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Kolmogorov-Arnold Wavefunctions
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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.
Forward citations
Cited by 2 Pith papers
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Neural Wavefunctions in Quantum Field Theory I: Asymptotic Freedom
Neural network wavefunctions enable variational calculations that reproduce asymptotic freedom, dynamical mass generation, and step-scaling in the 2D nonlinear sigma model.
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Neural Wavefunctions in Quantum Field Theory I: Asymptotic Freedom
Neural-network wavefunctions enable variational Monte Carlo calculations that reproduce asymptotic freedom, dynamical mass generation, and the step-scaling function in the 2D nonlinear sigma-model.
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