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Journal of Chemical Theory and Computation

Reinforcement Learning Configuration Interaction

Joshua J. Goings, Hang Hu, Chao Yang, Xiaosong Li

Published Aug 23, 2021• 32 citations
Publisher

Abstract

Selected configuration interaction (sCI) methods exploit the sparsity of the full configuration interaction (FCI) wave function, yielding significant computational savings and wave function compression without sacrificing the accuracy. Despite recent advances in sCI methods, the selection of important determinants remains an open problem. We explore the possibility of utilizing reinforcement learning approaches to solve the sCI problem. By mapping the configuration interaction problem onto a sequential decision-making process, the agent learns on-the-fly which determinants to include and which to ignore, yielding a compressed wave function at near-FCI accuracy. This method, which we call reinforcement-learned configuration interaction, adds another weapon to the sCI arsenal and highlights how reinforcement learning approaches can potentially help solve challenging problems in electronic structure theory.

DOI
10.1021/acs.jctc.1c00010

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Selected configuration interaction (sCI) methods exploit the sparsity of the full configuration interaction (FCI) wave function, yielding significant computational savings and wave function compression without sacrificing the accuracy. Despite recent advances in sCI methods, the selection of important determinants remains an open problem. We explore the possibility of utilizing reinforcement learning approaches to solve the sCI problem. By mapping the configuration interaction problem onto a sequential decision-making process, the agent learns on-the-fly which determinants to include and which to ignore, yielding a compressed wave function at near-FCI accuracy. This method, which we call reinforcement-learned configuration interaction, adds another weapon to the sCI arsenal and highlights how reinforcement learning approaches can potentially help solve challenging problems in electronic structure theory.
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.
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.
Accurate solutions to the electronic Schrödinger equation remain a central challenge in quantum chemistry due to the exponential growth of the many-electron Hilbert space. Selected configuration interaction (SCI) methods mitigate this challenge by restricting the wavefunction expansion to a subset of important determinants, but their efficiency is limited by the quality/cost of determinant selection and Hamiltonian diagonalization. In this work, we propose QUBO-SCI, a novel approach that reformulates the selection step in SCI as a quadratic unconstrained binary optimization (QUBO) problem. This formulation enables the sampling of low-energy electronic configurations as bitstrings using both quantum-inspired approaches and quantum annealing hardware. The sampled configurations are then incorporated into an iterative SCI framework using a perturbative importance criterion. We demonstrate the method on small benchmark systems, including H 2 , C 2 , H 2 O, and N 2 , showing that QUBO-SCI achieves near-FCI accuracy with a significantly reduced number of determinants. The results highlight the potential of annealing-based sampling as an efficient alternative to both conventional determinant selection strategies and circuit-based quantum SCI approaches in electronic structure calculations.
Selected configuration interaction (SCI) methods are currently enjoying a resurgence due to several recent developments which improve either the overall computational efficiency or the compactness of the resulting SCI vector. These recent advances have made it possible to get full CI (FCI) quality results for much larger orbital active spaces compared to conventional approaches. However, due to the starting assumption that the FCI vector has only a small number of significant Slater determinants, SCI becomes intractable for systems with strong correlation. This paper introduces a method for developing SCI algorithms in a way which exploits local molecular structure to significantly reduce the number of SCI variables. The proposed method is defined by first grouping the orbitals into clusters over which we can define many-particle cluster states. We then directly perform the SCI algorithm in a basis of tensor products of cluster states instead of Slater determinants. While the approach is general for arbitrarily defined cluster states, we find significantly improved performance by defining cluster states through a Tucker decomposition of the global (and sparse) SCI vector. To demonstrate the potential of this method, called tensor product selected configuration interaction (TPSCI), we present numerical results for a diverse set of examples: (1) modified Hubbard model with different inter- and intracluster hopping terms, (2) less obviously clusterable cases of bond breaking in N 2 and F 2, and (3) ground state energies of large planar π-conjugated systems with active spaces of up to 42 electrons in 42 orbitals. These numerical results show that TPSCI can be used to significantly reduce the number of SCI variables in the variational space, thus paving a path for extending these deterministic and variational SCI approaches to a wider range of physical systems.