Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1808.05787 · Journal of Chemical Theory and Computation

Machine Learning Configuration Interaction

J. P. Coe

Published Oct 4, 2018• 106 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1021/acs.jctc.8b00849

Related papers

Efficient Machine Learning Configuration Interaction for Bond Breaking Problems

Madhumita Rano, Debashree Ghosh

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.

The Journal of Physical Chemistry A•Apr 16, 2023•10 citations

Chembot: A Machine Learning Approach to Selective Configuration Interaction

Sergio D. Pineda Flores

We introduce a machine learning-based approach to selective configuration interaction, dubbed Chembot, that utilizes many novel choices for its model design and training. These choices include the use of a support vector machine to select important configurations, the use of the charge density matrix and configuration energy as features, and heuristics to improve the quality of training data. We test Chembot’s ability to obtain near full configuration interaction quality energies and find that it definitively outperforms its purely Stochastic cousin Monte Carlo configuration interaction by requiring fewer iterations to converge, fewer determinants in the variational space, and fewer important configurations to achieve the same energy. In addition, Chembot at times requires fewer determinants in its variational space than the heat-bath configuration interaction method to achieve the same energy. We demystify Chembot’s innards and then showcase our claims on the set of small but challenging systems: the hydrogen ring (H 4 ), stretched methylene (H 2 C), and stretched water (H 2 O).

Journal of Chemical Theory and Computation•Jun 14, 2021•31 citations

Configuration interaction trained by neural networks: Application to model polyaromatic hydrocarbons

Sumanta K. Ghosh, Madhumita Rano, Debashree Ghosh

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.

The Journal of Chemical Physics•Mar 2, 2021•14 citations

Machine Learning Assisted Selective Configuration Interaction for Accurate Ground and Excited State Calculations

Bastien Casier, Maissa El Hamdi, Basile Herzog

In this work, we introduce a perturbative Selective Configuration Interaction (SCI) approach guided by a binary machine-learning classifier. The method leverages a lightweight feedforward neural network (FNN), purposefully designed for fast and efficient training. Within this framework, we show that our model attains the accuracy of the state-of-the-art SCI method CIPSI (Configuration Interaction using a Perturbative Selection done Iteratively). Across all tested configuration-space sizes, our approach reliably identifies the most important Slater determinants using a binary cross-entropy metric, achieving FCI/CASCI-level accuracy within 10 –4 Hartree for both ground and excited states. Finally, the method remains robust for strained geometries and conformational changes, successfully classifying Slater determinants across multiple points of potential energy curves and surfaces. This capability opens the door to new regression-based strategies for molecular electronic structure and the construction of machine-learning-driven potential energy surfaces.

Journal of Chemical Theory and Computation•Jan 31, 2026•2 citations

Enhancing quantum-classical configuration interaction methods using a neural-network classifier

Severino Zeni, Giovanni Varutti, Jacopo Nespolo +1 more

Selected configuration interaction methods achieve near-exact electronic structure calculations by iteratively constructing compact variational spaces, but their efficiency depends critically on the heuristics used to identify important determinants. Here, we introduce a data-driven selection framework that recasts determinant importance as a binary classification task and integrates a neural-network classifier into the iterative CI workflow through an active-learning loop. At each iteration, a random subset of candidate determinants is labelled via temporary diagonalisation, and the trained classifier guides selection of the remaining configurations. We demonstrate the utility of this framework for both classical and quantum CI methods by calculating the ground-state energy of a diatomic molecule. Our method achieves result parity with traditional configuration interaction methods at substantially lower computational cost: roughly a $\times 5$ reduction in memory and per-iteration cost for the classical cHCI variant, and convergence in markedly fewer iterations for the quantum-classical cSQD variant. These results establish classifier-assisted determinant selection as a lightweight, method-agnostic tool for compressing variational spaces and accelerating both classical and hybrid quantum-classical configuration interaction algorithms.

physics.chem-phCross-listedarXiv:2606.24332•Jun 24, 2026•0 citations

Learning to Rank for Selected Configuration Interaction

Wan Nie, Songwei Liu, Yingying Yu +2 more

Accurate description of electron correlation is a central challenge in computational chemistry, with selected configuration interaction (SCI) emerging as a powerful tool to approach the full CI limit. While recent machine learning (ML) integrations have accelerated determinant selection, existing regression and classification approaches suffer from a fundamental objective-loss mismatch: they evaluate the importance of determinants in isolation without explicitly accounting for their relative importance ranking. Here, we introduce ranking configuration interaction (RCI), a novel ML-supported SCI framework that reframes determinant selection as a pairwise ranking problem. Building upon a Transformer-based architecture to capture complex, nonlocal orbital dependencies, RCI progressively optimizes the partial ordering of determinants. By doing so, RCI aligns the training objective more closely with the intrinsic ranking nature of SCI. Extensive benchmarks across both plane-wave and Gaussian basis sets, including the molecules N2, CO, H2O, NH3, and C2, demonstrate the efficiency of RCI. Compared to previously reported classification baselines, RCI consistently accelerates convergence─reducing overall computational time by 23% to over 50% depending on the system and requiring only 55% of the determinant count in representative cases such as N2 and CO. Furthermore, RCI exhibits robust performance and reaches chemical accuracy on the highly challenging iron-sulfur cluster using only 12% of the full CI space. Notably, RCI outperforms recent regression-based SCI methods by delivering a more than 15% improvement in accuracy at comparable determinant counts. RCI also demonstrates higher efficiency than heat-bath CI on the strongly correlated chromium dimer, yielding a compact and accurate wave function. This pairwise learning-to-rank model provides a lightweight and modular plugin that can be seamlessly incorporated into other supervised learning frameworks.

arXiv:2605.10348•Journal of Chemical Theory and Computation•Aug 20, 2026•0 citations
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.
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 introduce a machine learning-based approach to selective configuration interaction, dubbed Chembot, that utilizes many novel choices for its model design and training. These choices include the use of a support vector machine to select important configurations, the use of the charge density matrix and configuration energy as features, and heuristics to improve the quality of training data. We test Chembot’s ability to obtain near full configuration interaction quality energies and find that it definitively outperforms its purely Stochastic cousin Monte Carlo configuration interaction by requiring fewer iterations to converge, fewer determinants in the variational space, and fewer important configurations to achieve the same energy. In addition, Chembot at times requires fewer determinants in its variational space than the heat-bath configuration interaction method to achieve the same energy. We demystify Chembot’s innards and then showcase our claims on the set of small but challenging systems: the hydrogen ring (H 4 ), stretched methylene (H 2 C), and stretched water (H 2 O).
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.
In this work, we introduce a perturbative Selective Configuration Interaction (SCI) approach guided by a binary machine-learning classifier. The method leverages a lightweight feedforward neural network (FNN), purposefully designed for fast and efficient training. Within this framework, we show that our model attains the accuracy of the state-of-the-art SCI method CIPSI (Configuration Interaction using a Perturbative Selection done Iteratively). Across all tested configuration-space sizes, our approach reliably identifies the most important Slater determinants using a binary cross-entropy metric, achieving FCI/CASCI-level accuracy within 10 –4 Hartree for both ground and excited states. Finally, the method remains robust for strained geometries and conformational changes, successfully classifying Slater determinants across multiple points of potential energy curves and surfaces. This capability opens the door to new regression-based strategies for molecular electronic structure and the construction of machine-learning-driven potential energy surfaces.
Selected configuration interaction methods achieve near-exact electronic structure calculations by iteratively constructing compact variational spaces, but their efficiency depends critically on the heuristics used to identify important determinants. Here, we introduce a data-driven selection framework that recasts determinant importance as a binary classification task and integrates a neural-network classifier into the iterative CI workflow through an active-learning loop. At each iteration, a random subset of candidate determinants is labelled via temporary diagonalisation, and the trained classifier guides selection of the remaining configurations. We demonstrate the utility of this framework for both classical and quantum CI methods by calculating the ground-state energy of a diatomic molecule. Our method achieves result parity with traditional configuration interaction methods at substantially lower computational cost: roughly a ×5\times 5×5 reduction in memory and per-iteration cost for the classical cHCI variant, and convergence in markedly fewer iterations for the quantum-classical cSQD variant. These results establish classifier-assisted determinant selection as a lightweight, method-agnostic tool for compressing variational spaces and accelerating both classical and hybrid quantum-classical configuration interaction algorithms.
Accurate description of electron correlation is a central challenge in computational chemistry, with selected configuration interaction (SCI) emerging as a powerful tool to approach the full CI limit. While recent machine learning (ML) integrations have accelerated determinant selection, existing regression and classification approaches suffer from a fundamental objective-loss mismatch: they evaluate the importance of determinants in isolation without explicitly accounting for their relative importance ranking. Here, we introduce ranking configuration interaction (RCI), a novel ML-supported SCI framework that reframes determinant selection as a pairwise ranking problem. Building upon a Transformer-based architecture to capture complex, nonlocal orbital dependencies, RCI progressively optimizes the partial ordering of determinants. By doing so, RCI aligns the training objective more closely with the intrinsic ranking nature of SCI. Extensive benchmarks across both plane-wave and Gaussian basis sets, including the molecules N2, CO, H2O, NH3, and C2, demonstrate the efficiency of RCI. Compared to previously reported classification baselines, RCI consistently accelerates convergence─reducing overall computational time by 23% to over 50% depending on the system and requiring only 55% of the determinant count in representative cases such as N2 and CO. Furthermore, RCI exhibits robust performance and reaches chemical accuracy on the highly challenging iron-sulfur cluster using only 12% of the full CI space. Notably, RCI outperforms recent regression-based SCI methods by delivering a more than 15% improvement in accuracy at comparable determinant counts. RCI also demonstrates higher efficiency than heat-bath CI on the strongly correlated chromium dimer, yielding a compact and accurate wave function. This pairwise learning-to-rank model provides a lightweight and modular plugin that can be seamlessly incorporated into other supervised learning frameworks.