Self-consistent Validation for Machine Learning Electronic Structure

TL;DR

This method integrates machine learning with self-consistent field methods to achieve both low validation cost and interpret-ability and enables exploration of the model's ability with active learning and instills confidence in its integration into real-world studies.

Abstract

Machine learning has emerged as a significant approach to efficiently tackle electronic structure problems. Despite its potential, there is less guarantee for the model to generalize to unseen data that hinders its application in real-world scenarios. To address this issue, a technique has been proposed to estimate the accuracy of the predictions. This method integrates machine learning with self-consistent field methods to achieve both low validation cost and interpret-ability. This, in turn, enables exploration of the model's ability with active learning and instills confidence in its integration into real-world studies.

Figures (4)

• Figure 1: The data stream under different methods. Left:the SCF iteration and the construction of strict DIIS error vector. Right: The definition of different loss functions. Here DIIS means the error measures the difference between A and B, and LE is labeled error, that measures the difference between the predicted matrix and its label
• Figure 2: The generalization ability of self-DIIS. We evaluated the strict DIIS loss and the self-DIIS loss on both the original validation dataset and a purturbed dataset of the same molecular(uracil). The line is fitted only on the original dataset and the orange points represents the related data drawn at the bottom.
• Figure 3: The statistic results on uracil(a) and QM9(b). The left panel showed the original data as green points, and the fitted mean value conditioned on DIIS error is drawn as the orange line. The shadow area is the 3$\sigma$ region estimated by the fitted standard deviation. The right 2 panels toke each group as a point, and the values are the related statistic result counted in that group. The orange line fitted directly on those points with a linear model, that provides with the statistics information used to draw the line and shadow on the left. On both datasets, that one is different in atom positions and another is different in element component, the error is well bound by the DIIS error in our test.
• Figure 4: Running AIMD with and without error conditioned corrector. A simulation with our predictor-corrector strategy and another simulation use the model prediction directly is drawn together. The left panel, the corrected one relaxed to the target temperature successfully while the other one diverged. The right panel shows the self-DIIS error and the max force applied to the atoms in each time step. In the failed case, the predicted force become exotic large with the increase of self-DIIS loss. While in the corrected case, the force is calculated from DFT results once the self-DIIS loss is above the threshold line, and the force was kept in a reasonable range.