Accelerating Phonon Thermal Conductivity Prediction by an Order of Magnitude - Machine Learning-Assisted Extraction of Anharmonic Force Constants

Aug 6, 2026

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Material phonon thermal conductivity calculations based on density functional theory require expensive evaluation of anharmonic interatomic force constants, which limits high-throughput material discovery. This work introduces a machine learning-assisted method that locally learns the potential energy surface and replaces DFT force evaluations during anharmonic force-constant extraction. Applied to 220 ternary materials, the total computational time drops from about 480,000 to under 12,000 CPU-hours, while preserving thermal conductivity prediction accuracy within 10% and reducing a key bottleneck for scalable screening.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages7

Reading Time18 min

AccessFree to download

Introduction

Background and limitations of conventional approaches

ML-based end-to-end prediction and dataset constraints

BTE framework and IFC bottlenecks

Methodology

Boltzmann transport equation and Fourier’s law formulation

Harmonic and anharmonic IFC requirements

Symmetry-related reduction of IFC counts

DFT cell setup and finite-difference extraction

Alternative force-displacement and sampling strategies

arXiv :2409 .00360v1 [ cond-mat .mtrl-sci ] 31 Aug 2024 Accelerating Phonon Thermal Conductivity Prediction by an Order of Magnitude Through Machine Learning-Assisted Extraction of Anharmonic Force Constants Yagyank Srivastava and Ankit Jain Mechanical Engineering Department, IIT Bombay, India (Dated: September 4, 2024) The calculation of material phonon thermal conductivity from density functional theory calculations requires computationally expensive evaluation of anharmonic interatomic force constants and has remained a computational bottleneck in the high-throughput discovery of materials. In this work, we present a machine learning-assisted approach for the extraction of anharmonic force constants through local learning of the potential energy surface. We demonstrate our approach on a diverse collection of 220 ternary materials for which the total computational time for anharmonic force constants evaluation is reduced by more than an order of magnitude from 480,000 cpu-hours to less than 12,000 cpu-hours while preserving the thermal conductivity prediction accuracy to within 10% . Our approach removes a major hurdle in computational thermal conductivity evaluation andwill pave the way forward for the high-throughput discovery of materials. I. INTRODUCTION The determination of phonon thermal conductivity (􀀔) is crucial in applications such as thermoelectrics, thermal barrier coating, and heat dissipation 1–4 . The conventional search of high/low-􀀔 materials is via the experimental trial-and-error approach, which is slow and resource-consuming. While data-driven structureproperty relation-based end-to-end machine learning (ML) approaches have been tested for 􀀔 prediction, these approaches are shown to have insu􀀎cient accuracy, owing mainly to the non-availability of high-quality systematic 􀀔-datasets5–7 . With recent developments in computational approaches, it is now possible to predict 􀀔 of materials via the Boltzmann transport equation (BTE) approach with input from ab initio calculations8–12 . This, however, requires interatomic force constants (IFCs) and phonon scattering rates, each of which, depending on the material system, requires several hundred to thousands of computational hours8,13 . Several ML approaches have been developed recently to accelerate the phonon scattering rates calculations 14,15 . The extraction of harmonic and anharmonic IFCs has remained a computational bottleneck in the high-throughput discovery of materials. In this work, an ML-assisted approach is presented for the extraction of IFCs from ab-initio based density functional theory (DFT) calculations. In this approach, an ML model is 􀀌rst trained to learn the local potential energy surface as experienced by atoms and this trained model is then used to replace DFT and predict forces needed in the IFCs extraction. With this seemingly simple approach, the computational cost of anharmonic IFCs extraction is reduced by more than an order of magnitude and the accuracy of 􀀔 prediction is preserved to within 10% . The approach presented here is di􀀋erent than frequently used ML force 􀀌eld development approaches where the objective is to sample the complete potential energy surface and the development/training of force- 􀀌eld itself requires computationally expensive training dataset16–22 . In the approach presented here, since the objective is to learn the local potential energy surface, only a handful of DFT calculations are su􀀎cient to train the ML model. II. METHODOLOGY The contribution of phonons towards the 􀀔 of material is obtainable using the BTE along with the Fourier’s lawas23–25 : 􀀔 = Xc􀀕 v2􀀕,􀀋 􀀜􀀕,􀀋 , (1) 􀀕 where the summation is over all phonon modes, c􀀕 is the phonon speci􀀌c heat, v􀀕,􀀋 is the 􀀋 component of phonon group velocity vector v 􀀕 , and 􀀜􀀕,􀀋 is the phonon scattering time. The calculation of phonon heat capacity (using the Bose-Einstein statistics) , group velocity, and scattering rate requires harmonic

FAQs

Why is anharmonic interatomic force constant evaluation a computational bottleneck for predicting phonon thermal conductivity?

Because extracting harmonic and anharmonic (cubic/quartic) IFCs and phonon scattering rates typically requires several hundred to thousands of DFT hours depending on the material system.

How does the proposed machine learning approach speed up the extraction of anharmonic force constants?

It first trains an ML model to learn the local potential energy surface, then uses the trained model to predict forces needed for IFC extraction instead of repeatedly performing DFT force calculations.

What computational savings and accuracy are achieved in the reported study?

For 220 ternary materials, anharmonic IFC evaluation time is reduced by more than an order of magnitude—from about 480,000 CPU-hours to under 12,000—while keeping thermal conductivity prediction accuracy within 10%.

Aug 6, 2026

Upload by Maeve