Conformal deep learning models pion form factor from first principles

Researchers have developed a Physics-Informed Neural Network (PINN) utilizing a conformal z-plane to extract the pion electromagnetic form factor $F_{\pi}(s)$. This novel approach integrates fundamental S-matrix principles like analyticity and dispersion relations directly into the neural network's loss function, ensuring adherence to first principles while using data as constraints. The method addresses known deep-learning optimization failures by mapping the complex plane to a unit disk, which bounds the Hessian norm and prevents Neural Tangent Kernel spectral starvation. The study incorporates data from $e^+e^-$ scattering and $\tau$-decay, yielding model-independent estimates for the pion charge radius, $\langle r_{\pi}^2 \rangle$, the $\rho(770)$ pole parameters, and the two-pion contribution to the muon anomalous magnetic moment, $a_{\mu}^{\pi\pi}$. AI

IMPACT Novel application of PINNs to fundamental physics problems, potentially improving accuracy and reducing model dependence in scientific research.

RANK_REASON This is a research paper detailing a novel application of Physics-Informed Neural Networks to a specific problem in high energy physics. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.LG →

• $a_{\mu}^{\pi\pi}$
• $ au$-decay
• $e^+e^-$
• $F_{\pi}(s)$
• $(g-2)_{\mu}$
• Monalisa Patra Dr.
• Physics-Informed Neural Network
• QCD

• paper
• infra

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