Extracting Interaction Kernels for Many-Particle Systems by a Two-Phase Approach
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912174790672384 |
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| author | Shi, Yangxuan Yang, Wuyue Hong, Liu |
| author_facet | Shi, Yangxuan Yang, Wuyue Hong, Liu |
| contents | This paper presents a two-phase method for learning interaction kernels of stochastic many-particle systems. After transforming stochastic trajectories of every particle into the particle density function by the kernel density estimation method, the first phase of our approach combines importance sampling with an adaptive threshold strategy to identify key terms in the kernel function, while the second phase uses the whole dataset to refine the coefficients. During the implementation of our method, the mean-field equation plays a key role in reformulating the task of extracting the interaction kernels into a learnable regression problem. We demonstrate the outstanding performance of our approach through extensive numerical examples, including interacting particle systems with a cubic potential, power-law repulsion-attraction potential, piecewise linear potential, as well as a two-dimensional radially symmetric potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00714 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extracting Interaction Kernels for Many-Particle Systems by a Two-Phase Approach Shi, Yangxuan Yang, Wuyue Hong, Liu Computational Physics Adaptation and Self-Organizing Systems Fluid Dynamics This paper presents a two-phase method for learning interaction kernels of stochastic many-particle systems. After transforming stochastic trajectories of every particle into the particle density function by the kernel density estimation method, the first phase of our approach combines importance sampling with an adaptive threshold strategy to identify key terms in the kernel function, while the second phase uses the whole dataset to refine the coefficients. During the implementation of our method, the mean-field equation plays a key role in reformulating the task of extracting the interaction kernels into a learnable regression problem. We demonstrate the outstanding performance of our approach through extensive numerical examples, including interacting particle systems with a cubic potential, power-law repulsion-attraction potential, piecewise linear potential, as well as a two-dimensional radially symmetric potential. |
| title | Extracting Interaction Kernels for Many-Particle Systems by a Two-Phase Approach |
| topic | Computational Physics Adaptation and Self-Organizing Systems Fluid Dynamics |
| url | https://arxiv.org/abs/2501.00714 |