[Paper Review] Measuring transferability issues in machine-learning force fields: The example of Gold-Iron interactions with linearized potentials

Magali Benoit, Jonathan Amodeo+4 more|arXiv (Cornell University)|Dec 23, 2019

Machine Learning in Materials Science63 references21 citations

TL;DR

This paper proposes a linearized machine-learning potential (MLIP) using LassoLars regression to model Au-Fe interactions, demonstrating that increased potential complexity improves training accuracy but reduces transferability. The method enables rapid, scalable MLIP construction with controlled complexity, revealing a critical trade-off between fitting the training data and predicting untrained configurations accurately.

ABSTRACT

Machine-learning force fields have been increasingly employed in order to extend the possibility of current first-principles calculations. However, the transferability of the obtained potential can not always be guaranteed in situations that are outside the original database. To study such limitation, we examined the very difficult case of the interactions in gold-iron nanoparticles. For the machine-learning potential, we employed a linearized formulation that is parameterized using a penalizing regression scheme which allows us to control the complexity of the obtained potential. We showed that while having a more complex potential allows for a better agreement with the training database, it can also lead to overfitting issues and a lower accuracy in untrained systems.

Motivation & Objective

• To investigate transferability limitations in machine-learning force fields for complex, non-miscible metal systems like Au-Fe nanoparticles.
• To develop a scalable, linearized MLIP framework that allows systematic control over potential complexity.
• To quantify the trade-off between fitting accuracy on training data and predictive performance on untrained configurations.
• To evaluate the effectiveness of LassoLars regression in selecting physically relevant descriptor functions for MLIPs.

Proposed method

• A linearized machine-learning potential is constructed using a universal analytical form parameterized via penalized regression.
• The LassoLars algorithm is employed to perform sparse regression, enabling automatic feature selection and control over model complexity.
• Descriptor functions include two-body (2B), three-body (3B), and many-body (NB) terms with varied parameters, derived from Lennard-Jones and similar functions.
• A C++ code generates descriptor matrices for each atomic configuration, parallelized via OpenMP for efficiency.
• A Python-based pipeline concatenates matrices, applies LassoLars fitting using scikit-learn, and outputs LAMMPS-compatible input files.
• The final MLIP combines 2B, 3B, and NB contributions using LAMMPS's hybrid/overlay pair style for simulation.

Experimental results

Research questions

• RQ1 How does increasing the complexity of a machine-learning potential affect its transferability to untrained configurations in Au-Fe systems?
• RQ2 Can LassoLars regression effectively identify and retain only the most relevant descriptor functions for accurate potential construction?
• RQ3 To what extent does overfitting to the training database degrade predictive accuracy in unseen atomic environments?
• RQ4 How does the linearized potential framework enable rapid, scalable development of MLIPs with tunable complexity?
• RQ5 What is the quantitative trade-off between training error and transferability in this MLIP approach?

Key findings

• The LassoLars method successfully identified and retained only the original Lennard-Jones interaction parameters in a test system, setting all other coefficients to zero, unlike Ridge and standard Lasso.
• A matrix for a 64-atom structure with all descriptors (2B, 3B, NB) was generated in ~3 minutes using parallel C++ code.
• LassoLars fitting took less than 20 seconds for a single descriptor type and under 2 minutes for all three types combined.
• The method achieved high accuracy on the training database, but increased complexity led to overfitting and reduced transferability to untrained systems.
• The study confirms that while higher complexity improves training fit, it compromises transferability, highlighting a critical design trade-off in MLIP development.
• The framework enables rapid, scalable construction of MLIPs with controlled complexity, suitable for high-throughput screening and on-the-fly refinement.