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Convergence to the fixed-node limit in deep variational Monte Carlo
Z Schätzle1, J Hermann1, F Noé1
1FU Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany.
The Journal of Chemical Physics
|April 3, 2021
Summary
Deep neural networks in variational quantum Monte Carlo (QMC) improve accuracy by overcoming basis set limitations and reaching the fixed-node limit. Larger networks yield more accurate variational energies, enhancing QMC
Area of Science:
- Computational Chemistry
- Quantum Mechanics
- Machine Learning
Background:
- Variational quantum Monte Carlo (QMC) is a powerful ab initio method for solving the electronic Schrödinger equation.
- The accuracy of variational QMC is often limited by the flexibility of trial wavefunctions (Ansätze).
- Deep neural networks offer a promising new avenue for constructing highly flexible Ansätze in QMC.
Purpose of the Study:
- To analyze the convergence behavior of deep neural network Ansätze in variational QMC.
- To understand how increasing network size impacts the approach to the fixed-node limit.
- To benchmark the performance of deep variational QMC against traditional methods.
Main Methods:
- Investigated deep neural network Ansätze (PauliNet, FermiNet) within variational QMC.
- Analyzed the impact of network size on achieving the mean-field complete-basis-set limit.
- Performed hyperparameter scans for deep Jastrow factors in LiH and H4 systems.
- Benchmarked mean-field and many-body Ansätze for H2O, including Slater-Jastrow and Slater-Jastrow-backflow variations.
Main Results:
- Deep neural networks successfully overcome small basis set limitations, reaching the mean-field complete-basis-set limit.
- Sufficiently large deep neural network Ansätze achieve variational energies at the fixed-node limit for electron correlation.
- Deep variational QMC significantly improved the recovery of fixed-node correlation energy compared to previous methods.
- A single-determinant Slater-Jastrow-backflow Ansatz demonstrated the ability to overcome fixed-node limitations.
Conclusions:
- Deep neural networks provide a pathway to highly accurate variational QMC calculations, approaching the accuracy of diffusion QMC.
- The flexibility of deep Ansätze allows for overcoming limitations of traditional trial wavefunctions.
- This work provides insights into the convergence of deep variational QMC and guides future neural network architecture development.
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