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The Innovation Informatics

Optimization of neural network wave functions in variational Monte Carlo

Yuyang Wang, Xin Liu

Published Nov 27, 2025• 1 citation
Publisher

Abstract

The central challenge in materials science and quantum chemistry is solving the electronic Schrodinger equation, complicated by the curse of dimensionality as system size grows. Neural network-based variational Monte Carlo (NN-VMC) offers a promising path forward, achieving unprecedented accuracy at far lower cost than traditional high-level methods. However, the flexibility of neural network wavefunctions introduces a bottleneck: their optimization is high-dimensional, stochastic, and non-convex. This Perspective reviews the evolution of optimization methods in NN-VMC, from stochastic reconfiguration to approximate second-order algorithms and geometric insights. We highlight key challenges currently limiting scalability and efficiency, and outline future opportunities to advance the field. With continued progress in optimization, neural network techniques, and computer architectures, NN-VMC can tackle larger and more complex quantum systems and move from trailing experiments to guiding them.

DOI
10.59717/j.xinn-inform.2025.100025

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Computing accurate yet efficient approximations to the solutions of the electronic Schrödinger equation has been a paramount challenge of computational chemistry for decades. Quantum Monte Carlo methods are a promising avenue of development as their core algorithm exhibits a number of favorable properties: it is highly parallel and scales favorably with the considered system size, with an accuracy that is limited only by the choice of the wave function Ansatz. The recently introduced machine-learned parametrizations of quantum Monte Carlo Ansätze rely on the efficiency of neural networks as universal function approximators to achieve state of the art accuracy on a variety of molecular systems. With interest in the field growing rapidly, there is a clear need for easy to use, modular, and extendable software libraries facilitating the development and adoption of this new class of methods. In this contribution, the DeepQMC program package is introduced, in an attempt to provide a common framework for future investigations by unifying many of the currently available deep-learning quantum Monte Carlo architectures. Furthermore, the manuscript provides a brief introduction to the methodology of variational quantum Monte Carlo in real space, highlights some technical challenges of optimizing neural network wave functions, and presents example black-box applications of the program package. We thereby intend to make this novel field accessible to a broader class of practitioners from both the quantum chemistry and the machine learning communities.
Obtaining accurate solutions to many-electron quantum systems is of critical importance, in principle, such solutions allow computing most of possible chemical and physical properties from first principles. Exact solutions require utilizing exponentially scaling algorithms, which are not practical for large systems. Neural networks provide a new approach to approximating the solution while keeping a high level of accuracy. In this work, we explore a novel method of optimizing neural network wavefunctions by employing Evolution Strategies (ES) within a Variational Monte Carlo (VMC) framework. This allows us to more robustly find solutions while keeping a small number of parameters, making it an efficient alternative to traditional methods.
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Computing accurate yet efficient approximations to the solutions of the electronic Schrödinger equation has been a paramount challenge of computational chemistry for decades. Quantum Monte Carlo methods are a promising avenue of development as their core algorithm exhibits a number of favorable properties: it is highly parallel and scales favorably with the considered system size, with an accuracy that is limited only by the choice of the wave function Ansatz. The recently introduced machine-learned parametrizations of quantum Monte Carlo Ansätze rely on the efficiency of neural networks as universal function approximators to achieve state of the art accuracy on a variety of molecular systems. With interest in the field growing rapidly, there is a clear need for easy to use, modular, and extendable software libraries facilitating the development and adoption of this new class of methods. In this contribution, the DeepQMC program package is introduced, in an attempt to provide a common framework for future investigations by unifying many of the currently available deep-learning quantum Monte Carlo architectures. Furthermore, the manuscript provides a brief introduction to the methodology of variational quantum Monte Carlo in real space, highlights some technical challenges of optimizing neural network wave functions, and presents example black-box applications of the program package. We thereby intend to make this novel field accessible to a broader class of practitioners from both the quantum chemistry and the machine learning communities.