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The Journal of Physical Chemistry A

Efficient Machine Learning Configuration Interaction for Bond Breaking Problems

Madhumita Rano, Debashree Ghosh

Published Apr 16, 2023• 10 citations
Publisher

Abstract

Machine learning-assisted configuration interaction (MLCI) has been shown earlier as a promising method in determining the electronic structure of the model and molecular Hamiltonians. In the MLCI approach to molecular Hamiltonians, it has been noticed that prediction is strongly dependent on the connectedness of the training and validation spaces. In this work, we have tested three different models with different output parameters (abs-MLCI, transformed-MLCI, and log-MLCI) to verify the robustness of training these models. We define robustness as the extent of error in prediction even when the spaces (training and validation) are not connected. We notice that the log-MLCI model is best suited to this approach and is therefore a powerful model for accurate one-shot variational energies. This is tested for chemical bond breaking in water, carbon monoxide, nitrogen, and dicarbon molecules.

DOI
10.1021/acs.jpca.2c09103

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Machine learning-assisted configuration interaction (MLCI) has been shown earlier as a promising method in determining the electronic structure of the model and molecular Hamiltonians. In the MLCI approach to molecular Hamiltonians, it has been noticed that prediction is strongly dependent on the connectedness of the training and validation spaces. In this work, we have tested three different models with different output parameters (abs-MLCI, transformed-MLCI, and log-MLCI) to verify the robustness of training these models. We define robustness as the extent of error in prediction even when the spaces (training and validation) are not connected. We notice that the log-MLCI model is best suited to this approach and is therefore a powerful model for accurate one-shot variational energies. This is tested for chemical bond breaking in water, carbon monoxide, nitrogen, and dicarbon molecules.
We propose the concept of machine learning configuration interaction (MLCI) whereby an artificial neural network is trained on-the-fly to predict important new configurations in an iterative selected configuration interaction procedure. We demonstrate that the neural network can discriminate between important and unimportant configurations, that it has not been trained on, much better than by chance. MLCI is then used to find compact wave functions for carbon monoxide at both stretched and equilibrium geometries. We also consider the multireference problem of the water molecule with elongated bonds. Results are contrasted with those from other ways of selecting configurations: first-order perturbation, random selection, and Monte Carlo configuration interaction. Compared with these other serial calculations, this prototype MLCI is competitive in its accuracy, converges in significantly fewer iterations than the stochastic approaches, and requires less time for the higher-accuracy computations.
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The individual optimization of quantum circuit parameters is currently one of the main practical bottlenecks in variational quantum eigensolvers for electronic systems. To this end, several machine learning approaches have been proposed to mitigate the problem. However, such method predominantly aims at training and predicting parameters tailored to individual molecules: either a specific structure, or several structures of the same molecule with varying bond lengths. This work explores machine learning based modeling strategies to include transferability between different molecules. We use a well investigated quantum circuit design and apply it to model properties of hydrogenic systems where we show parameter prediction that is systematically transferable to instances significantly larger than the training instances.
The main bottleneck of a stochastic or deterministic configuration interaction method is determining the relative weights or importance of each determinant or configuration, which requires large scale matrix diagonalization. Therefore, these methods can be improved significantly from a computational standpoint if the relative importance of each configuration in the ground and excited states of molecular/model systems can be learned using machine learning techniques such as artificial neural networks (ANNs). We have used neural networks to train the configuration interaction coefficients obtained from full configuration interaction and Monte Carlo configuration interaction methods and have tested different input descriptors and outputs to find the more efficient training techniques. These ANNs have been used to calculate the ground states of one- and two-dimensional Heisenberg spin chains along with Heisenberg ladder systems, which are good approximations of polyaromatic hydrocarbons. We find excellent efficiency of training and the model this trained was used to calculate the variational ground state energies of the systems.
Abstract The individual optimization of quantum circuit parameters is currently one of the main practical bottlenecks in variational quantum eigensolvers for electronic systems. To this end, several machine learning approaches have been proposed to mitigate the problem. However, such method predominantly aims at training and predicting parameters tailored to individual molecules: either a specific structure, or several structures of the same molecule with varying bond lengths. This work explores machine learning based modeling strategies to include transferability between different molecules. We use a well investigated quantum circuit design and apply it to model properties of a variety of molecular systems where we show parameter prediction that is systematically transferable to instances significantly larger than the training instances.
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