A public database of thermoelectric materials and system-identified material representation for data-driven discovery

Thermoelectric materials, capable of converting heat energy into electrical energy and vice-versa, have gained significant attention for applications in energy harvesting, thermoelectric cooling, and power generation. The discovery of novel high-performance thermoelectric materials is challenging due to the structural diversity and complexity, especially with alloys and dopants. Density Functional Theory (DFT) is computationally expensive for complex materials. Machine learning (ML) offers a promising alternative, with Graph Neural Networks (GNNs) demonstrating strong prediction capabilities using crystal structures. However, crystal structures for doped materials are often unavailable. Existing ML approaches, like Roost and DopNet, address chemical composition-based prediction but have limitations in handling the complexities of thermoelectric materials and extrapolation to unseen materials. This research aims to overcome these limitations by creating a comprehensive public dataset and a novel material descriptor for improved data-driven discovery.

Several machine learning methods have been developed to predict material properties from their chemical compositions. Roost, employing elemental graphs, achieved state-of-the-art accuracy in band gap prediction for pristine materials. DopNet, using a material space embedding approach, improved predictions for alloy and doped materials. However, these methods often struggle with the complexities of thermoelectric materials where different material groups have different thermodynamics. Other neural network and ensemble methods have also been explored for thermoelectric property prediction, but a public database and a dedicated descriptor for extrapolation to discover new materials were lacking prior to this work.

The researchers constructed the ESTM dataset, a public database of experimentally synthesized thermoelectric materials (ESTM) and their thermoelectric properties, comprising 5205 experimental observations covering 880 unique materials and 65 elements. The dataset includes five experimentally measured properties: Seebeck coefficient, electrical conductivity, thermal conductivity, power factor, and figure of merit (ZT). To predict thermoelectric properties from chemical compositions, six machine learning methods were evaluated using k-fold cross-validation: Ridge regression, K-nearest neighbor regression, Support vector regression, Gaussian process regression, Fully-connected neural network, and XGBoost. Chemical compositions were converted to numerical vectors using sparse encoding. For interpolation, XGBoost significantly outperformed other methods. To address extrapolation challenges, the researchers developed the System-Identified Material Descriptor (SIMD). SIMD involves three steps: (1) Material cluster generation, grouping similar materials based on chemical composition; (2) Material cluster characterization, calculating system vectors (representing relationships between materials and properties) and target statistics vectors (summarizing property distributions) for each cluster using the least-squares method; (3) System-identified feature generation, creating material representations by combining atomic features, input conditions, and weighted sums of system and target statistics vectors from the nearest clusters (using KNN in an anchor space). Transfer learning was applied using the Starry dataset as a source dataset, augmenting the training dataset and utilizing the SIMD descriptor in the training process. The effectiveness of SIMD was evaluated through extrapolation tasks and high-throughput screening experiments focusing on ZT prediction for unexplored materials. High-throughput screening was conducted using different ZT thresholds and temperature ranges, evaluating performance using the F1-score. Finally, virtual dopant spaces were explored to identify promising dopants for a host material (Bi0.5Sb1.5Te3) using the trained models. The hyperparameter *K* (number of nearest material clusters) was also analyzed to determine its influence on prediction accuracy. A case study on the Mg1-xLixGe0.9Si0.1 system is presented to illustrate how SIMD addresses false positive predictions.

The ESTM dataset proved effective in training highly accurate machine learning interpolation models. XGBoost achieved R²-scores greater than 0.9 for all four properties (Seebeck coefficient, electrical conductivity, thermal conductivity, and ZT), significantly outperforming other methods. The SIMD descriptor dramatically improved extrapolation capabilities. In predicting ZT of materials from unseen material groups, the R²-score increased from 0.13 (XGBoost without SIMD) to 0.71 (XGBoost with SIMD). High-throughput screening using SIMD-enhanced models (SXGBt) significantly reduced false positives. For a target ZT ≥ 1.5, the F1-score improved from 0.49 (XGBt) to 0.61 (SXGBt), decreasing false positives by approximately 50%. The improvement in reducing false positives was consistent across various temperature ranges. Virtual dopant space exploration identified promising dopants (Ag and Ti) for Bi0.5Sb1.5Te3, aligning with experimental findings. Analysis of hyperparameter *K* showed consistent high performance across various values, particularly in larger training datasets. The case study highlighted SIMD's ability to mitigate false positives by generating distinct representations for materials with similar sparse encodings but distinct chemical properties and belonging to different clusters. The study also shows the integration of SIMD with global search methods for materials discovery.

The creation of the ESTM dataset and the development of the SIMD descriptor represent significant advancements in data-driven thermoelectric materials discovery. The high accuracy achieved in interpolation tasks validates the dataset's quality and the models' effectiveness in predicting properties within known material spaces. The substantial improvement in extrapolation, particularly with SIMD, is crucial for exploring novel materials. The reduction in false positives during high-throughput screening translates to reduced experimental costs and increased efficiency in materials discovery. The successful prediction of promising dopants demonstrates the potential for using SIMD-based models for guided materials design. This work paves the way for more efficient and cost-effective discovery of high-performance thermoelectric materials.

This research successfully developed and validated a comprehensive workflow for data-driven thermoelectric material discovery. The public ESTM dataset offers a valuable resource for the community. The novel SIMD descriptor effectively addresses extrapolation limitations inherent in conventional machine learning approaches. The significant reduction in false positives during high-throughput screening improves the efficiency and cost-effectiveness of materials discovery. Future work could focus on expanding the ESTM dataset, refining the SIMD descriptor, and integrating SIMD with other global optimization methods to further accelerate the discovery of novel high-performance thermoelectric materials.

The accuracy of the predictions depends heavily on the quality and completeness of the experimental data in the ESTM dataset. The SIMD's performance might be affected by the choice of hyperparameters, particularly *K*, although the study demonstrated robustness across various values. The study primarily focused on ZT prediction; applying SIMD to predict other thermoelectric properties could be explored in future work. The generalizability of the SIMD method to other material systems beyond thermoelectrics would need further investigation. The study relies on existing experimental data and does not incorporate theoretical calculations.