KANs for deuteron wave function approximation with simplified chiral EFT

This study introduces Kolmogorov-Arnold Networks (KANs) as an innovative framework for variational Monte Carlo (VMC) calculations of the deuteron ground state, serving as a proof of concept toward computationally demanding larger nuclear systems, using a leading-order Chiral Effective Field Theory (EFT) potential. KANs leverage trainable spline activations to provide superior flexibility in approximating short-range cusps and enhanced smoothness in high-order derivatives, directly addressing key challenges in quantum wave function representation. We employ VMC with the Adam optimizer to sample the KAN-parameterized wave function and compute energy and spatial observables. The optimized results yield a binding energy of [Formula: see text]MeV, a mean radius of [Formula: see text]fm, and a root-mean-square radius of [Formula: see text]fm, showing excellent agreement with reference Hulthen and GFMC calculations (relative energy deviation < 0.2%). Crucially, a direct performance comparison reveals that the KAN-based model converges ~ 10x faster in wall-clock time and captures the short-range cusp behavior more accurately and stably than a comparable multilayer perceptron (MLP), eliminating the need for ad hoc cusp-correction terms. These results confirm KAN's capability to accurately model the non-trivial short-range dynamics of nuclear interactions. As a proof of concept for systems where computational cost becomes a genuine bottleneck, this work establishes KAN-VMC as a highly promising, scalable approach for future ab initio studies of larger nuclear systems, such as ⁴He, and for extensions to higher chiral orders (NLO/NNLO).