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

TL;DR

FlowMixer is a novel depth-agnostic neural architecture that models complex spatiotemporal patterns with interpretability, leveraging constrained matrix operations and dynamical systems theory for long-horizon forecasting.

Contribution

It introduces a single-layer, depth-agnostic neural architecture with interpretable eigenmodes, bridging statistical learning and dynamical systems for improved forecasting.

Findings

Achieves state-of-the-art performance in long-horizon forecasting.

Effectively models physical phenomena like chaotic attractors and turbulence.

Provides interpretable eigenmodes directly from the architecture.

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.