# Physics Informed Neural Networks for design optimisation of diamond particle detectors for charged particle fast-tracking at high luminosity hadron colliders

arXiv: https://arxiv.org/abs/2509.21123 · HTML: https://mlsanity.com/paper/2509.21123/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Builds on (most cited first, 6 of 6)

- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks](https://mlsanity.com/paper/2012.10047/) (2020)
- [Efficient training of physics-informed neural networks via importance sampling](https://mlsanity.com/paper/2104.12325/) (2021)
- [Self-scalable Tanh (Stan): Faster Convergence and Better Generalization in Physics-informed Neural Networks](https://mlsanity.com/paper/2204.12589/) (2022)

## Abstract (arXiv)

Future high-luminosity hadron colliders demand tracking detectors with extreme radiation tolerance, high spatial precision, and sub-nanosecond timing. 3D diamond pixel sensors offer these capabilities due to diamond's radiation hardness and high carrier mobility. Conductive electrodes, produced via femtosecond IR laser pulses, exhibit high resistivity that delays signal propagation. This effect necessitates extending the classical Ramo-Shockley weighting potential formalism. We model the phenomenon through a 3rd-order, 3+1D PDE derived as a quasi-stationary approximation of Maxwell's equations. The PDE is solved numerically and coupled with charge transport simulations for realistic 3D sensor geometries. A Mixture-of-Experts Physics-Informed Neural Network, trained on Spectral Method data, provides a meshless solver to assess timing degradation from electrode resistance.