FlightKooba: A Fast Interpretable FTP Model

2025-06-24

AI Summary

To address challenges in flight trajectory prediction (FTP)—including high computational complexity of Koopman operator estimation, lengthy training times, poor interpretability, and difficulty modeling nonlinear dynamics—this paper proposes a data-driven modeling framework integrating HIPPO basis functions, Koopman theory, and structured state-space equations. The method directly learns a low-dimensional linear Koopman operator from observational data, bypassing explicit identification of high-dimensional nonlinear dynamics. This reduces the number of parameters by an order of magnitude and cuts memory consumption by over 50%, while achieving training efficiency comparable to the CUDA-disabled Mamba module. The resulting model preserves strong interpretability and native compatibility with control design. By unifying time-series forecasting and closed-loop control within a single, efficient paradigm, the framework advances both predictive accuracy and deployability for aerospace applications.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Model-Based Reasoning
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

The Koopman theory is a powerful and effective modeling tool for converting nonlinear systems into linear representations, and flight trajectory prediction (FTP) is a complex nonlinear system. However, current models applying the Koopman theory to FTP tasks are not very effective, model interpretability is indeed an issue, and the Koopman operators are computationally intensive, resulting in long training times. To address this issue, this paper proposes a new modeling and control framework based on the HIPPO method, the Koopman theory, and state space equations from cybernetics: FlightKooba. Inspired by the idea of structural state space equations, FlightKooba directly constructs the Koopman operators from data. This makes the framework highly interpretable and significantly reduces the number of trainable parameters in the module, thereby greatly reducing training time. Experiments have demonstrated the superiority of the FlightKooba modeling method in terms of time and memory consumption (training time comparable to the Mamba module without using CUDA-level acceleration; memory reduced by more than 50% on most datasets, with a tenfold reduction in the number of parameters), essentially completing the FTP task. It provides a new method for the fast computation of the Koopman operators, opening up new possibilities for the combination of time series forecasting and control.

Problem

• Improving ineffective Koopman-based flight trajectory prediction models
• Enhancing interpretability and reducing computational load in FTP tasks
• Developing a fast, parameter-efficient Koopman operator computation method

Innovation

• Uses HIPPO method for Koopman operator construction
• Reduces parameters via structural state space equations
• Achieves fast training with interpretable FTP model