Emulators for Scarce and Noisy Data: Application to Auxiliary-Field Diffusion Monte Carlo for Neutron Matter

TL;DR

The paper addresses the EOS of pure neutron matter, quantified by the energy per particle $E/A$, and the propagation of EFT truncation uncertainties from chiral EFT low-energy couplings (LECs) to the EOS, which is computationally prohibitive with direct AFDMC. It introduces a parametric matrix model (PMM) emulator for AFDMC, constructing an affine Hamiltonian $\,\hat{H}(\{c_i\}) = H_0 + \sum_i c_i H_i$ that maps LEC posteriors to $E/A$ across densities from 1 to 3 $n_{sat}$. PMMs enable rapid propagation of LEC posteriors to $E/A$ with about 250k samples, after roughly 22.4 million CPU-hours of training, producing EOS uncertainty bands that are slightly skewed rather than Gaussian. At $2n_{sat}$, the inferred $p_{\beta}(2n_{sat}) = 16.8^{+6.0}_{-5.7}$ MeV fm$^{-3}$, consistent with GW170817 constraints $p_{\beta}(2n_{sat}) = 21.8^{+16.9}_{-10.6}$ MeV fm$^{-3}$. This framework enables direct inference of nuclear-interaction couplings from multi-messenger neutron-star observations.

Abstract

Understanding the equation of state (EOS) of pure neutron matter is necessary for interpreting multimessenger observations of neutron stars. Reliable data analyses of these observations require well-quantified uncertainties for the EOS input, ideally propagating uncertainties from nuclear interactions directly to the EOS. This, however, requires calculations of the EOS for a prohibitively large number of nuclear Hamiltonians, solving the nuclear many-body problem for each one. Quantum Monte Carlo methods, such as auxiliary-field diffusion Monte Carlo (AFDMC), provide precise and accurate results for the neutron matter EOS, but they are very computationally expensive, making them unsuitable for the fast evaluations necessary for uncertainty propagation. Here, we employ parametric matrix models to develop fast emulators for AFDMC calculations of neutron matter and use them to directly propagate uncertainties of coupling constants in the Hamiltonian to the EOS. As these uncertainties include estimates of the effective field theory truncation uncertainty, this approach provides robust uncertainty estimates for use in astrophysical data analyses. This Letter will enable novel applications such as using astrophysical observations to put constraints on coupling constants for nuclear interactions.

Figures (12)

• Figure 1: Full propagated error bands for the energy per particle of PNM as function of number density at 68% and 90% confidence intervals. The red band shows the mean and 68% uncertainty of Ref. Tews:2024owl using a Gaussian Process error prescription Drischler:2020hwi.
• Figure 1: Accuracy for reproducing eigenvalues of a randomly generated 10-dimensional eigenvalue equation. We show the logarithm of the relative error between the full 10-dimensional model and PMM emulation for different numbers of training points. From left to right, the PMM is trained on 5, 10, and 15 points which are shown in red. Each subsequent row increases the number of dimensions in the matrices fit starting from 2-dimensional matrices for the top row and ending with 5-dimensional matrices for the bottom row.
• Figure 2: Convergence of the relative error of the PMM reproduction of the AFDMC validation energies with the number of training points N$_{\rm train}$ for N$_{\rm dim}=1-4$ at N$^2$LO at nuclear saturation density, $n_{\rm sat}=0.16 \; \rm{fm^{-3}}$. The training and validation sets are the same for all N$_{\rm dim}$.
• Figure 2: The evolution of the average validation error as function of N$_{\rm train} = 1-100$ for N$_{\rm dim}=2$ for a toy problem with 9 control parameters.
• Figure 3: Probability density functions (PDFs) for the neutron-matter energy per particle at 5 different densities when propagating full posterior distributions for all LECs. Where available, we compare the PDFs to the previous uncertainty estimation method using Gaussian Processes Drischler:2020hwiTews:2024owl. For both distributions, we specify the mean by a vertical line.