Kolmogorov-Arnold Wavefunctions

TL;DR

This paper explores Kolmogorov-Arnold network wavefunctions as efficient and scalable ansatz for quantum Monte Carlo, demonstrating their computational advantages and novel handling of strong short-range potentials in quantum systems.

Contribution

It introduces a new neural network-based wavefunction ansatz, the Kolmogorov-Arnold network, with improved efficiency and a novel method for strong short-range potential handling.

Findings

KAN wavefunctions are roughly 10 times cheaper computationally than other neural network ansatz.

The method scales well with system size and desired precision.

A new approach effectively manages strong short-range potentials in quantum systems.

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.