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arXiv:2202.10126 · International Journal of Quantum Chemistry

Improving the performance of fermionic neural networks with the Slater exponential Ansatz

Denis Bokhan, Maria M. Kolchenko, Aleksey S. Boev, Aleksey K. Fedorov, Dmitrii N. Trubnikov

Published Feb 17, 2023• 0 citations
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Abstract

Abstract In this work, we propose a technique for the use of fermionic neural networks (FermiNets) with the Slater exponential Ansatz for electron‐nuclear and electron–electron distances, which provides faster convergence of target ground‐state energies due to a better description of the interparticle interaction in the vicinities of the coalescence points, while the accuracies of results, obtained with original and input‐modified FermiNets are similar due to high expressiveness of underlying neural network. Our analysis of learning curves indicates on the possibility to obtain accurate energies with smaller batch sizes using arguments of the bagging approach. In order to obtain even more accurate results for the ground‐state energies, we propose an extrapolation scheme for estimating Monte Carlo integrals in the limit of an infinite number of points. Numerical tests for a set of molecules demonstrate a good agreement with the results of the original FermiNets approach (achieved with larger batch sizes than required by our approach) and with results of the coupled‐cluster singles and doubles with perturbative triples (CCSD(T)) method that are calculated in the complete basis set limit.

DOI
10.1002/qua.27107

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Abstract In this work, we propose a technique for the use of fermionic neural networks (FermiNets) with the Slater exponential Ansatz for electron‐nuclear and electron–electron distances, which provides faster convergence of target ground‐state energies due to a better description of the interparticle interaction in the vicinities of the coalescence points, while the accuracies of results, obtained with original and input‐modified FermiNets are similar due to high expressiveness of underlying neural network. Our analysis of learning curves indicates on the possibility to obtain accurate energies with smaller batch sizes using arguments of the bagging approach. In order to obtain even more accurate results for the ground‐state energies, we propose an extrapolation scheme for estimating Monte Carlo integrals in the limit of an infinite number of points. Numerical tests for a set of molecules demonstrate a good agreement with the results of the original FermiNets approach (achieved with larger batch sizes than required by our approach) and with results of the coupled‐cluster singles and doubles with perturbative triples (CCSD(T)) method that are calculated in the complete basis set limit.
The Fermionic Neural Network (FermiNet) is a recently-developed neural network architecture that can be used as a wavefunction Ansatz for many-electron systems, and has already demonstrated high accuracy on small systems. Here we present several improvements to the FermiNet that allow us to set new records for speed and accuracy on challenging systems. We find that increasing the size of the network is sufficient to reach chemical accuracy on atoms as large as argon. Through a combination of implementing FermiNet in JAX and simplifying several parts of the network, we are able to reduce the number of GPU hours needed to train the FermiNet on large systems by an order of magnitude. This enables us to run the FermiNet on the challenging transition of bicyclobutane to butadiene and compare against the PauliNet on the automerization of cyclobutadiene, and we achieve results near the state of the art for both.
Deep learning techniques have opened a new venue for electronic structure theory in recent years. In contrast to traditional methods, deep neural networks provide much more expressive and flexible wave function Ans\"atze, resulting in better accuracy and timescale behavior. In order to study larger systems while retaining sufficient accuracy, we integrate a powerful neural-network-based model (FermiNet) with the effective core potential method, which helps to reduce the complexity of the problem by replacing inner core electrons with additional semilocal potential terms in the Hamiltonian. In this work, we calculate the ground-state energy of 3d3d3d transition metal atoms and their monoxides, which is quite challenging for the original FermiNet work, and the results are consistent with both experimental data and other state-of-the-art computational methods. Our work is an important step for a broader application of deep learning in the electronic structure calculation of molecules and materials.
Deep neural networks have been very successful as highly accurate wave function Ansätze for variational Monte Carlo calculations of molecular ground states. We present an extension of one such Ansatz, FermiNet, to calculations of the ground states of periodic Hamiltonians, and study the homogeneous electron gas. FermiNet calculations of the ground-state energies of small electron gas systems are in excellent agreement with previous initiator full configuration interaction quantum Monte Carlo and diffusion Monte Carlo calculations. We investigate the spin-polarized homogeneous electron gas and demonstrate that the same neural network architecture is capable of accurately representing both the delocalized Fermi liquid state and the localized Wigner crystal state. The network converges on the translationally invariant ground state at high density and spontaneously breaks the symmetry to produce the crystalline ground state at low density, despite being given no a priori knowledge that a phase transition exists.
Understanding superfluidity remains a major goal of condensed matter physics. Here, we tackle this challenge utilizing the recently developed fermionic neural network (FermiNet) wave function [D. Pfau , .] for variational Monte Carlo calculations. We study the unitary Fermi gas, a system with strong, short-range, two-body interactions known to possess a superfluid ground state but difficult to describe quantitatively. We demonstrate key limitations of the FermiNet in studying the unitary Fermi gas and propose a simple modification based on the idea of an antisymmetric geminal power singlet (AGPs) wave function. The new AGPs FermiNet outperforms the original FermiNet significantly in paired systems, giving results which are more accurate than fixed-node diffusion Monte Carlo and are consistent with experiment. We prove mathematically that the new , which differs from the original only by the method of antisymmetrization, is a strict generalization of the original FermiNet architecture, despite the use of fewer parameters. Our approach shares several advantages with the original FermiNet: The use of a neural network removes the need for an underlying basis set; sand the flexibility of the network yields extremely accurate results within a variational quantum Monte Carlo framework that provides access to unbiased estimates of arbitrary ground-state expectation values. We discuss how the method can be extended to study other superfluid. Published by the American Physical Society 2024
Given access to accurate solutions of the many-electron Schrödinger equation, nearly all chemistry could be derived from first principles.Exact wave functions of interesting chemical systems are out of reach because they are NP-hard to compute in general, but approximations can be found using polynomially scaling algorithms.The key challenge for many of these algorithms is the choice of wave function approximation, or Ansatz, which must trade off between efficiency and accuracy.Neural networks have shown impressive power as accurate practical function approximators and promise as a compact wave-function Ansatz for spin systems, but problems in electronic structure require wave functions that obey Fermi-Dirac statistics.Here we introduce a novel deep learning architecture, the Fermionic neural network, as a powerful wave-function Ansatz for many-electron systems.The Fermionic neural network is able to achieve accuracy beyond other variational quantum Monte Carlo Ansatz on a variety of atoms and small molecules.Using no data other than atomic positions and charges, we predict the dissociation curves of the nitrogen molecule and hydrogen chain, two challenging strongly correlated systems, to significantly higher accuracy than the coupled cluster method, widely considered the most accurate scalable method for quantum chemistry at equilibrium geometry.This demonstrates that deep neural networks can improve the accuracy of variational quantum Monte Carlo to the point where it outperforms other ab initio quantum chemistry methods, opening the possibility of accurate direct optimization of wave functions for previously intractable many-electron systems.
We present an algorithm to estimate the excited states of a quantum system by variational Monte Carlo, which has no free parameters and requires no orthogonalization of the states, instead transforming the problem into that of finding the ground state of an expanded system. Arbitrary observables can be calculated, including off-diagonal expectations, such as the transition dipole moment. The method works particularly well with neural network ansätze, and by combining this method with the FermiNet and Psiformer ansätze, we can accurately recover excitation energies and oscillator strengths on a range of molecules. We achieve accurate vertical excitation energies on benzene-scale molecules, including challenging double excitations. Beyond the examples presented in this work, we expect that this technique will be of interest for atomic, nuclear, and condensed matter physics.