Source-linked AI summary
Machine Learning Models for the Lattice Thermal Conductivity Prediction of Inorganic Materials
Lihua Chen, Huan Tran, Rohit Batra, Chiho Kim, Rampi Ramprasad
TL;DR
Predicting κL matters because applications seek different conductivity ranges, while prior ML training data can diverge from experimental values and key features are difficult to identify. This work trains a Gaussian process model using experimental inorganic-material data and engineered features; its performance is comparable to semi-empirical models, and it identifies feature relationships relevant to thermal transport.
Problem
Prior ML models trained on DFT-computed κL can diverge from experimental values, especially for high-κL solids, and identifying key features governing κL remains difficult.
Source: §1 · p. 3Method
The study curates experimental κL data for inorganic compounds, engineers material features, and trains Gaussian process regression models.
Source: §2.2 · p. 4, §4 · p. 9Results
GPR-RFE achieved an AFD of 1.36 ±0.03, comparable to 1.38 for Slack and 1.46 for Debye-Callaway models.
Source: §3 · p. 8Takeaways & Limitations
The authors conclude that the model may support screening inorganic materials for desired κL and identify bulk modulus and mean average bond length as related to κL.
Source: §3 · p. 6, §4 · p. 9The dataset is concentrated in space groups 225 and 216, so the model relies on space-group number to distinguish structures; broader space-group data may address this limitation.
Source: §3 · p. 9
Abstract
from arXiv · showhide
The lattice thermal conductivity ($\kappa_{\rm L} $) is a critical property of thermoelectrics, thermal barrier coating materials and semiconductors. While accurate empirical measurements of $\kappa_{\rm L} $ are extremely challenging, it is usually approximated through computational approaches, such as semi-empirical models, Green-Kubo formalism coupled with molecular dynamics simulations, and first-principles based methods. However, these theoretical methods are not only limited in terms of their accuracy, but sometimes become computationally intractable owing to their cost. Thus, in this work, we build a machine learning (ML)-based model to accurately and instantly predict $\kappa_{\rm L}$ of inorganic materials, using a benchmark data set of experimentally measured $\kappa_{\rm L} $ of about 100 inorganic solids. We use advanced and universal feature engineering techniques along with the Gaussian process regression algorithm, and compare the performance of our ML model with past theoretical works. The trained ML model is not only helpful for rational design and screening of novel materials, but we also identify key features governing the thermal transport behavior in non-metals.
1. Introduction
Applications need materials with different lattice thermal conductivities, but established computational approaches face accuracy, input-availability, or cost constraints. Prior ML work also faces a gap between computed training values and experiments, motivating an experimentally benchmarked model that can identify relevant features.
1. Introduction
- Thermoelectrics favor low κL, whereas semiconductors need high κL to avoid overheating, making targeted thermal-conductivity prediction useful across applications.Thermal barrier coatings are another application for which κL is a critical design parameter.Source: §1 · pp. 1–2
- Slack-model predictions depend on Debye temperature and Gruneisen parameter inputs whose uncertainty can impair accuracy, while those inputs may be unavailable for new materials.Green-Kubo methods require reliable atomistic force fields or costly convergence calculations, and first-principles BTE calculations are generally restricted to small unit cells by cost.Source: §1 · p. 2
- Earlier ML models trained on DFT-computed κL face discrepancies from experimental values, especially for high-κL solids, and identifying governing features remains difficult.Source: §1 · pp. 2–3
- The study builds an ML model from 100 empirically measured inorganic compounds, using feature selection and Gaussian process regression to predict κL and assess uncertainty for new materials.The dataset spans three orders of magnitude, and the authors propose screening materials with targeted κL as a use for the model.Source: §1 · p. 3
2. Technical Details
The technical workflow curates a diverse experimental dataset, constructs and reduces material descriptors, then trains and evaluates Gaussian process models with cross-validation and separate held-out cases.
2.1. Data set
- 100 single-crystal inorganic materials, including 81 binary and 19 ternary compounds, span κL values of 0.4–760 Wm−1K−1; five cases were held out from training.The target was log(κL), and reported literature values for a material were averaged when multiple values were available.Source: §2.1 · p. 4
2.2. Feature set and dimensionality reduction
- The initial 63-dimensional feature vector combined elemental, structural, valence-electron, bulk-modulus, and space-group descriptors; RFE reduced it to 29 features.Random-forest importance identified nearly 40 features, most consistent with those retained by RFE; a bulkmodulus/density feature was derived from those two features.Source: §2.2 · pp. 4–5, §2.3 · p. 6
2.3. Gaussian Process Regression
- GPR used an RBF covariance function, with hyperparameters fitted by log-likelihood maximization and 5-fold cross-validation to limit overfitting.Learning-curve RMSEs were averaged over 100 random training/test splits; five separate held-out materials were reserved for evaluation.Source: §2.3 · pp. 5–6
3. Results and Discussion
The GPR-RFE model’s average factor difference is comparable to those of the Slack and Debye-Callaway models, while using readily accessible chemical and structural features. Feature trends, learning curves, and predictions for five unseen solids further characterize its performance and scope.
3. Results and Discussion
- Bulk modulus and bulk modulus/density track log(κ_L) positively, mean average bond length inversely, while density alone and mean atomic mass are weaker indicators.The authors connect the bulk modulus/density trend to group velocity and the bond-length trend to stronger bond anharmonicity for shorter bonds.Source: §3 · p. 6
- At about 80% of the data (76 points), GPR-RFE test RMSE converged to 0.28 and train RMSE to 0.18; test-set R2 was at least 0.93 in both illustrated cases.Recursive feature elimination improved test performance over the initial 63-feature GPR model.Source: §3 · pp. 6, 8, Figure 4 · p. 7
- On five unseen inorganic solids spanning different space groups, GPR-RFE predictions performed well, while high uncertainty for Ca5Al2Sb6 signaled an extrapolative case.The caption identifies the unseen examples and shows parity plots using 29 features and, after removing space-group number, 28 features.Source: Figure 4 · p. 7, §3 · pp. 8–9
- AFD was 1.36 ±0.03 for GPR-RFE, compared with 1.38 for Slack and 1.46 for Debye-Callaway.The ML model uses chemical and structural features derived directly from material identity, rather than features that are more difficult to obtain for the semi-empirical models.Source: Table 2 · p. 8, §3 · p. 8
- The model is more suitable for defect-free inorganic materials; its accuracy is limited for defective, allotropic, and intermetallic materials.The authors note that more diverse training data could help address limitations, including through active learning.Source: §3 · p. 9
4. Conclusion
The conclusion presents a general ML model for inorganic-solid κL that is faster than traditional physics-based computational methods and at par or more accurate. It also reports key-feature identification and potential uses in materials screening and understanding heat transport.
4. Conclusion
- The model is faster than traditional physics-based computational methods and is at par or more accurate.Source: §4 · p. 9
- The work curates experimental κL values for 100 inorganic compounds, engineers features with Matminer, and trains a Gaussian Process Regression model.Source: §4 · p. 9
- The model's accuracy is comparable to past semi-empirical models, and the work identifies key features governing κL.Source: §4 · p. 9
- The authors say the model may support rational design and screening of materials with desired κL and understanding heat transport in inorganic solids.Source: §4 · p. 9