Machine learning one-dimensional spinless trapped fermionic systems with neural-network quantum states

Keeble, J. W. T.; Drissi, M.; Rojo-Francàs, A.; Juliá-Díaz, B.; Rios, A.

doi:10.1103/physreva.108.063320

Cited by 3 publications

(18 citation statements)

References 75 publications

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“…The inputs to our network are the A positions of fermions in the system, x i , i = 1, …, A , and the output is the many-body wave function Ψ θ x 1 , …, x A in the log domain. The state depends on a series of network weights and biases, succinctly summarized by a variable θ of dimension N [7]. The network is composed of four core components: equivariant layers, generalized Slater matrices (GSMs), Gaussian log-envelope functions and a summed signed-log determinant function [46].…”

Section: (C) Neural Quantum States and Monte Carlo Samplingmentioning

confidence: 99%

“…HF and CI results are displayed for reference, with horizontal green and orange dashed lines. CI results are displayed for A ≤ 5 and V 0 ≥ − 10 where we have access to converged results [7].…”

Section: (D) Improving the Scaling Estimationmentioning

confidence: 99%

“…As an additional example that showcases the optimization power of DGD, we now proceed to compare DGD results with Adam [26]. We have relied on Adam in the NQS applications of [7], where we employ the default hyperparameters and a learning rate of 10 −4 . In that case, we train the network to minimize the energy for 10 5 epochs.…”

Section: (C) Application To Vmcmentioning

confidence: 99%

“…Finally, to provide a reasonable starting point for the energy minimization algorithms, we drive the NQS through a pre-training phase. This is a supervised learning problem, where we demand that the network reproduces the many-body wave function of the non-interacting system [7,46]. Throughout this work, the parameters of the network are randomly initialized before going through 10 3 pre-training epochs using the Adam optimizer.…”

mentioning

confidence: 99%

“…The top (bottom) left panels show results for A = 2 (A = 4) for V 0 = − 10.HF and CI benchmarks are displayed for reference with green-and orange-dashed lines, respectively. Since we do not have access to converged CI results in all cases, we also display for reference results obtained in Ref [7]. with blue-dotted lines and referred to as E g .…”

mentioning

confidence: 99%

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Second-order optimization strategies for neural network quantum states

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The Variational Monte Carlo (VMC) method has recently seen important advances through the use of neural network quantum states. While more and more sophisticated ansatze have been designed to tackle a wide variety of quantum many-body problems, modest progress has been made on the associated optimization algorithms. In this work, we revisit the Kronecker-Factored Approximate Curvature (KFAC), an optimizer that has been used extensively in a variety of simulations. We suggest improvements in the scaling and the direction of this optimizer and find that they substantially increase its performance at a negligible additional cost. We also reformulate the VMC approach in a game theory framework, to propose a novel optimizer based on decision geometry. We find that on a practical test case for continuous systems, this new optimizer consistently outperforms any of the KFAC improvements in terms of stability, accuracy and speed of convergence. Beyond VMC, the versatility of this approach suggests that decision geometry could provide a solid foundation for accelerating a broad class of machine learning algorithms. This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.

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Section: (C) Neural Quantum States and Monte Carlo Samplingmentioning

confidence: 99%

Section: (D) Improving the Scaling Estimationmentioning

confidence: 99%

Section: (C) Application To Vmcmentioning

confidence: 99%

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Second-order optimization strategies for neural network quantum states

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Radial and angular correlations in a confined system of two atoms in two-dimensional geometry

Kościk

2024

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We study the ground-state entanglement between two atoms in a two-dimensional isotropic harmonic trap. We consider a finite-range soft-core interaction that can be applied to simulate various atomic systems. We provide detailed results on the dependence of the correlations on the parameters of the system. Our investigations show that in the hardcore limit, the wave function can be approximated as the product of the radial and angular components regardless of the interaction range. This implies that the radial and angular correlations are independent of one another. However, correlations within the radial and angular components persist and are heavily influenced by the interaction range. The radial correlations are generally weaker than the angular correlations. When soft-core interactions are considered, the correlations exhibit more complex behavior.

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Neural-network quantum states for ultra-cold Fermi gases

Kim,

Pescia,

Fore

et al. 2024

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Ultra-cold Fermi gases exhibit a rich array of quantum mechanical properties, including the transition from a fermionic superfluid Bardeen-Cooper-Schrieffer (BCS) state to a bosonic superfluid Bose-Einstein condensate (BEC). While these properties can be precisely probed experimentally, accurately describing them poses significant theoretical challenges due to strong pairing correlations and the non-perturbative nature of particle interactions. In this work, we introduce a Pfaffian-Jastrow neural-network quantum state featuring a message-passing architecture to efficiently capture pairing and backflow correlations. We benchmark our approach on existing Slater-Jastrow frameworks and state-of-the-art diffusion Monte Carlo methods, demonstrating a performance advantage and the scalability of our scheme. We show that transfer learning stabilizes the training process in the presence of strong, short-ranged interactions, and allows for an effective exploration of the BCS-BEC crossover region. Our findings highlight the potential of neural-network quantum states as a promising strategy for investigating ultra-cold Fermi gases.

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Machine learning one-dimensional spinless trapped fermionic systems with neural-network quantum states

Cited by 3 publications

References 75 publications

Second-order optimization strategies for neural network quantum states

Second-order optimization strategies for neural network quantum states

Radial and angular correlations in a confined system of two atoms in two-dimensional geometry

Neural-network quantum states for ultra-cold Fermi gases

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