Accelerating Multi-Objective Collaborative Optimization of Doped Thermoelectric Materials via Artificial Intelligence

TL;DR

This work tackles the challenge of discovering high-$zT$ doped thermoelectric materials by introducing WaveTENet, a wavelet-enhanced deep network that predicts five transport properties directly from chemical formulas. It couples WaveTENet with NSGA-III to enable multi-objective inverse design, balancing large nonlinear dopant effects with practical constraints and providing interpretability via SHAP analyses. The approach delivers state-of-the-art predictive accuracy, demonstrates transferability to a new dataset, and identifies Pareto-optimal candidates, including BiSe- and Bi$_2$Te$_3$-derived systems, with experimental validation showing promising but not yet optimal $zT$ values. The framework offers a data-efficient route to navigate vast dopant-host compositional spaces and can be extended to other material domains, thereby accelerating materials discovery and design.

Abstract

The thermoelectric performance of materials exhibits complex nonlinear dependencies on both elemental types and their proportions, rendering traditional trial-and-error approaches inefficient and time-consuming for material discovery. In this work, we present a deep learning model capable of accurately predicting thermoelectric properties of doped materials directly from their chemical formulas, achieving state-of-the-art performance. To enhance interpretability, we further incorporate sensitivity analysis techniques to elucidate how physical descriptors affect the thermoelectric figure of merit (zT). Moreover, we establish a coupled framework that integrates a surrogate model with a multi-objective genetic algorithm to efficiently explore the vast compositional space for high-performance candidates. Experimental validation confirms the discovery of a novel thermoelectric material with superior $zT$ values in the medium-temperature regime.

Figures (9)

• Figure 1: The proposed deep learning–optimization algorithm coupled framework is designed for multi-objective collaborative optimization in the design of thermoelectric materials with high $zT$ values. (a) Two datasets are employed separately for deep learning training and transfer learning testing, both derived from experimental sources. (b) Digitized descriptors are used to represent different materials. (c) Deep learning is utilized to construct the mapping between descriptors and thermoelectric performance. (d) The Pareto-front is adopted to select a subset of candidate materials with optimal performance from the dataset. (e) The optimization algorithm is applied to explore promising virtual samples from the vast compositional space. (f) Upon completion of the optimization iterations, the most promising candidate(s) are selected for experimental characterization and mechanistic investigation.
• Figure 2: $k$-means clustering and t-SNE 2D visualization. (a) All samples at 600 K are divided into 9 clusters, from $C_0$ to $C_8$, distinguished by different scatter plot markers. (b) and (c) show local zoom-ins of $C_0$ and $C_2$, respectively, with color mapping indicating the $zT$ values of the samples.
• Figure 3: Architecture of WaveTENet. (a) The network is composed of three main components: the input block, the stacked residual branch, and the output block. (b) The structure of the deep residual module. The modules depicted as rectangles with embedded circles represent linear layers.
• Figure 4: The scatter plots of WaveTENet’s predictions for $S$, $\sigma$, PF, $\kappa$, and $zT$ are presented. Each point in the plots corresponds to a sample from the dataset, with the $x$-axis representing the ground truth (experimentally measured values) and the $y$-axis indicating the model's predicted values. The black dashed diagonal line denotes the ideal case where predictions perfectly match the true values. The solid blue and red lines represent the regression fits for the training and test sets, respectively.
• Figure 5: Performance comparison between WaveTENet and CatBoost on the transfer learning dataset. In the prediction tasks of PF, $\kappa$, and $zT$, WaveTENet consistently outperforms CatBoost in accuracy.