Modeling Liquid Metals with Machine Learning: A New Dataset Approach

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Author: Denis Avetisyan

Researchers have developed a novel strategy for creating accurate machine learning models capable of simulating the complex behavior of liquid metals, offering a faster and more efficient alternative to traditional computational methods.

Machine learning predictions, trained on density functional theory data using both PBE and r2SCAN functionals, accurately model temperature-dependent liquid densities and diffusivities for a range of elemental metals-including aluminum, copper, magnesium, molybdenum, nickel, titanium, and tungsten-and successfully predict melting points, with detailed error analyses available for each system.
Machine learning predictions, trained on density functional theory data using both PBE and r2SCAN functionals, accurately model temperature-dependent liquid densities and diffusivities for a range of elemental metals-including aluminum, copper, magnesium, molybdenum, nickel, titanium, and tungsten-and successfully predict melting points, with detailed error analyses available for each system.

This work introduces a physically motivated dataset engineering strategy to create stable and accurate machine learning interatomic potentials for liquid metals, bypassing the need for extensive ab initio molecular dynamics calculations.

Accurate modeling of liquid metal behavior remains a significant challenge despite their importance in diverse technologies. This limitation is addressed in ‘Stable Machine Learning Potentials for Liquid Metals via Dataset Engineering’, which introduces a novel dataset engineering strategy to create robust machine learning interatomic potentials. By synthetically generating liquid-like training data based on established principles of metallic short-range order, the research overcomes the sampling deficiencies of traditional approaches and yields potentials that accurately reproduce experimental thermophysical properties. Will this framework unlock predictive modeling capabilities for complex liquid-phase phenomena beyond the reach of conventional simulations?

The Challenge of Simulating Liquid Metal Behavior

The design of novel metallic alloys with enhanced properties relies heavily on understanding liquid metal behavior, yet simulating these systems presents a significant challenge. While ab initio molecular dynamics (AIMD) offers a highly accurate approach, directly solving the quantum mechanical equations for many interacting atoms is exceptionally demanding computationally. This limitation restricts AIMD simulations to incredibly short timescales – often nanoseconds or less – which are insufficient to observe crucial processes like atomic diffusion, phase transformations, or the evolution of microstructures. Consequently, researchers face a trade-off between accuracy and accessibility, often needing to employ less accurate, empirical methods or seek innovative approaches to bridge the gap between fundamental physics and practical material design.

Despite their foundational accuracy, first-principles methods like Ab initio molecular dynamics face a significant challenge in modeling the extended timescales governing liquid metal behavior. Phenomena such as atomic diffusion – the gradual mixing of elements – and phase transitions, where a material shifts between solid, liquid, or other states, unfold over nanoseconds to microseconds, yet current computational resources often limit simulations to picosecond durations. This discrepancy arises because accurately describing the intricate interplay of electrons and atoms in liquid metals demands immense processing power, particularly when tracking the collective movements necessary to observe these slower processes. Consequently, critical insights into material properties governed by long-timescale dynamics remain elusive, hindering the rational design of novel alloys and metallic materials with tailored characteristics.

The difficulty in simulating liquid metals stems from the intricate interplay of many-body interactions, where the behavior of each atom is influenced by the collective state of numerous others – a far cry from simpler, pairwise potentials. This necessitates accounting for complex electronic correlations that dictate bonding and material properties. Furthermore, accurately capturing the short-range order – the fleeting, local arrangements of atoms within the liquid – is paramount, as these transient structures significantly impact transport phenomena and phase behavior. Unlike crystalline solids with long-range order, liquid metals exhibit a constantly evolving network of these short-lived motifs, demanding simulations that can resolve these subtle, yet critical, structural details to faithfully reproduce realistic material responses.

The advancement of materials science hinges on the ability to predict and refine material behaviors, yet current computational limitations significantly impede this process for liquid metals. The inability to accurately simulate these systems over relevant timescales restricts the design of novel alloys with specifically tailored properties – such as enhanced conductivity, improved strength, or increased resistance to corrosion. Without access to detailed simulations, researchers are forced to rely heavily on empirical experimentation, a costly and time-consuming approach. This bottleneck prevents the efficient exploration of vast compositional spaces and hinders the development of materials optimized for demanding applications, ranging from advanced electronics to high-performance structural components. Consequently, progress in areas reliant on liquid metal innovation is slowed, highlighting the urgent need for more efficient simulation techniques.

Training machine learning potentials with synthetically generated liquid structures, which incorporate short-range interactions absent in ab initio molecular dynamics (AIMD) data, significantly improves the stability of molecular dynamics simulations at high temperatures and across varying system sizes by capturing the icosahedral order inherent in metallic liquids.
Training machine learning potentials with synthetically generated liquid structures, which incorporate short-range interactions absent in ab initio molecular dynamics (AIMD) data, significantly improves the stability of molecular dynamics simulations at high temperatures and across varying system sizes by capturing the icosahedral order inherent in metallic liquids.

Bridging the Computational Gap with Machine Learning Potentials

Machine learning interatomic potentials (MLPs) represent a computational approach to determine the potential energy surface (PES) of a material, circumventing the computational expense of traditional methods. Instead of directly solving the many-body Schrödinger equation, MLPs are trained on datasets generated from high-fidelity, first-principles calculations – such as density functional theory (DFT) – which provide accurate energy and force information for a limited set of atomic configurations. The trained MLP then approximates the PES, allowing for rapid calculation of energies and forces for new, unseen configurations. This learned PES can then be used within molecular dynamics simulations, effectively substituting the computationally intensive first-principles calculations with a much faster machine learning model, thereby enabling simulations of larger systems and longer timescales.

The application of machine learning interatomic potentials (MLPs) to molecular dynamics simulations yields substantial computational speedups, typically ranging from 10x to 1000x compared to simulations based on density functional theory. This acceleration stems from the MLP’s ability to approximate potential energy and forces with a neural network trained on a dataset of first-principles calculations. Consequently, simulations can be performed with significantly larger system sizes – increasing the number of atoms from thousands to millions – and extended to much longer timescales, enabling the study of rare events and slow processes relevant to materials science, chemistry, and biology that were previously inaccessible due to computational cost. These gains facilitate investigations into phenomena occurring over microseconds to milliseconds, exceeding the practical limits of traditional methods.

The predictive power of machine learning interatomic potentials (MLPs) is fundamentally limited by the dataset used for training. Insufficient or biased training data will directly translate to inaccuracies in the learned potential energy surface, compromising the reliability of subsequent simulations. Specifically, the training data must adequately sample the relevant configuration space, including variations in atomic environments, chemical compositions, and structural arrangements. A lack of diversity in the training set-for example, an over-representation of specific atomic configurations-can lead to poor generalization and inaccurate predictions when applied to previously unseen structures or conditions. Therefore, careful consideration must be given to the selection, generation, and validation of training data to ensure the MLP accurately represents the underlying physics of the system under investigation.

Training machine learning interatomic potentials (MLPs) exclusively on crystalline structures introduces significant limitations when applied to liquid systems. Crystalline materials exhibit long-range order and periodic arrangements, resulting in a potential energy surface (PES) dominated by specific, repeating configurations. Liquids, conversely, lack this long-range order and present a far more complex PES with a greater diversity of atomic arrangements and bonding environments. An MLP trained solely on crystalline data will therefore be unable to accurately represent the energy and forces associated with the disordered configurations prevalent in liquids, leading to inaccurate predictions of dynamic and thermodynamic properties. Consequently, training datasets must include a representative sampling of liquid configurations to ensure the MLP generalizes effectively to these non-crystalline states.

Increasing the maximum bond angle <span class="katex-eq" data-katex-display="false">\alpha_{max}</span> during training improves the accuracy of force predictions and simulation stability of machine learning potentials, as demonstrated by reduced mean absolute error and increased simulation longevity across various temperatures.
Increasing the maximum bond angle \alpha_{max} during training improves the accuracy of force predictions and simulation stability of machine learning potentials, as demonstrated by reduced mean absolute error and increased simulation longevity across various temperatures.

Generating Synthetic Liquid Data to Enrich Training Sets

Synthetic Liquid Training generates a diverse dataset of atomic configurations by systematically perturbing a face-centered cubic (Fcc) structure. This perturbation process involves applying random displacements to atoms within the Fcc lattice, creating arrangements that statistically resemble the short-range order observed in liquid metals. The magnitude and distribution of these displacements are controlled to produce a range of configurations spanning the potential energy surface relevant to the liquid state. This method allows for the creation of a large, labeled dataset without requiring computationally expensive ab initio molecular dynamics simulations of actual liquids, providing a training set that effectively captures the structural characteristics of liquid metals.

The accuracy of machine learning potentials (MLPs) in predicting the behavior of liquid metals is improved by incorporating the phenomenon of short-range order into the training data. Liquid metals, unlike fully disordered liquids, exhibit preferential arrangements of atoms even without long-range crystalline order. By specifically training the MLP on configurations that reflect these short-range ordering patterns – such as clustering and preferred interatomic distances – the model learns to more accurately represent the potential energy surface of the liquid state. This allows for improved predictions of energies and forces, critical for molecular dynamics simulations and materials modeling, as the MLP can better generalize to configurations beyond those seen in purely crystalline training datasets.

The incorporation of synthetic liquid data significantly augments the training dataset used for the machine learning potential (MLP), moving beyond the limitations of datasets comprised solely of crystalline structures. Traditional MLP training relies heavily on perfectly ordered, low-energy crystalline configurations; however, many materials science applications require accurate potential energy surfaces for disordered states. By exposing the MLP to a wider range of atomic configurations representative of the liquid state, the model’s ability to generalize to unseen, disordered structures is demonstrably improved. This expanded training set allows the MLP to better approximate potential energies and forces across a broader configurational space, resulting in increased predictive accuracy for liquid materials and amorphous solids.

To improve the accuracy of the machine learning potential (MLP), training data was generated using calculations performed with both the Perdew-Burke-Ernzerhof (PBE) functional and the r2SCAN functional, both within the density functional theory (DFT) framework. PBE is a widely used generalized gradient approximation (GGA) functional, while r2SCAN is a strongly constrained and appropriately scaled GGA functional. Utilizing data from both functionals during MLP training effectively exposes the network to a broader range of possible electronic structures and energy landscapes, mitigating potential biases inherent to any single functional and resulting in a more robust and accurate potential for predicting material properties.

A strong correlation between solid and liquid phase density errors, as determined by comparing density errors from DFT calculations and <span class="katex-eq" data-katex-display="false">MLP</span> simulations at the melting point, suggests that functional binding tendencies observed in solids also apply to liquids.
A strong correlation between solid and liquid phase density errors, as determined by comparing density errors from DFT calculations and MLP simulations at the melting point, suggests that functional binding tendencies observed in solids also apply to liquids.

Validating and Expanding Simulation Capabilities for Accelerated Discovery

Machine learning potentials (MLPs), specifically those trained on synthetically generated liquid metal data, have proven remarkably effective at replicating crucial material properties. These models accurately predict both liquid density and diffusivity-fundamental characteristics governing a material’s behavior-demonstrating a high degree of fidelity to physical reality. The success of this approach hinges on the quality and scope of the synthetic dataset, which provides the MLPs with a diverse and representative training ground. This ability to accurately reproduce key properties opens avenues for simulating liquid metals with unprecedented accuracy and efficiency, surpassing the limitations of traditional methods and enabling detailed investigations into complex metallurgical phenomena.

To enhance the predictive power of the machine learning potential, an Atomic Cluster Expansion (ACE) potential was seamlessly integrated into the model’s training process. This strategic combination leveraged the strengths of both approaches: the ACE potential provided a robust, physically-grounded basis for describing atomic interactions, while the machine learning framework efficiently learned complex relationships from the synthetic liquid metal data. By incorporating the ACE potential as a prior, the resulting model demonstrated improved accuracy and generalization capabilities, allowing for more reliable predictions of material properties beyond those explicitly present in the training dataset. This synergy significantly refined the machine learning potential, resulting in a model that not only reproduces known liquid metal behaviors but also exhibits enhanced stability and transferability to new conditions and system sizes.

Machine learning potentials (MLPs) developed in this study demonstrate a marked advancement in computational stability, enabling simulations that surpass the limitations of traditional ab initio molecular dynamics (AIMD). These MLPs maintain stable trajectories across a broad spectrum of temperatures and system sizes-a critical improvement over AIMD-trained models, which frequently exhibit instability as system complexity increases. This enhanced stability unlocks the ability to explore materials behavior over extended timescales and larger length scales, previously inaccessible due to computational constraints. Consequently, researchers can now investigate dynamic processes and emergent phenomena with greater accuracy and efficiency, paving the way for accelerated materials discovery and a more comprehensive understanding of liquid metal properties.

To maximize the impact of this research, the machine learning potentials (MLPs) and the synthetic datasets utilized in their training have been made openly available through the ColabFit Exchange. This commitment to open science allows researchers worldwide to readily reproduce these results, validate the models against their own data, and build upon this foundation for accelerated materials discovery. By providing both the trained potentials and the underlying datasets, the workflow becomes fully transparent and easily adaptable, circumventing the typical barriers to entry associated with computationally intensive simulations and fostering collaborative innovation in the field of liquid metal research. This accessibility promises to significantly broaden participation and expedite the design of novel materials with tailored properties.

Evaluations reveal a compelling alignment between the model’s predictions and established experimental findings; calculated melting points demonstrate a remarkably small error range, fluctuating between -6% and 1%. Furthermore, predictions for crucial liquid-state properties – density and diffusivity – consistently fall within the boundaries defined by existing experimental data, mirroring the inherent reproducibility limitations observed in physical measurements. This level of agreement not only validates the accuracy of the simulation approach but also suggests its potential as a reliable and efficient tool for materials discovery, offering insights comparable to, and potentially exceeding, the scope of purely experimental investigations.

The pursuit of stable machine learning potentials, as detailed in this research, resonates with a fundamental principle of systemic design. The work elegantly demonstrates that focusing on the dataset-the very foundation of the model-yields more robust and reliable results than attempting to ‘fix’ deficiencies within the model itself. This echoes Michel Foucault’s observation: “There is no power relation without resistance.” In the context of machine learning, resistance manifests as instability or inaccuracy; however, carefully engineered datasets – akin to a well-defined structure – serve as a countervailing force, promoting stability and predictability in simulations of complex liquid metal behavior. The emphasis on physically motivated dataset engineering acknowledges that the whole system-data generation, model training, and simulation-must be considered to achieve meaningful results.

Beyond the Potential

The pursuit of accurate interatomic potentials for liquid metals, as demonstrated by this work, reveals a recurring truth: the map is not the territory. While machine learning offers a powerful shortcut around the computational cost of ab initio methods, the quality of that shortcut hinges entirely on the thoughtfulness of the underlying dataset. This research rightly emphasizes physical motivation in dataset engineering, yet it also implicitly highlights the limitations of focusing solely on pairwise or short-range order. Liquid metals are, after all, complex systems. A truly robust potential will require a more holistic representation of the many-body interactions governing their behavior, lest the model optimize for a fleeting resemblance to reality.

The elegance of this approach lies in its pragmatism. It acknowledges that cleverness has its limits, and simplicity, in the form of carefully curated data, can scale further than any intricately designed functional form. However, the true cost of freedom from computational expense isn’t merely the time saved, but the hidden dependencies introduced by the machine learning model itself. Future work must address the generalizability of these potentials-how well do they perform outside the specific conditions used for training? And, crucially, how can we quantify the uncertainty inherent in any such approximation?

Ultimately, the field will progress not by chasing ever more sophisticated algorithms, but by focusing on the fundamental physics. Good architecture, in this context, is invisible until it breaks-until the potential fails to capture an essential aspect of the liquid metal’s behavior. The challenge, then, isn’t simply to build a better potential, but to build a system that reveals its limitations as quickly as possible.

Original article: https://arxiv.org/pdf/2601.05003.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2026-01-11 09:28