Thermal Conductivity Predictions with Foundation Atomistic Models

Abstract

Advances in machine learning have led to the development of foundation models for atomistic materials chemistry, enabling quantum-accurate descriptions of interatomic forces across chemically diverse compounds at reduced computational cost. Hitherto, the accuracy and utility of these models have been assessed relying on descriptors based on formation energies or idealized harmonic atomic vibrations. Yet, the rigorous and physically interpretable quantification of their capability to describe both realistic anharmonic atomic dynamics and technologically relevant observables remains a pressing problem. Here, we address this problem, leveraging the Wigner formulation of heat transport and the Grüneisen approach to thermal expansion to connect the atomic-physics awareness of foundation models to their utility in predicting experimentally observable thermomechanical properties, presenting standards and fine-tuning protocols needed to achieve first-principles accuracy. We apply our framework to a database of 103 solids with diverse compositions and structures, demonstrating that it overcomes the major bottlenecks of current methods for designing heat-management materials -- high cost, limited transferability, or lack of physics awareness -- and its potential to discover materials for next-gen technologies ranging from thermal insulation to neuromorphic computing.

Figures (16)

• Figure 1: Conductivity (left) and Grüneisen parameter (right) at 300 K from DFT-PBE and MACE-MP-0 large, for 103 compounds taken from the phononDB-PBE database, which have rocksalt (green), zincblende (orange), or wurtzite (blue) structure. The solid line indicates perfect agreement and the dashed lines discrepancies of a factor of 2. The arrows highlight materials discussed in detail later. Inset, distribution of relative deviations between the conductivities predicted by DFT-PBE and MACE-MP-0. The color gradient in the left panel shows the transition from the WTE regime where heat transport occurs through both propagation and tunneling mechanisms (red) to the semiclassical propagation-dominated BTE regime (white).
• Figure 2: Phonon dispersion, linewidth & mode-Grüneisen distributions, along with macroscopic conductivity & Grüneisen parameter for wurtzite BeO (panel a), zincblende BeTe (b), and rocksalt LiBr (c). DFT-PBE values are computed using the data from Refs. phono3pyseko_prediction_2015, while 'MACE' values are computed using the MACE-MP-0 fMLPbatatia_foundation_2024. For the DFT-PBE phonons, we show the effect of considering (red) or not (green) the long-range non-analytical contribution (NAC); MACE-MP-0 does not fully account for NAC (see text). In the frequency-linewidths distributions at 300 K, we resolve the anharmonic ($\Gamma_a$) and isotopic ($\Gamma_i$) parts of the linewidths; the markers' areas are proportional to the contribution of the given phonon mode to the conductivity. Similarly, the mode Grüneisen parameter distribution against phonon energy is evaluated at 300K with marker size describing the contribution of the modes to the macroscopic Grüneisen parameter.
• Figure 3: SRE & SRME errors on: conductivity (a), Grüneisen parameter (b), and their correlation (c) in 103 chemically and structurally diverse compounds. For conductivity (panel a), large discrepancies between DFT-PBE and mp-fMLP (MACE-MP-0) on microscopic, single-phonon conductivity contributions are described by large conductivity SRME (\ref{['eq:SRME_mode_kappa']}). The microscopic SRME metric is more informative than the macroscopic SRE metric, since it captures the cases where microscopic (in)accuracy translates into macroscopic (in)accuracy --- e.g., in BeO (LiBr) a low (high) SRME implies a low (high) SRE --- and, because SRME is a sum of non-negative contributions, it detects also cases in which compensation of microscopic errors occurs (e.g., BeTe exhibits high SRME but low SRE). For Grüneisen parameter (panel b), the behavior of macroscopic (SRE, Eq. (\ref{['eq:SRE_gamma']})) and microscopic (SRME, Eq. (\ref{['eq:SRME_mode_gamma']})) errors is more complex due to the possibility of having both positive and negative microscopic contributions, which can lead to both cancellation of single-phonon errors and amplification of macroscopic relative errors when large negative and positive contributions coexist, as discussed in the text. However, most of the materials studied here (b) display large SRME and positive microscopic contributions to the Grüneisen parameters, implying that cancellation of errors can be detected, as for the conductivity, by large SRME and low SRE. The insets in panels a and b show materials with very low SRE, while panel c displays the comparison of SRME in thermal conductivity and Grüneisen parameter, demonstrating no clear correlation.
• Figure 4: Performance of mp-fMLPs in predicting thermal conductivity and Grüneisen parameter.a and c violin plots for the Symmetric Relative Difference (SRD) in the total Wigner conductivity (\ref{['eq:SPD_kappa']}) and in the total Grüneisen parameter, respectively, for the materials in phononDB-PBE simulated with ORB-v1-MPtrajorb_github, SevenNetpark_scalable_2024, MACE-MP-0batatia_foundation_2024, CHGNetdeng_chgnet_2023, M3GNetchen_universal_2022. b and d are $\text{SRME}[\{\mathcal{K}(\bm{q})_s\}]$ and $\text{SRME}[\{\mathcal{G}(\bm{q})_s\}]$, respectively, in the same materials database. In all panels, the medians are marked with white scatter points, the widths of the boxes represent the interquartile range, and the whiskers show the range of data points without outliers. The pie charts in e display the number of compounds with non-negative frequencies that retained or not the correct crystal symmetry after unconstrained relaxation (green and blue, respectively); we also show whether structural instabilities (imaginary phonon frequencies) were observed in relaxations performed with (orange) or without (red) enforcing symmetries. Unstable structures with imaginary phonon frequencies were included considering $\kappa_{\mathrm{fMLP}} = 0$ and $\gamma_{\mathrm{fMLP}} = 0$, i.e., SRD${=}-2$, SRME${=}2$.
• Figure 5: Achieving first-principles accuracy on LiBr's vibrational & thermal properties through fine-tuning. Top of panel a (b), conductivity (Grüneisen parameter) as a function of number of DFT-PBE supercell frames (see text) in the fine-tuning dataset, and number of fine-tuning epochs. The MACE zero-shot prediction for conductivity (Grüneisen parameter) is purple; performing fine-tuning on one single DFT frame and 100 fine-tuning epochs yields compatibility within 7% for conductivity (5.5% for Grüneisen) with the reference DFT-PBE value (green), while with datasets containing 3 frames with rattling and volume variations yields compatibility within 2% for conductivity (0.5% for Grüneisen) at 200 epochs. The bottom of panel a (b) show that SRME$[\{\mathcal{K}(\bm{q})_s\}]$ (SRME$[\{\mathcal{G}(\bm{q})_s\}]$) converges to a minimum upon increasing the number of epochs, and larger datasets yield faster convergence. After fine-tuning on 3 frames for 200 epochs, remarkable agreement between fine-tuned MACE and DFT-PBE is observed for: specific heat (c), phonons (d), microscopic phonon energy-linewidth (f) and energy-mode Grüneisen parameter distributions (h), macroscopic $\kappa(T)$ (e) and $\gamma(T)$ (g). We note that after fine-tuning, our WTE $\kappa(T)$ predictions agree with experimentshakansson_thermal_1989, as well as with predictions from ab-initio (PBE) molecular-dynamics (aiMD) at 300 Kknoop_anharmonicity_2023.