OpenNovelty.org

Micro-Macro Coupled Koopman Modeling on Graph for Traffic Flow Prediction

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Koopman Operator; Traffic Flow Prediction
Abstract:

Traffic systems are inherently multi-scale: microscopic vehicle interactions and macroscopic flow co-evolve nonlinearly. Microscopic models capture local interactions but miss flow evolution; macroscopic models enforce aggregated consistency yet overlook stochastic vehicle-level dynamics. We propose Micro–Macro Coupled Koopman Modeling (MMCKM), which lifts the coupled dynamics to a high-dimensional linear observation space for a unified linear-operator representation. Unlike grid-based discretizations, MMCKM adopts a vehicle-centric dynamic graph that preserves microscopic perturbations while respecting macroscopic conservation laws by discretizing PDEs onto this graph. At the micro scale, scenario-adaptive Koopman evolvers selected by an Intent Discriminator are designed to model vehicle dynamics. A Koopman control module explicitly formulate how flow state influences individual vehicles, yielding bidirectional couplings. To our knowledge, this is the first work to jointly model vehicle trajectories and traffic flow density using a unified Koopman framework without requiring historical trajectories. The proposed MMCKM is validated for trajectory prediction on NGSIM and HighD. While MMCKM uses only real-time measurement, it achieves comparable or even higher accuracy than history-dependent baselines. We further analyze the effect of the operator interval and provide ablations to show the improvement by intent inference, macro-to-micro control, and diffusion. Code and implementation details are included to facilitate reproducibility.

Disclaimer
This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper introduces a unified Koopman framework that jointly models microscopic vehicle trajectories and macroscopic traffic flow density on dynamic graphs. It resides in the 'Micro-Macro Coupled Vehicle Trajectory and Flow Prediction' leaf, which currently contains only this work—indicating a sparse, emerging research direction. Within the broader taxonomy of Koopman-based traffic methods (six papers total across six leaf nodes), this contribution occupies a distinct niche focused on multi-scale coupling rather than single-scale flow forecasting or control-oriented applications.

The taxonomy reveals two main branches: control-oriented applications (signal timing, ramp metering, oscillation mitigation) and prediction-focused methods (spatiotemporal highway flow, aerodrome trajectories). The paper's leaf sits within the prediction branch, neighboring 'Spatiotemporal Highway Flow Prediction' and 'Aerodrome Traffic Pattern Trajectory Prediction.' Unlike these siblings—which address either aggregate flow patterns or specialized aviation contexts—this work explicitly bridges microscopic vehicle dynamics and macroscopic conservation laws. The taxonomy's scope notes clarify that single-scale flow prediction and control applications belong elsewhere, reinforcing the paper's unique positioning at the micro-macro interface.

Among fourteen candidates examined, one contribution ('Unified history-free Koopman framework') encountered a refutable candidate, while the other two ('Vehicle-centric PDE discretization' and 'Physics-guided multi-regime dynamics') showed no clear refutation across one and three candidates respectively. The limited search scope (top-K semantic matches plus citation expansion) suggests that while some overlap exists for the core Koopman modeling claim, the vehicle-centric graph discretization and multi-regime control components appear less contested. The statistics indicate moderate prior work density for the unified framework concept, but sparser coverage for the specific graph-based PDE discretization and regime-adaptive control mechanisms.

Given the restricted search scale and the paper's placement in a singleton taxonomy leaf, the work appears to explore a relatively novel intersection of Koopman theory, dynamic graphs, and micro-macro traffic coupling. However, the presence of at least one refutable candidate for the central framework claim—among only fourteen examined—suggests that the core idea of history-free Koopman modeling may have partial precedent. The analysis does not cover exhaustive literature beyond top-K semantic matches, leaving open the possibility of additional related work in adjacent fields.

Taxonomy

Core-task Taxonomy Papers
6
3
Claimed Contributions
14
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: Micro-macro coupled traffic flow prediction using Koopman operators. The field applies Koopman operator theory to traffic systems, organizing into two main branches: one focused on control and optimization, and another on flow and trajectory prediction. The control branch typically addresses signal timing, ramp metering, and oscillation suppression—exemplified by works such as Koopman Signalized Traffic[1], Deep Koopman Ramp[2], and Koopman Oscillation Control[3]—while the prediction branch emphasizes forecasting vehicle trajectories and aggregate flow patterns, often leveraging graph-based or data-driven representations like Non-Stationary Koopman GCN[5] and Dictionary-free Koopman[4]. These branches share a common foundation in linearizing nonlinear traffic dynamics via Koopman embeddings, yet differ in whether the primary goal is real-time intervention or accurate forecasting. Recent work highlights trade-offs between model complexity and interpretability, with some studies pursuing dictionary-free or purely data-driven approaches to avoid hand-crafted basis functions, while others integrate domain knowledge through graph structures or aerodrome-specific constraints as in Aerodrome Koopman Operator[6]. Micro-Macro Koopman Graph[0] sits within the prediction branch, specifically targeting the coupling of microscopic vehicle trajectories and macroscopic flow variables. Compared to Non-Stationary Koopman GCN[5], which handles non-stationary spatial dependencies, and Dictionary-free Koopman[4], which emphasizes learning embeddings without predefined dictionaries, Micro-Macro Koopman Graph[0] appears to bridge individual and aggregate scales more explicitly. This positioning reflects an ongoing effort to unify multi-resolution traffic representations under a single Koopman framework, addressing the challenge of capturing both local maneuvers and network-wide congestion patterns simultaneously.

Claimed Contributions

Vehicle-centric PDE discretization on dynamic graphs

The authors propose a Lagrangian discretization approach that discretizes traffic flow PDEs directly onto vehicles as graph nodes, rather than using traditional fixed spatial grids. This vehicle-centric graph formulation preserves microscopic perturbations while maintaining macroscopic conservation laws through skew-symmetric advection and positive semi-definite diffusion operators.

1 retrieved paper
Unified history-free Koopman framework for micro-macro traffic modeling

The authors develop a unified Koopman operator framework that lifts both microscopic vehicle trajectories and macroscopic flow evolution into linear observation spaces. This approach leverages the Markovian property of Koopman operators to enable prediction using only current state information, eliminating the need for historical trajectory data.

10 retrieved papers
Can Refute
Physics-guided multi-regime microscopic dynamics with Koopman control

The authors design a scenario-adaptive mechanism using an Intent Discriminator to select appropriate Koopman operators for different driving scenarios, combined with a Koopman control module that explicitly formulates how macroscopic flow states influence individual vehicle dynamics, establishing bidirectional micro-macro coupling.

3 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Vehicle-centric PDE discretization on dynamic graphs

The authors propose a Lagrangian discretization approach that discretizes traffic flow PDEs directly onto vehicles as graph nodes, rather than using traditional fixed spatial grids. This vehicle-centric graph formulation preserves microscopic perturbations while maintaining macroscopic conservation laws through skew-symmetric advection and positive semi-definite diffusion operators.

Contribution

Unified history-free Koopman framework for micro-macro traffic modeling

The authors develop a unified Koopman operator framework that lifts both microscopic vehicle trajectories and macroscopic flow evolution into linear observation spaces. This approach leverages the Markovian property of Koopman operators to enable prediction using only current state information, eliminating the need for historical trajectory data.

Contribution

Physics-guided multi-regime microscopic dynamics with Koopman control

The authors design a scenario-adaptive mechanism using an Intent Discriminator to select appropriate Koopman operators for different driving scenarios, combined with a Koopman control module that explicitly formulates how macroscopic flow states influence individual vehicle dynamics, establishing bidirectional micro-macro coupling.

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