Context

Machine-learned interatomic potentials (MLIPs) are trained on quantum-mechanical (DFT) calculations. They reproduce DFT at a fraction of its cost and have become a standard tool to simulate materials. Our team studies how to train these potentials and how to quantify their uncertainty.

Different potentials make different predictions, and so does the same potential trained with different random seeds. Universal “foundation” potentials such as MACE-MP-0, for instance, are known to be too soft.

The question

Do these differences matter for a real application? We consider the ultrasonic non-destructive testing (NDT) of aluminium, simulated at CEA List with the CIVA platform.

In ultrasonic NDT, a sound wave is sent into a metal part to detect defects. A metal is made of many small crystals, the grains, and part of the wave is scattered when it crosses from one grain to the next. Each grain is a copy of the same crystal with a different orientation. The atomistic simulations therefore only need to describe a single crystal. The grains enter the wave-propagation model through their orientations and sizes.

How much the grains scatter depends on the anisotropy of the crystal, ΔC = C11 − C12 − 2C44, built from its three elastic constants. Aluminium is almost isotropic, so ΔC is a small difference of large numbers. A rough estimate suggests that an independent 1% error on each constant could become an error of about 13% on ΔC.

The question spans several scales: from atoms, to the elastic constants of a crystal, to a wave crossing many grains. A small uncertainty at the smallest scale may be amplified or damped on the way up.

What do we expect from you?

• Review the literature on interatomic potentials, the computation of elastic constants and ultrasonic scattering.
• Build a small family of potentials from DFT data provided by the team: MACE-MP-0, versions of it fine-tuned on aluminium, and potentials trained from scratch, each with several seeds.
• Compute the elastic constants of aluminium at 0 K with each potential, and compare them with DFT.
• Compute the constants at room temperature with molecular dynamics, and compare them with experimental values.
• Estimate the mean and the full covariance of (C11, C12, C44) across potentials, and from it an error bar on ΔC. Correlated errors partly cancel in ΔC, so three separate error bars are not enough.
• Compare the spread between potentials with the error of DFT itself with respect to experiment.

To go further

With the CIVA team, propagate these constants and their error bars to the simulated ultrasonic attenuation. Then compare their effect with that of the uncertainty on grain size. Which uncertainty dominates for aluminium? How accurate should a potential be to be useful for NDT?

Working environment

The intern will work closely with a PhD student of the team who works on the training and uncertainty quantification of MLIPs. The working language is English.

#Cea-List

M2 student / Engineering school students in one of these fields:

• computational materials physics or condensed matter physics;
• complex systems or statistical physics.

We are looking for a student interested in how macroscopic properties emerge from microscopic simulations. Experience with numerical simulation is expected (e.g. molecular dynamics, Monte Carlo or other stochastic models), as are good Python skills. No prior knowledge of machine learning is required. Fluent English is required; French is not.