A simple approach to rotationally invariant machine learning of a vector quantity

Area of Science:

• Computational Chemistry
• Machine Learning in Chemistry
• Molecular Dynamics

Background:

• Predicting vector and tensor properties in machine learning (ML) requires handling molecular rotation invariance, unlike scalar properties such as energy.
• Existing methods for ensuring rotational covariance include constructing virtual quantities or designing equivariant neural networks.

Purpose of the Study:

• To introduce a simpler, effective method for achieving rotational covariance in ML predictions of vector and tensor properties.
• To present the rotate-predict-rotate (RPR) technique as an alternative to complex equivariant ML models.

Main Methods:

• The proposed rotate-predict-rotate (RPR) method involves three steps: rotating the molecule to its principal axes using the tensor of inertia, performing ML prediction in this fixed frame, and rotating the prediction back.
• Implementation utilized MLatom and Newton-X programs for ML and molecular dynamics (MD).
• The method was assessed on dipole moment prediction during MD trajectories of 1,2-dichloroethane.

Main Results:

• The RPR procedure successfully guarantees proper covariance of vector properties, demonstrated by accurate dipole moment prediction.
• This method allows for rapid training of accurate ML models for numerous molecular configurations, beneficial for active learning.

Conclusions:

• The RPR technique offers a straightforward and efficient way to ensure rotational covariance for ML predictions of molecular vector and tensor properties.
• This approach simplifies the development of ML models for applications like molecular dynamics, where rotational invariance is crucial.