporal forecasting—namely, poor interpretability, inflexible prediction horizons, and weak incorporation of physical mechanisms. We propose the Kronecker-Koopman eigenmode framework, which integrates nonnegative matrix factorization (NMF) with invertible neural networks. Specifically, we design a constrained nonnegative matrix mixing layer and an invertible mapping architecture to disentangle spatiotemporal dynamics into Koopman eigenmodes, while explicitly modeling multidimensional couplings via the Kronecker product. Our core contributions are: (i) the first algebraic adjustment of prediction horizon—e.g., direct computation of the *t*+10 step forecast—without retraining; and (ii) rigorous preservation of structural interpretability and physical consistency. Extensive evaluation on the Lorenz chaotic system and turbulent flow simulation data demonstrates substantial improvements in long-horizon prediction accuracy, robustness, and cross-system generalizability.

Technology Category

Machine Learning: Mixture of Experts (MoE)Cognitive Modeling & Cognitive Systems: Neural Spike CodingKnowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

We introduce FlowMixer, a neural architecture that leverages constrained matrix operations to model structured spatiotemporal patterns. At its core, FlowMixer incorporates non-negative matrix mixing layers within a reversible mapping framework-applying transforms before mixing and their inverses afterward. This shape-preserving design enables a Kronecker-Koopman eigenmode framework that bridges statistical learning with dynamical systems theory, providing interpretable spatiotemporal patterns and facilitating direct algebraic manipulation of prediction horizons without retraining. Extensive experiments across diverse domains demonstrate FlowMixer's robust long-horizon forecasting capabilities while effectively modeling physical phenomena such as chaotic attractors and turbulent flows. These results suggest that architectural constraints can simultaneously enhance predictive performance and mathematical interpretability in neural forecasting systems.

Problem

• Model structured spatiotemporal patterns interpretably
• Bridge statistical learning with dynamical systems theory
• Enhance predictive performance with architectural constraints

Innovation

• Constrained matrix operations for structured patterns
• Reversible mapping with non-negative matrix mixing
• Kronecker-Koopman eigenmode for interpretable predictions