[Paper Review] Accelerating Materials-Space Exploration for Thermal Insulators by Mapping Materials Properties via Artificial Intelligence

Thomas A. R. Purcell, Matthias Scheffler+2 more|arXiv (Cornell University)|Apr 27, 2022

Machine Learning in Materials Science4 citations

TL;DR

This paper presents a symbolic regression and sensitivity analysis framework that accelerates materials discovery for thermal insulators by deriving an explainable, analytic model for lattice thermal conductivity using only 75 experimental data points. The method identifies key material properties—such as molar volume, Debye temperature, and phonon anharmonicity—enabling hierarchical screening of 732 materials and identifying 80 ultra-insulating candidates with κ < 1 W/mK at 300 K.

ABSTRACT

Reliable artificial-intelligence models have the potential to accelerate the discovery of materials with optimal properties for various applications, including superconductivity, catalysis, and thermoelectricity. Advancements in this field are often hindered by the scarcity and quality of available data and the significant effort required to acquire new data. For such applications, reliable surrogate models that help guide materials space exploration using easily accessible materials properties are urgently needed. Here, we present a general, data-driven framework that provides quantitative predictions as well as qualitative rules for steering data creation for all datasets via a combination of symbolic regression and sensitivity analysis. We demonstrate the power of the framework by generating an accurate analytic model for the lattice thermal conductivity using only 75 experimentally measured values. By extracting the most influential material properties from this model, we are then able to hierarchically screen 732 materials and find 80 ultra-insulating materials.

Motivation & Objective

• To overcome data scarcity in materials discovery for thermal insulators by developing a reliable, explainable AI model that generalizes beyond existing data.
• To identify the most influential material properties governing lattice thermal conductivity using symbolic regression and sensitivity analysis.
• To guide future data collection by predicting regions of materials space most likely to yield ultra-low thermal conductivity materials.
• To create a surrogate model that combines the accuracy of machine learning with the interpretability of analytical physics-based models.
• To enable high-throughput screening of materials for thermal insulation by prioritizing candidates based on predictive rules derived from the model.

Proposed method

• Employing symbolic regression via SISSO (Sparse Identification of Nonlinear Dynamics) to derive an explicit, analytic expression for lattice thermal conductivity (κ_L) from 75 experimental data points.
• Using Gaussian copulas to model the joint probability distribution of input features (e.g., molar volume, Debye temperature, phonon anharmonicity) to enable robust sensitivity analysis.
• Applying global sensitivity analysis (e.g., Sobol’ indices) to rank feature importance and extract physical insights into the dominant mechanisms governing thermal transport.
• Integrating uncertainty quantification via ensemble sampling to estimate prediction reliability across materials space.
• Validating the model’s predictive power by comparing expected κ_L values against known experimental data across diverse crystal structures.
• Using the derived model to perform hierarchical screening of 732 materials, prioritizing those with low predicted κ_L based on key descriptors.

Experimental results

Research questions

• RQ1 Can a symbolic regression model trained on only 75 experimental data points accurately predict lattice thermal conductivity across diverse crystalline materials?
• RQ2 Which material properties are most influential in determining ultra-low thermal conductivity, and how do they interplay?
• RQ3 How can sensitivity analysis and uncertainty quantification guide future data collection to maximize discovery efficiency in sparse materials spaces?
• RQ4 To what extent can an explainable AI model outperform black-box ML models in extrapolating to novel materials with extreme properties?
• RQ5 Can the derived model identify new ultra-insulating materials with κ_L < 1 W/mK at 300 K, and what physical conditions enable such behavior?

Key findings

• The symbolic regression model achieved high predictive accuracy for lattice thermal conductivity using only 75 experimental data points, with a mean absolute error comparable to state-of-the-art kernel-based methods.
• The most influential properties for low κ_L were identified as molar volume (V_m), Debye temperature (Θ_D), phonon anharmonicity (ω_Γ,max), and ionicity (σ^A), with strong non-linear interactions.
• Sensitivity analysis revealed that materials with high molar volume, low Debye temperature, and high phonon anharmonicity are most likely to exhibit ultra-low thermal conductivity.
• The model successfully predicted 80 materials with κ_L < 1 W/mK at 300 K from a screening of 732 candidates, significantly expanding the known set of thermal insulators.
• The framework’s uncertainty estimates highlighted regions of materials space where predictions are less reliable, enabling targeted future data acquisition.
• The model’s analytic form revealed a counterintuitive inverse relationship between κ_L and atomic volume (V_a), which is explained by its strong negative correlation with Debye temperature (Θ_a), underscoring the importance of correlated descriptors.