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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:E=-2.2246\pm\:0.0012\)</EquationSource> </InlineEquation>MeV, a mean radius of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\:\langle r \rangle=1.96\pm\:0.03\)</EquationSource> </InlineEquation>fm, and a root-mean-square radius of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\:\langle {r}^{2}{ \rangle}^{1/2}=2.14\pm\:0.04\)</EquationSource> </InlineEquation>fm, showing excellent agreement with reference Hulthen and GFMC calculations (relative energy deviation &lt; 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 <sup>4</sup>He, and for extensions to higher chiral orders (NLO/NNLO).</p>

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KANs for deuteron wave function approximation with simplified chiral EFT

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月14日

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  • Hassan Khalili,
  • Ali Shabani,
  • Mahdi Azad Marzabadi,
  • Mahdi Khalili

摘要

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 \(\:E=-2.2246\pm\:0.0012\) MeV, a mean radius of \(\:\langle r \rangle=1.96\pm\:0.03\) fm, and a root-mean-square radius of \(\:\langle {r}^{2}{ \rangle}^{1/2}=2.14\pm\:0.04\) 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).