Application-specific machine-learned interatomic potentials: exploring the trade-off between DFT convergence, MLIP expressivity, and computational cost

Machine-learned interatomic potentials (MLIPs) are revolutionizing computational materials science and chemistry by offering an efficient alternative to {\em ab initio} molecular dynamics (MD) simulations. However, fitting high-quality MLIPs remains a challenging, time-consuming, and computationally intensive task where numerous trade-offs have to be considered, e.g., How much and what kind of atomic configurations should be included in the training set? Which level of {\em ab initio} convergence should be used to generate the training set? Which loss function should be used for fitting the MLIP? Which machine learning architecture should be used to train the MLIP? The answers to these questions significantly impact both the computational cost of MLIP training and the accuracy and computational cost of subsequent MLIP MD simulations. In this study, we use a configurationally diverse beryllium dataset and quadratic spectral neighbor analysis potential. We demonstrate that joint optimization of energy versus force weights, training set selection strategies, and convergence settings of the {\em ab initio} reference simulations, as well as model complexity can lead to a significant reduction in the overall computational cost associated with training and evaluating MLIPs. This opens the door to computationally efficient generation of high-quality MLIPs for a range of applications which demand different accuracy versus training and evaluation cost trade-offs.

💡 Research Summary

This paper presents a comprehensive investigation into the multifaceted trade-offs involved in creating efficient and accurate machine-learned interatomic potentials (MLIPs). The central thesis is that the development of high-quality MLIPs is not merely about maximizing accuracy but about navigating a complex Pareto optimization between predictive performance and total computational cost, which includes the expense of generating the reference data, training the model, and evaluating it in production simulations.

The study uses a configurational diverse beryllium dataset, generated via an information entropy maximization method to ensure broad coverage of atomic environments, making it a stringent test for MLIP robustness. Reference energies and forces are computed using DFT at six distinct levels of convergence (varying plane-wave energy cutoff and k-point sampling), creating a hierarchy of data quality with computational costs differing by up to two orders of magnitude. The MLIP architecture employed is the quadratic Spectral Neighbor Analysis Potential (qSNAP), chosen for its linear regression-based training efficiency, allowing for the training of thousands of models. Model complexity is controlled via the 2Jmax parameter, which affects the number of bispectrum descriptors and consequently the evaluation speed of the potential.

The core analysis systematically varies four key parameters: DFT convergence level, training set size (using leverage score sampling for intelligent sub-selection), the relative weighting of energy versus force errors (wE/wF) in the loss function, and MLIP complexity (2Jmax). The findings reveal several critical insights:

1. DFT Convergence & Error Propagation: Errors from using lower-convergence DFT calculations are not random but structure-dependent. While they degrade MLIP accuracy, their impact can be mitigated by adjusting the energy-force weighting during training, often favoring a higher weight on forces for low-convergence data.
2. Interaction of Model Complexity and Data: The benefit of increased training data quality (size and convergence) is highly dependent on model complexity. Highly complex models (high 2Jmax) only improve with large, high-convergence datasets. In contrast, simpler models saturate quickly with smaller datasets and can even overfit to excessively precise data, offering no further benefit and sometimes degrading performance.
3. Efficient Training Set Curation: Leverage score sampling is shown to be highly effective in identifying the most informative configurations. A small fraction (e.g., 10%) of the full dataset, selected via this method, can often yield MLIPs with accuracy comparable to those trained on the full set, dramatically reducing training data generation costs.
4. Pareto-Optimal Frontiers: By performing a joint optimization across all parameters, the study maps out Pareto fronts that define the optimal trade-offs between total computational cost (DFT + training + evaluation), energy RMSE, and force RMSE. This framework demonstrates that for a given target accuracy in an application, there exists an optimal combination of lower-convergence DFT, a lean training set, and a simpler MLIP that achieves the goal at a fraction of the cost of a conventional high-convergence, large-data, complex-model approach.

In conclusion, the work argues powerfully against a one-size-fits-all approach to MLIP development. It provides a systematic methodology for tailoring MLIPs to specific application needs—be it high-throughput screening, large-scale molecular dynamics, or long-time-scale simulations—by consciously balancing and optimizing the entire pipeline from reference data generation to model deployment. This shifts the paradigm from solely pursuing state-of-the-art accuracy to designing cost-effective, application-specific potentials.