FlowNet: Modeling Dynamic Spatio-Temporal Systems via Flow Propagation

TL;DR

FlowNet introduces a physics-inspired, flow-based approach to model complex dynamic spatio-temporal systems, outperforming existing methods by explicitly capturing flow-mediated interactions and ensuring conservation principles.

Contribution

The paper presents FlowNet, a novel architecture that models dynamic node interactions via flow tokens and adaptive spatial masking, incorporating physical conservation laws for improved accuracy.

Findings

Outperforms state-of-the-art methods on seven metrics across three real-world systems.

Demonstrates improved modeling accuracy and interpretability.

Validates the effectiveness of flow-based modeling in complex systems.

Abstract

Accurately modeling complex dynamic spatio-temporal systems requires capturing flow-mediated interdependencies and context-sensitive interaction dynamics. Existing methods, predominantly graph-based or attention-driven, rely on similarity-driven connectivity assumptions, neglecting asymmetric flow exchanges that govern system evolution. We propose Spatio-Temporal Flow, a physics-inspired paradigm that explicitly models dynamic node couplings through quantifiable flow transfers governed by conservation principles. Building on this, we design FlowNet, a novel architecture leveraging flow tokens as information carriers to simulate source-to-destination transfers via Flow Allocation Modules, ensuring state redistribution aligns with conservation laws. FlowNet dynamically adjusts the interaction radius through an Adaptive Spatial Masking module, suppressing irrelevant noise while enabling context-aware propagation. A cascaded architecture enhances scalability and nonlinear representation capacity. Experiments demonstrate that FlowNet significantly outperforms existing state-of-the-art approaches on seven metrics in the modeling of three real-world systems, validating its efficiency and physical interpretability. We establish a principled methodology for modeling complex systems through spatio-temporal flow interactions.