Benchmarking Universal Machine-Learning Interatomic Potentials for Temperature-Dependent Elasticity of Binary and High-Entropy Refractory Carbides

Introduction to the show: ident: Condensed Matter. The day in condensed matter: materials, phases and the measurements under them.

Kai: I'm Kai.

Mira: And I'm Mira, here with Lev.

Kai: We're looking at the paper: "Benchmarking Universal Machine-Learning Interatomic Potentials for Temperature-Dependent Elasticity of Binary and High-Entropy Refractory Carbides".

Mira: Here's the gist of the paper. Accurate prediction of temperature-dependent elasticity is important for assessing refractory carbides under high-temperature conditions, but the computational cost of ab initio molecular dynamics (AIMD) limits systematic investigations across compositions and temperatures Benchmarking Methodology The study benchmarks nine universal machine-learning interatomic potentials (uMLIPs) against consistent AIMD reference data for five binary and two high-entropy carbides between 300 and 1200 K Elastic constants and the corresponding bulk, shear, and Young’s moduli are obtained using stressstrain molecular dynamics, explicitly sampling thermal atomic motion and anharmonic effects beyond thermal expansion alone The researchers assess absolute elastic properties and normalized thermal softening separately Model Performance Metrics The predictive performance of the uMLIPs is evaluated using two main metrics: (i) the absolute stiffness at each investigated temperature and (ii) the normalized temperature dependence relative to 300 K Absolute accuracy is assessed by the mean absolute percentage error (MAPE) of each elastic constant and Hill modulus, averaged over all carbides and temperatures from 300 to 1200 K Temperature dependence is assessed by the softening error, defined as the difference, in percentage points (pp), between the uMLIP and AIMD relative changes

X(1200 K) − X(300 K): /X(300 K) of each property Sensitivity to Chemical Complexity The HE carbides are described with accuracy comparable to that of the binary carbides, indicating no apparent accuracy penalty from chemical complexity Accuracy instead varies with transition-metal composition, with group-V carbides, particularly TaC, presenting the greatest challenge The HE carbides are predicted as accurately as the binary carbides, with only approximately 0.5% variation between SQS configurations Chemical disorder therefore does not appear to introduce an additional accuracy reduction for these systems (within the measure of comparing to the ab initio reference) Key Findings on Accuracy and Softening MACE-MH-1 achieves the lowest overall mean absolute percentage error (5.7%) and is the only model with errors below 10% for every property Most uMLIPs systematically underestimate the stiffness MACE-MH-1 gives the lowest mean error (5.7%) and remains below 10% for every property, followed by PETMAD-1.5-S (9.7%) and several models with errors of 10 – 11% The overall model accuracy across materials and the temperature dependence are discussed in the following section Material-Specific Discrepancies Accuracy varies systematically with the constituent transition metals, with the lowest mean errors obtained for the group-IV carbides ZrC (6.6%), HfC (10.2%), and TiC (10.9%) Errors are larger for the group-V carbides VC (13.5%) and TaC (20.1%) The largest errors for the group-V-based carbides arise mainly from the shear response, with C44 being underestimated by 13 - 18% for VC, TaC, and (V,Nb,Ta,Mo,W)C Computational Efficiency SevenNet-Nano is the fastest model but has the largest mean error (18.7%) The H100 provides a speedup by a factor of 1.1–1.7 (1.7 for Orb-v3) The GPU memory requirements are also moderate, ranging from 5.5 GiB for ALIGNN-FF Overall, MACE-MH-1 provides the best combined description of absolute values and thermal softening The high-entropy carbides are predicted as accurately as the binary carbides, with only approximately 0.5% variation between SQS configurations Accuracy instead varies with the transition-metal group Overall, these results demonstrate that pretrained uMLIPs can predict finite-temperature elastic properties of refractory carbides without additional training, typically within 5 - 15% of AIMD and at substantially lower computational cost Declarations This work was supported by the Grant Agency of the Czech Technical University in Prague

grant No. [Kai: SGS24/121/OHK2/3T/12] Computational resources were provided through the project “Development of infrastructure facilities for PhD programmes at CTU” (registration no.

Mira: CZ.02.01.01/00/22 012/0006347), supported by the Johannes Amos Comenius Programme During the preparation of this manuscript, the authors used GPT-6 Astra and Claude Opus 5.

Title and authors: Kai: The paper, "Benchmarking Universal Machine-Learning Interatomic Potentials for Temperature-Dependent Elasticity of Binary and High-Entropy Refractory Carbides," is essentially testing if these universal machine learning interatomic potentials can actually predict the temperature dependence of elasticity without needing any extra training.

Mira: That’s the central question they’re addressing, because finite-temperature molecular dynamics benchmarks have shown a lot of model dependence when predicting bulk moduli and thermal expansion across different material classes.

Lev: So, what they’re really asking is if these pre-trained machine learning potentials can reproduce the temperature dependence of the single crystal elastic tensor for refractory carbides without needing system-specific training.

Kai: To answer that, they use a dataset compiled by Sangiovanni et al., which includes rocksalt TiC, ZrC, HfC, VC, and TaC along with high-entropy carbides like (Ti,Zr,Hf,Ta,W)C and (V,Nb,Ta,Mo)W.

Mira: They test nine different universal machine-learning interatomic potentials against this consistent AIMD reference data across a range of temperatures from three hundred K up to one thousand two hundred K <ref:2610.11878#pg1,universal machine-learning interatomic potentials>.

Lev: They are checking the accuracy of these models for three properties: robust behavior in configurations and thermodynamic conditions underrepresented in their training, plus finite-temperature MD benchmarks which report substantial model dependence.

Kai: The authors are looking for a way to make these potentials reliable enough for designing new materials that operate under extreme conditions where temperature changes are significant.

Mira: They note that while the ability of pre-trained universal machine learning interatomic potentials to reproduce the temperature dependence of the single crystal elastic tensor remains comparatively underexplored, especially for refractory carbides and chemically disordered high-entropy ceramics.

Lev: The practical obstacle they point out is that there’s limited availability of directly comparable finite-temperature AIMD elastic data covering multiple compositions, which makes this benchmarking study necessary.

The paper's summary: Kai: So, to summarize the approach, the paper benchmarks nine universal machine-learning interatomic potentials against consistent ab initio molecular dynamics reference data for five binary and two high-entropy carbides between three hundred K and one thousand two hundred K <ref:2610.11878#pg1,reference data for five binary and two high-entropy>.

Mira: They obtain the elastic constants and the corresponding bulk, shear, and Young’s moduli using stressstrain molecular dynamics, making sure to sample thermal atomic motion and anharmonic effects beyond just thermal expansion.

Lev: The results are split into two parts: assessing absolute stiffness at each investigated temperature, and assessing the normalized temperature dependence relative to three hundred K <ref:2610.11878#pg1>.

Kai: For accuracy, they use the mean absolute percentage error of each elastic constant and Hill modulus, averaged over all carbides and temperatures from three hundred K to one thousand two hundred K <ref:2610.11878#pg1>.

Mira: For the temperature dependence, they use a softening error, which is defined as the difference in percentage points between the universal machine-learning interatomic potential and ab initio molecular dynamics relative changes of each property from three hundred K to one thousand two hundred K divided by the value at three hundred K <ref:2610.11878#pg1>.

Lev: This method allows them to separate absolute accuracy from temperature dependence, which is a key thing because you can have a model that’s good at predicting the stiffness at one point but terrible when you move to another.

Kai: The paper then looks at how accuracy varies with chemical complexity, and they find that the high-entropy carbides are described with accuracy comparable to binary carbides, meaning there isn't an obvious penalty from having more elements.

Mira: They also find that the chemical disorder doesn't seem to introduce an additional accuracy reduction for these systems when compared against the ab initio reference data.

The paper's improvements: Kai: The authors suggest that universal machine-learning interatomic potentials can predict the finite-temperature elastic response of refractory carbides without needing any additional system-specific training.

Mira: They point to a key finding: MACE-MH-one achieves the lowest overall mean absolute percentage error, which is five point seven percent, and it’s actually below ten percent for every property they tested <ref:2610.11878#pg1>.

Lev: That low error rate for MACE-MH-one is significant because it suggests that this model might be a promising candidate for use in real hardware simulations, even though we still need to see how it runs on actual hardware <ref:2610.11878#pg1>.

Kai: They also show that most universal machine learning interatomic potentials systematically underestimate the stiffness, but MACE-MH-one gives the lowest mean error at five point seven percent, followed by PETMAD-one point five-S with an error of nine point seven percent.

Mira: They also highlight that accuracy isn't uniform across all materials; it varies with the constituent transition metals, and they find that group IV carbides like ZrC have the lowest mean errors, at six point six percent <ref:2610.11878#pg1>.

Lev: Conversely, they see larger errors for group V carbides like VC and TaC, especially in the shear response where C44 is underestimated by thirteen to eighteen percent for those materials.

Kai: So, while MACE-MH-one is the best overall performer on accuracy and softening error, there are still material-specific discrepancies they have to manage <ref:2610.11878#pg1>.

Conclusion: Mira: So, wrapping up the paper "Benchmarking Universal Machine-Learning Interatomic Potentials for Temperature-Dependent Elasticity of Binary and High-Entropy Refractory Carbides," the main point is that MACE-MH-one provides the best combined description of both absolute values and thermal softening <ref:2610.11878#pg1,Benchmarking Universal Machine-Learning Interatomic Potentials for Temperature-Dependent Elasticity of Binary>.

Kai: They conclude that high-entropy carbides are predicted as accurately as binary carbides, with only approximately zero point five percent variation between SQS configurations, showing chemical disorder doesn't add much error here.

Lev: From an engineering standpoint, this means we can use these pretrained universal machine learning interatomic potentials to predict the finite-temperature elastic properties of refractory carbides without needing any extra training data for each new material we want to study.

Kai: It shows that these pretrained universal machine learning interatomic potentials can predict finite-temperature elastic properties of refractory carbides within about five to fifteen percent of ab initio molecular dynamics, and at a much lower computational cost.

Mira: So, the implication is that these models are becoming a practical tool for assessing material stability under high-temperature conditions in ways that were previously too expensive to explore systematically.

Lev: For our work on real hardware, this suggests we should probably focus on verifying models like MACE-MH-one because it shows promise for handling both the absolute stiffness and the temperature dependence simultaneously <ref:2610.11878#pg1>.