Machine Learning Interatomic Potentials Refined by Experimental X-ray Data.

Researchers refine machine-learned interatomic potentials (MLIPs), initially trained using density functional theory, by aligning them with experimental Extended X-ray Absorption Fine Structure (EXAFS) data. This trajectory re-weighting improves predictions of structural properties for uranium dioxide and uranium mononitride, reducing reliance on costly nuclear experiments.

The pursuit of accurate material modelling underpins advances across diverse fields, from materials science to nuclear engineering. Computational methods frequently rely on interatomic potentials, mathematical functions describing the interactions between atoms, to simulate material behaviour. These potentials are increasingly informed by machine learning techniques, yet their ultimate accuracy remains constrained by the quality of the training data, typically derived from density functional theory (DFT) calculations, which themselves contain approximations. Researchers at Los Alamos National Laboratory and the University of Southern California now present a refinement strategy, detailed in their article, ‘Going beyond density functional theory accuracy: Leveraging experimental data to refine pre-trained machine learning interatomic potentials’, which integrates experimental data to improve the predictive power of these machine learning interatomic potentials (MLIPs). Shriya Gumber, Lorena Alzate-Vargas, Benjamin T. Nebgen, Arjen van Veelen, Smit Kadvani, Tammie Gibson, and Richard Messerly demonstrate a trajectory re-weighting technique, utilising Extended X-ray Absorption Fine Structure (EXAFS) spectra – a method sensitive to local atomic arrangements – to refine MLIPs pre-trained with DFT data. This approach, applied to both uranium dioxide (UO₂) and uranium mononitride (UN), significantly enhances the prediction of structural and thermodynamic properties, offering a pathway to reduce reliance on costly and hazardous physical nuclear fuel testing.

Researchers demonstrate a novel methodology to refine machine learning interatomic potentials (MLIPs) for uranium dioxide (UO₂) and uranium mononitride (UN) by integrating experimental Extended X-ray Absorption Fine Structure (EXAFS) spectra, substantially improving their predictive capabilities for nuclear materials. MLIPs, which approximate the complex interactions between atoms, are crucial for atomistic simulations, allowing researchers to model material behaviour at the atomic level. Traditional MLIP development relies heavily on density functional theory (DFT) calculations, a computational method used to describe the electronic structure of materials. However, DFT approximations can introduce inaccuracies, limiting the reliability of MLIPs. This new approach addresses these limitations by incorporating real-world material data, offering a pathway to reduce the need for expensive and potentially dangerous physical nuclear tests traditionally required for fuel qualification.

The research team initially trained MLIPs using DFT calculations, establishing a foundational model before incorporating experimental data. They then employed a trajectory re-weighting technique, adjusting the MLIP to better align with experimental EXAFS spectra. EXAFS is a sensitive probe of the local atomic environment, providing information about the distances and coordination numbers of atoms within a material. By matching the MLIP predictions to EXAFS data, the researchers effectively embed real-world material behaviour into the model, enhancing its ability to accurately predict material properties under diverse conditions. Rigorous analysis followed, comparing predictions from the refined MLIPs with both DFT calculations and experimental data to validate the improvements achieved.

Initial investigations revealed that unconstrained refinement of the potential led to overfitting, hindering its ability to generalise to new, unseen data. Overfitting occurs when a model learns the training data too well, including its noise and specific characteristics, resulting in poor performance on new data. To mitigate this, researchers successfully implemented techniques such as freezing specific layers within the MLIP architecture. This prevents the model from memorising the limited experimental data and encourages physically realistic behaviour. By constraining the model’s flexibility, the researchers ensured the resulting potential accurately reflects material behaviour across a broader range of conditions.

For UO₂, freezing layers during refinement yielded a potential that accurately predicts thermal expansion, closely matching experimental results, and provides a more accurate prediction of oxygen atom mean square displacement (MSD) at elevated temperatures. MSD quantifies the average displacement of atoms from their equilibrium positions and is crucial for understanding diffusion processes within the material. The frozen layers act as constraints, preventing the MLIP from deviating too far from the physically plausible behaviour established during the initial DFT training. This approach ensures the refined potential maintains a balance between fitting the experimental data and adhering to fundamental physical principles.

In the case of UN, the researchers investigated different weighting schemes within the refinement process’s loss function, discovering that prioritising force terms over energy terms substantially improves predictions of defect energies and elastic constants. The loss function quantifies the discrepancy between the MLIP’s predictions and the experimental data, guiding the refinement process towards minimising this difference. By assigning a higher weight to force terms, the researchers emphasised the importance of accurately capturing the interatomic forces that govern the material’s mechanical properties. This optimisation brought the predictions closer to both DFT calculations and experimental values.

These findings underscore the value of incorporating experimental data into MLIP refinement, demonstrating that careful regulation, through techniques like layer freezing or loss function weighting, is essential to prevent overfitting and ensure the resulting potential accurately reflects material behaviour. The team meticulously compared the performance of refined MLIPs with those trained solely on DFT data, confirming the significant improvements achieved through the incorporation of experimental information.

The material-specific optimisation of these techniques highlights the need for tailored approaches depending on the system under investigation, as the optimal refinement strategy can vary significantly between different materials. Researchers observed that the effectiveness of layer freezing and loss function weighting depended on the specific characteristics of UO₂ and UN, highlighting the importance of understanding the underlying physics of each material.

Future work should focus on extending this refinement methodology to a broader range of nuclear materials and exploring the application of alternative regularisation techniques, expanding the scope of this approach to encompass a wider variety of fuel candidates. Investigating the transferability of refined MLIPs across different compositions and temperatures represents a key area for advancement, allowing for the development of more versatile and robust simulations. Furthermore, incorporating additional experimental data, such as neutron diffraction, could further enhance the accuracy and reliability of these refined potentials.

The development of robust and accurate MLIPs is vital for enabling reliable atomistic simulations, reducing the reliance on costly and hazardous nuclear experiments, and accelerating the development of advanced nuclear fuels. By combining the strengths of DFT calculations and experimental data, researchers can create MLIPs that accurately capture the complex behaviour of nuclear materials under extreme conditions. This approach promises to revolutionise the field of nuclear materials science, enabling the design of safer, more efficient, and more sustainable nuclear energy systems. The team plans to continue refining this methodology, exploring new techniques and expanding the range of materials that can be accurately simulated.