Solving the Cosmological Vlasov-Poisson Equations with Physics-Informed Kolmogorov-Arnold Networks
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| Format: | Preprint |
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2025
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| _version_ | 1866915671590305792 |
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| author | Cerardi, Nicolas Tolley, Emma Mishra, Ashutosh |
| author_facet | Cerardi, Nicolas Tolley, Emma Mishra, Ashutosh |
| contents | Cold dark matter (CDM) evolves as a collisionless fluid under the Vlasov-Poisson equations, but N-body simulations approximate this evolution by discretising the distribution function into particles, introducing discreteness effects at small scales. We present a physics-informed neural network approach that evolves CDM fields without any use of N-body data or methods, using a Kolmogorov-Arnold network (KAN) to model the continuous displacement field for one-dimensional halo collapse. Physical constraints derived from the Vlasov-Poisson equations are embedded directly into the loss function, enabling accurate evolution beyond the first shell crossing. The trained model achieves sub-percent errors on the residuals even after seven shell crossings and matches N-body results while providing a resolution-free representation of the displacement field. In addition, displacement errors do not grow over time, a very interesting feature with respect to N-body methods. It can also reconstruct initial conditions through backward evolution when sufficient final-state information is available. Although current runtimes exceed those of N-body methods, this framework offers a new route to high-fidelity CDM evolution without particle discretisation, with prospects for extension to higher dimensions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_11795 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solving the Cosmological Vlasov-Poisson Equations with Physics-Informed Kolmogorov-Arnold Networks Cerardi, Nicolas Tolley, Emma Mishra, Ashutosh Cosmology and Nongalactic Astrophysics Cold dark matter (CDM) evolves as a collisionless fluid under the Vlasov-Poisson equations, but N-body simulations approximate this evolution by discretising the distribution function into particles, introducing discreteness effects at small scales. We present a physics-informed neural network approach that evolves CDM fields without any use of N-body data or methods, using a Kolmogorov-Arnold network (KAN) to model the continuous displacement field for one-dimensional halo collapse. Physical constraints derived from the Vlasov-Poisson equations are embedded directly into the loss function, enabling accurate evolution beyond the first shell crossing. The trained model achieves sub-percent errors on the residuals even after seven shell crossings and matches N-body results while providing a resolution-free representation of the displacement field. In addition, displacement errors do not grow over time, a very interesting feature with respect to N-body methods. It can also reconstruct initial conditions through backward evolution when sufficient final-state information is available. Although current runtimes exceed those of N-body methods, this framework offers a new route to high-fidelity CDM evolution without particle discretisation, with prospects for extension to higher dimensions. |
| title | Solving the Cosmological Vlasov-Poisson Equations with Physics-Informed Kolmogorov-Arnold Networks |
| topic | Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2512.11795 |