# Unraveling particle dark matter with Physics-Informed Neural Networks

arXiv: https://arxiv.org/abs/2502.17597 · HTML: https://mlsanity.com/paper/2502.17597/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 119 references that are in the map.
- First posted on arXiv 24 Feb 2025.

## Builds on (most cited first, 29 of 29)

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism](https://mlsanity.com/paper/2009.04544/) (2020)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [An Expert's Guide to Training Physics-informed Neural Networks](https://mlsanity.com/paper/2308.08468/) (2023)
- [Implicit Reparameterization Gradients](https://mlsanity.com/paper/1805.08498/) (2018)
- [A Living Review of Machine Learning for Particle Physics](https://mlsanity.com/paper/2102.02770/) (2021)
- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [Kolmogorov Arnold Informed neural network: A physics-informed deep learning framework for solving forward and inverse problems based on Kolmogorov Arnold Networks](https://mlsanity.com/paper/2406.11045/) (2024)
- [PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks](https://mlsanity.com/paper/2307.11833/) (2023)
- [A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications](https://mlsanity.com/paper/2010.02011/) (2020)
- [Asymptotic self-similar blow-up profile for three-dimensional axisymmetric Euler equations using neural networks](https://mlsanity.com/paper/2201.06780/) (2022)
- [Exploring the flavor structure of quarks and leptons with reinforcement learning](https://mlsanity.com/paper/2304.14176/) (2023)
- [Machine learning a manifold](https://mlsanity.com/paper/2112.07673/) (2021)
- [Reinforcement learning-based statistical search strategy for an axion model from flavor](https://mlsanity.com/paper/2409.10023/) (2024)
- [Learning the Simplicity of Scattering Amplitudes](https://mlsanity.com/paper/2408.04720/) (2024)
- [Stiff Transfer Learning for Physics-Informed Neural Networks](https://mlsanity.com/paper/2501.17281/) (2025)
- [Truth, beauty, and goodness in grand unification: a machine learning approach](https://mlsanity.com/paper/2411.06718/) (2024)
- [Solving differential equations using physics informed deep learning: a hand-on tutorial with benchmark tests](https://mlsanity.com/paper/2302.12260/) (2023)
- [Physics-informed neural networks in the recreation of hydrodynamic simulations from dark matter](https://mlsanity.com/paper/2303.14090/) (2023)
- [Learning solutions of parametric Navier-Stokes with physics-informed neural networks](https://mlsanity.com/paper/2402.03153/) (2024)
- [GRINN: A Physics-Informed Neural Network for solving hydrodynamic systems in the presence of self-gravity](https://mlsanity.com/paper/2308.08010/) (2023)
- [Seeking Truth and Beauty in Flavor Physics with Machine Learning](https://mlsanity.com/paper/2311.00087/) (2023)
- [Brain-Inspired Physics-Informed Neural Networks: Bare-Minimum Neural Architectures for PDE Solvers](https://mlsanity.com/paper/2401.15661/) (2024)
- [Approximating Rayleigh Scattering in Exoplanetary Atmospheres using Physics-informed Neural Networks (PINNs)](https://mlsanity.com/paper/2408.00084/) (2024)
- [Physics-informed neural networks viewpoint for solving the Dyson-Schwinger equations of quantum electrodynamics](https://mlsanity.com/paper/2411.02177/) (2024)
- [Accelerating lensed quasar discovery and modeling with physics-informed variational autoencoders](https://mlsanity.com/paper/2412.12709/) (2024)
- [Application of Neural Networks for the Reconstruction of Supernova Neutrino Energy Spectra Following Fast Neutrino Flavor Conversions](https://mlsanity.com/paper/2401.17424/) (2024)
- [Reconstructions of Jupiter's magnetic field using physics informed neural networks](https://mlsanity.com/paper/2403.07507/) (2024)
- [Advancing Physics Data Analysis through Machine Learning and Physics-Informed Neural Networks](https://mlsanity.com/paper/2410.14760/) (2024)

## Built on by (most cited first, 1 of 1)

- [Solving stiff dark matter equations via Jacobian Normalization with Physics-Informed Neural Networks](https://mlsanity.com/paper/2602.21988/) (2026)

## Abstract (arXiv)

We parametrically solve the Boltzmann equations governing freeze-in dark matter (DM) in alternative cosmologies with Physics-Informed Neural Networks (PINNs), a mesh-free method. Through inverse PINNs, using a single DM experimental point -- observed relic density -- we determine the physical attributes of the theory, namely power-law cosmologies, inspired by braneworld scenarios, and particle interaction cross sections. The expansion of the Universe in such alternative cosmologies has been parameterized through a switch-like function reproducing the Hubble law at later times. Without loss of generality, we model more realistically this transition with a smooth function. We predict a distinct pair-wise relationship between power-law exponent and particle interactions: for a given cosmology with negative (positive) exponent, smaller (larger) cross sections are required to reproduce the data. Lastly, via Bayesian methods, we quantify the epistemic uncertainty of theoretical parameters found in inverse problems.