Going beyond density functional theory accuracy: Leveraging experimental data to refine pre-trained machine learning interatomic potentials

TL;DR

A trajectory re-weighting technique is used to refine DFT pre-trained MLIPs to match the target experimental Extended X-ray Absorption Fine Structure (EXAFS) spectra and improves the MLIP prediction of other structural properties that are not directly involved in the refinement process.

Abstract

Machine learning interatomic potentials (MLIPs) are inherently limited by the accuracy of the training data, usually consisting of energies and forces obtained from quantum mechanical calculations, such as density functional theory (DFT). Since DFT itself is based on several approximations, MLIPs may inherit systematic errors that lead to discrepancies with experimental data. In this paper, we use a trajectory re-weighting technique to refine DFT pre-trained MLIPs to match the target experimental Extended X-ray Absorption Fine Structure (EXAFS) spectra. EXAFS spectra are sensitive to the local structural environment around an absorbing atom. Thus, refining an MLIP to improve agreement with experimental EXAFS spectra also improves the MLIP prediction of other structural properties that are not directly involved in the refinement process. We combine this re-weighting technique with transfer learning and a minimal number of training epochs to avoid overfitting to the limited experimental data. The refinement approach demonstrates significant improvement for two MLIPs reported in previous work, one for an established nuclear fuel: uranium dioxide (UO2) and second one for a nuclear fuel candidate: uranium mononitride (UN). We validate the effectiveness of our approach by comparing the results obtained from the original (unrefined) DFT-based MLIP and the EXAFS-refined MLIP across various properties, such as lattice parameters, bulk modulus, heat capacity, point defect energies, elastic constants, phonon dispersion spectra, and diffusion coefficients. An accurate MLIP for nuclear fuels is extremely beneficial as it enables reliable atomistic simulation, which greatly reduces the need for large number of expensive and inherently dangerous experimental nuclear integral tests, traditionally required for the qualification of efficient and resilient fuel candidates.

Figures (26)

• Figure 1: Flowchart for the MLIP refinement process. In this process, the current MLIP for a given iteration is used to generate the MD trajectory. The EXAFS spectra for every atom are calculated for a subset of snapshots from the full trajectory. The atomic energy shifts $(\Delta E)$ are determined by minimizing the loss function, which depends on the difference between the re-weighted simulated EXAFS spectra and the target EXAFS spectra (bottom right box). To avoid large changes in the MLIP between iterations, a regularization term is included in the loss function to penalize large values of $\Delta E_i$. The MLIP is then re-trained with the updated atomic energies, $E_i + \Delta E_i$, where transfer learning is employed to avoid overfitting. At every iteration, the agreement between simulated and target EXAFS spectra improves.
• Figure 2: Comparison of experimental EXAFS spectra of U in UO$_2$ with the simulated EXAFS spectra computed with unrefined MLIP and refined MLIP at (a) 77 K and (b) 300 K. While the refinement process is performed at a single temperature (75 K), the refined MLIP predicts improved EXAFS spectra even at higher temperatures. To ensure an unbiased comparison with experiments, accurate SCF method was used to generate the EXAFS spectra corresponding to unrefined and refined MLIP. The simulated EXAFS spectra is obtained by averaging over all U atoms in a single $4 \times 4 \times 4$ supercell of UO$_2$ from molecular dynamics trajectory at respective temperatures.
• Figure 3: Temperature dependence of thermophysical properties of UO$_2$, (a) lattice parameter, (b) heat capacity, and (c) bulk modulus over a range of temperature from 300 K to 3000 K. Predictions obtained using refined and unrefined MLIPs are compared with the experimental values. In (b), the dashed line is plotted at T=2670 K corresponding to the Bredig temperature. The experimental lattice parameters are from Ref. international2006iaeaFINK20001, the polynomial fit to experimental heat capacity data is from Fink et al. FINK20001, and the experimental bulk modulus data is from Hutchings et al. F29878301083.
• Figure 4: Phonon dispersion spectra for UO$_2$ calculated using unrefined and refined MLIPs, for a shorter path (a) $\Gamma \to X \to \Gamma \to L$, and an extended path (b) $\Gamma \to X \to K \to \Gamma \to L \to X \to W \to \Gamma$. The experimental inelastic neutron scattering data at 300 K in (a) is obtained from Peng et al. PhysRevLett.110.157401, and DFT+U calculated dispersion spectra from phonon_dftu.
• Figure 5: Oxygen diffusion coefficients in UO$_2$$log(D)$ as a function of inverse temperature (1000/T) (K$^{-1}$) calculated with unrefined and refined MLIPs at temperatures between 2100 K and 3000 K. Linear fits of Arrhenius equation for two regimes are shown as dashed lines.