Discovery of interaction and diffusion kernels in particle-to-mean-field multi-agent systems
arXiv:2603.15927v1 Announce Type: new Abstract: We propose a data-driven framework to learn interaction kernels in stochastic multi-agent systems. Our approach aims at identifying the functional form of nonlocal interaction and diffusion terms directly from trajectory data, without any a priori knowledge of the underlying interaction structure. Starting from a discrete stochastic binary-interaction model, we formulate the inverse problem as a sequence of sparse regression tasks in structured finite-dimensional spaces spanned by compactly supported basis functions, such as piecewise linear polynomials. In particular, we assume that pairwise interactions between agents are not directly observed and that only limited trajectory data are available. To address these challenges, we propose two complementary identification strategies. The first based on random-batch sampling, which compensates for latent interactions while preserving the statistical structure of the full dynamics in expectat
arXiv:2603.15927v1 Announce Type: new Abstract: We propose a data-driven framework to learn interaction kernels in stochastic multi-agent systems. Our approach aims at identifying the functional form of nonlocal interaction and diffusion terms directly from trajectory data, without any a priori knowledge of the underlying interaction structure. Starting from a discrete stochastic binary-interaction model, we formulate the inverse problem as a sequence of sparse regression tasks in structured finite-dimensional spaces spanned by compactly supported basis functions, such as piecewise linear polynomials. In particular, we assume that pairwise interactions between agents are not directly observed and that only limited trajectory data are available. To address these challenges, we propose two complementary identification strategies. The first based on random-batch sampling, which compensates for latent interactions while preserving the statistical structure of the full dynamics in expectation. The second based on a mean-field approximation, where the empirical particle density reconstructed from the data defines a continuous nonlocal regression problem. Numerical experiments demonstrate the effectiveness and robustness of the proposed framework, showing accurate reconstruction of both interaction and diffusion kernels even from partially observed. The method is validated on benchmark models, including bounded-confidence and attraction-repulsion dynamics, where the two proposed strategies achieve comparable levels of accuracy.
Executive Summary
This article presents a data-driven framework for learning interaction kernels in stochastic multi-agent systems. The proposed approach formulates the inverse problem as a sequence of sparse regression tasks using compactly supported basis functions. Two identification strategies are proposed: random-batch sampling and mean-field approximation. Numerical experiments demonstrate the effectiveness and robustness of the framework in reconstructing interaction and diffusion kernels from partially observed data. The method is validated on benchmark models, including bounded-confidence and attraction-repulsion dynamics. The study contributes to the field of multi-agent systems by providing a novel solution for identifying interaction kernels from trajectory data. The results have implications for understanding and simulating complex systems, such as social networks and animal collectives.
Key Points
- ▸ The proposed framework is data-driven and does not rely on a priori knowledge of the underlying interaction structure.
- ▸ Two identification strategies are proposed to address challenges in latent interactions and limited trajectory data.
- ▸ The framework is validated on benchmark models and demonstrates accurate reconstruction of interaction and diffusion kernels.
Merits
Strength
The proposed framework provides a novel solution for identifying interaction kernels from trajectory data, which is a significant contribution to the field of multi-agent systems.
Robustness
The framework is demonstrated to be robust in reconstructing interaction and diffusion kernels even from partially observed data.
Flexibility
The proposed framework can be applied to various types of multi-agent systems, including social networks and animal collectives.
Demerits
Limitation
The proposed framework relies on compactly supported basis functions, which may not be suitable for all types of multi-agent systems.
Assumptions
The framework assumes that pairwise interactions between agents are not directly observed, which may not always be the case in real-world systems.
Computational Complexity
The proposed framework may require significant computational resources for large-scale multi-agent systems.
Expert Commentary
The proposed framework is a significant contribution to the field of multi-agent systems, providing a novel solution for identifying interaction kernels from trajectory data. The combination of machine learning techniques with multi-agent systems is a growing area of research, and this study demonstrates the potential of such approaches. However, the framework relies on compactly supported basis functions, which may not be suitable for all types of multi-agent systems. Additionally, the framework assumes that pairwise interactions between agents are not directly observed, which may not always be the case in real-world systems. Despite these limitations, the study has implications for understanding and simulating complex systems, such as social networks and animal collectives.
Recommendations
- ✓ Further research is needed to explore the applicability of the proposed framework to various types of multi-agent systems.
- ✓ The framework should be tested on real-world data to evaluate its performance and robustness in different scenarios.
