Approximation of the Basset force in the Maxey-Riley-Gatignol equations via universal differential equations
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910116493656064 |
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| author | Sommer, Finn Rathi, Vamika Goetschel, Sebastian Ruprecht, Daniel |
| author_facet | Sommer, Finn Rathi, Vamika Goetschel, Sebastian Ruprecht, Daniel |
| contents | The Maxey-Riley-Gatignol equations (MaRGE) model the motion of spherical inertial particles in a fluid. They contain the Basset force, an integral term which models history effects due to the formation of wakes and boundary layer effects. This causes the force that acts on a particle to depend on its past trajectory and complicates the numerical solution of MaRGE. Therefore, the Basset force is often neglected, despite substantial evidence that it has both quantitative and qualitative impact on the movement patterns of modelled particles. Using the concept of universal differential equations, we propose an approximation of the history term via neural networks which approximates MaRGE by a system of ordinary differential equations that can be solved with standard numerical solvers like Runge-Kutta methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_08194 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Approximation of the Basset force in the Maxey-Riley-Gatignol equations via universal differential equations Sommer, Finn Rathi, Vamika Goetschel, Sebastian Ruprecht, Daniel Machine Learning Numerical Analysis 68T07 (Primary) 65L05(Secondary) The Maxey-Riley-Gatignol equations (MaRGE) model the motion of spherical inertial particles in a fluid. They contain the Basset force, an integral term which models history effects due to the formation of wakes and boundary layer effects. This causes the force that acts on a particle to depend on its past trajectory and complicates the numerical solution of MaRGE. Therefore, the Basset force is often neglected, despite substantial evidence that it has both quantitative and qualitative impact on the movement patterns of modelled particles. Using the concept of universal differential equations, we propose an approximation of the history term via neural networks which approximates MaRGE by a system of ordinary differential equations that can be solved with standard numerical solvers like Runge-Kutta methods. |
| title | Approximation of the Basset force in the Maxey-Riley-Gatignol equations via universal differential equations |
| topic | Machine Learning Numerical Analysis 68T07 (Primary) 65L05(Secondary) |
| url | https://arxiv.org/abs/2604.08194 |