FlowMixer: A Depth-Agnostic Neural Architecture for Interpretable Spatiotemporal Forecasting

Fares B. Mehouachi, Saif Eddin Jabari

Keywords: forecasting, spatiotemporal forecasting, neural architecture, interpretability, Koopman operators, dynamical systems, long-horizon prediction, non-negative matrix factorization

TL;DR: We propose FlowMixer, a single-layer architecture using semi-group properties to eliminate neural depth search, achieving competitive multivariate forecasting with interpretable Kronecker-Koopman eigenmodes and algebraic horizon manipulation.

Abstract:

We introduce FlowMixer, a single-layer neural architecture that leverages constrained matrix operations to model structured spatiotemporal patterns with enhanced interpretability. 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 eigenmodes framework that bridges statistical learning with dynamical systems theory, providing interpretable spatiotemporal patterns and facilitating direct algebraic manipulation of prediction horizons without retraining. The architecture's semi-group property enables this single layer to mathematically represent any depth through composition, eliminating depth search entirely.
Extensive experiments across diverse domains demonstrate FlowMixer's long-horizon forecasting capabilities while effectively modeling physical phenomena such as chaotic attractors and turbulent flows. Our results achieve performance matching state-of-the-art methods while offering superior interpretability through directly extractable eigenmodes.
This work suggests that architectural constraints can simultaneously maintain competitive performance and enhance mathematical interpretability in neural forecasting systems.

Primary Area: Machine learning for sciences (e.g. climate, health, life sciences, physics, social sciences)

Submission Number: 7178