Simulation-Based Inference of Ginzburg--Landau Parameters in Type--1.5 Superconductors

TL;DR

This paper introduces a novel method combining differentiable TDGL simulations with Simulation-Based Inference to accurately infer microscopic parameters in complex, glassy vortex patterns of Type-1.5 superconductors.

Contribution

It develops a new approach that uses neural ratio estimation with a differentiable solver to perform Bayesian inference on vortex configurations, overcoming sampling challenges.

Findings

Successfully recovers interband Josephson coupling from synthetic vortex data.

Quantifies the energy landscape's metastability and soft modes.

Demonstrates reliable parameter inference with calibrated uncertainty.

Abstract

Inferring microscopic couplings in multi-component superconductors directly from vortex configurations is a challenging inverse problem. In Type-1.5 systems, Time-Dependent Ginzburg-Landau (TDGL) dynamics generate complex, glassy vortex patterns with high metastability. We explicitly quantify this intractability by analyzing the Hessian spectrum of the energy landscape, revealing a proliferation of soft modes that hinders traditional sampling. We address this challenge by combining a differentiable TDGL solver with Simulation-Based Inference (SBI). Our approach treats the solver as a stochastic forward model mapping physical parameters ({\theta} = ({\eta}, B, {\nu})) to vortex density fields. Using Neural Ratio Estimation (NRE), we train a classifier to approximate the likelihood-to-evidence ratio and perform Bayesian inference for the interband Josephson coupling from vortex density fields. On synthetic data, the proposed method reliably recovers the coupling with calibrated uncertainty.