FlowMixer用单一结构实现可解释的长期时空预测，无需调参深度。
FlowMixer: A Depth-Agnostic Neural Architecture for Interpretable Spatiotemporal Forecasting
- 单层架构结合可逆映射与非负矩阵混合，保持数据形状不变。
- 通过克罗内克-库普曼特征模式直接提取可解释的动态模式。
- 支持零样本调整预测时长，适合需要物理可解释性的场景。
我们提出FlowMixer，一种单层神经架构，通过约束矩阵运算建模有结构的时空模式，并提升可解释性。FlowMixer在可逆映射框架中引入非负矩阵混合层——先应用变换再进行混合，最后使用逆变换恢复。这种保形设计实现了克罗内克-库普曼特征模式框架，将统计学习与动力系统理论相连接，提供可解释的时空模式，并支持无需重新训练即可直接代数调整预测时长。该架构的半群性质使其能通过组合数学表示任意深度，完全消除深度搜索需求。在多个领域的广泛实验表明，FlowMixer具备出色的长期预测能力，能有效建模混沌吸引子和湍流等物理现象。结果性能达到或超过当前最优方法，同时通过可直接提取的特征模式实现更优可解释性。研究揭示，架构约束可在保持竞争力的同时显著提升神经预测系统的数学可解释性。
原文摘要 · Abstract (English)
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.
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