Surrogate Models for Linear Response

Abstract

Linear response theory is a well-established method for exploring excitations of many-body systems. The Quasiparticle Random-Phase Approximation (QRPA), in particular, provides a powerful microscopic framework but is limited by high computational costs. This work presents two complementary QRPA surrogate models that achieve 0.1%–1% accuracy while offering a six to seven order-of-magnitude speedup over state-of-the-art solvers. These emulators enable large-scale studies and Bayesian calibration of computationally expensive physics models.

The Computational Challenge

Conventional QRPA calculations, while providing a detailed microscopic description, are computationally intensive. This expense presents a significant bottleneck for model calibration and uncertainty quantification, which require thousands or millions of model evaluations. Such studies are often intractable with high-fidelity QRPA solvers.

A Surrogate Model Approach

To address this challenge, we developed emulators that approximate the output of the full-order model with high speed and accuracy. Two distinct approaches were benchmarked:

Emulator 1 (EM1): A hybrid data- and model-driven emulator that preserves the underlying structure of the QRPA eigensystem.
Emulator 2 (EM2): A fully data-driven model using Parametric Matrix Models (PMMs) to construct a direct map from system parameters to observables.

Interactive Visualization

The 3D plot shows the Gamow-Teller strength function in ⁸⁰Ni as a function of the isoscalar pairing (V₀is) and Landau-Migdal (g₀') coupling parameters. This function is critical for modeling ß-decay processes. The visualization is fully interactive.

Key Findings

Both emulators demonstrated high performance in reproducing key nuclear observables—the electric dipole polarizability of ¹⁸⁰Yb and the ß-decay half-life of ⁸⁰Ni. Our models successfully captured highly non-linear system behaviors and variations spanning several orders of magnitude, even in extrapolation regions beyond their training data. The physics-informed EM1 showed more consistent performance between training and testing sets, highlighting the value of incorporating domain knowledge into emulator design.

Significance and Impact

This research provides a viable path for implementing QRPA-based methods in the Bayesian optimization of nuclear Energy Density Functionals and subsequent uncertainty quantification. The dramatic reduction in computational cost opens the door to scalable, large-scale studies of complex physical systems. The agnosticism of our approach suggests it can be straightforwardly extended to other problems in physics and chemistry that rely on linear-response theory.