Kolmogorov-Arnold Wavefunctions

Abstract

This work investigates Kolmogorov-Arnold network-based wavefunction ansatz as viable representations for quantum Monte Carlo simulations. Through systematic analysis of one-dimensional model systems, we evaluate their computational efficiency and representational power against established methods. Our numerical experiments suggest some efficient training methods and we explore how the computational cost scales with desired precision, particle number, and system parameters. Roughly speaking, KANs seem to be 10 times cheaper computationally than other neural network based ansatz. We also introduce a novel approach for handling strong short-range potentials-a persistent challenge for many numerical techniques-which generalizes efficiently to higher-dimensional, physically relevant systems with short-ranged strong potentials common in atomic and nuclear physics.

Comments: 19 pages, 6 figures