Reinforcement learning-guided optimization of critical current in high-temperature superconductors

TL;DR

The paper addresses optimizing the critical current density $J_c$ in high-temperature superconductors through defect engineering, acknowledging that microstructural defects govern vortex pinning. It introduces an integrated framework that couples time-dependent Ginzburg–Landau (TDGL) simulations with deep reinforcement learning (RL), using TDGL-derived $I$–$V$ characteristics as rewards for defect-configuration optimization. The approach achieves up to $J_c ightarrow 0.6J_{dp}$ (about 60% of the depairing limit) and up to a 15-fold improvement over random defect initializations, aided by a surrogate ML predictor for $J_c$ and physics-informed defect descriptors. This work provides a scalable, physics-informed route for autonomous defect engineering in HTS and potentially other quantum materials, with implications for fusion magnets, particle accelerators, and high-field technologies.

Abstract

High-temperature superconductors are essential for next-generation energy and quantum technologies, yet their performance is often limited by the critical current density ($J_c$), which is strongly influenced by microstructural defects. Optimizing $J_c$ through defect engineering is challenging due to the complex interplay of defect type, density, and spatial correlation. Here we present an integrated workflow that combines reinforcement learning (RL) with time-dependent Ginzburg-Landau (TDGL) simulations to autonomously identify optimal defect configurations that maximize $J_c$. In our framework, TDGL simulations generate current-voltage characteristics to evaluate $J_c$, which serves as the reward signal that guides the RL agent to iteratively refine defect configurations. We find that the agent discovers optimal defect densities and correlations in two-dimensional thin-film geometries, enhancing vortex pinning and $J_c$ relative to the pristine thin-film, approaching 60\% of theoretical depairing limit with up to 15-fold enhancement compared to random initialization. This RL-driven approach provides a scalable strategy for defect engineering, with broad implications for advancing HTS applications in fusion magnets, particle accelerators, and other high-field technologies.

Figures (4)

• Figure 1: Overview of deep reinforcement learning (RL) framework for optimizing the critical current $J_c$. The Environment Module (top panel) evaluates the $J_c$ for defect configurations proposed by the agent using time-dependent Ginzburg-Landau (TDGL) equation. A surrogate machine learning model is concurrently trained to directly predict the $J_c$, reducing the need for repeated TDGL simulations. The Agent Module (bottom panel) performs defect engineering by selecting actions to update the defect configuration via proximal policy optimization (PPO) with an actor-critic network.
• Figure 2: Machine learning prediction of $J_c$ in HTS thin films. (a) Physics-informed defect descriptors used for model training, including defect-defect pair correlation $D(r)$ (top), boundary-defect correlation $B(b)$ (middle), global descriptors for defect geometry and concentration (bottom). (b) Distribution of simulated $J_c$ with increasing defect concentration $n$ with same diameter $d=2\xi$. The shaded blue area denotes the range of the standard error. Here $\xi^2$ stands for coherence length of the HTS thin film in our simulation. (c) Correlation plot for machine learning prediction of $J_c$ with defect diameter $d=2\xi$, where both training and testing results are shown.
• Figure 3: Reinforcement learning (RL) optimization of the critical current density $J_c$ for different defect diameters. (a) Evolution of the average of the most recent 100 rewards $J_c/J_{\mathrm{dp}}$ as a function of training steps for defect diameters $d = 2\xi$, $4\xi$, and $6\xi$. (b) Best-achieved $J_c$ as a function of training steps for defect diameters $d = 2\xi$, $4\xi$, and $6\xi$. The dashed lines mark the final validation using full TDGL simulations, whereas the solid curves represent the RL optimization guided by the surrogate model.
• Figure 4: Shapley Additive Explanation (SHAP) analysis of feature importance in the RL optimization model. (a) Mean SHAP values for correlation descriptors ($B_1(b)$, $B_2(b)$, $D(r)$), global descriptors ($S = \{N, \bar{x}, \bar{y}, \sigma_x, \sigma_y, N_c\}$), and the entire image ($G$), averaged over all training samples. (b) SHAP value distribution for the correlation descriptor $D(r)$. (c) SHAP value distributions for boundary–defect correlation descriptors $B_1(b)$ and $B_2(b)$. (d) SHAP value components corresponding to global descriptors.