Quantum Gaussian process model of potential energy surface for a polyatomic molecule

Dai, Jun; Krems, Roman V.

doi:10.1063/5.0088821

Cited by 5 publications

(4 citation statements)

References 77 publications

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“…Each function f i is chosen to have properties of kernel functions of a reproducing kernel Hilbert space, which guarantees that the resulting complex function can be used as the kernel function for a kernel ML model. As was previously demonstrated, this kernel construction algorithm yields GP models that produce accurate PES by both interpolation and extrapolation [21,36,38,56]. However, the iterative optimization of kernel complexity for identifying optimal kernel functions for a given PES is numerically expensive [21,36,38,39].…”

Section: Gp Models With Complex Kernelsmentioning

confidence: 91%

Neural network Gaussian processes as efficient models of potential energy surfaces for polyatomic molecules

Dai,

Krems

2023

Mach. Learn.: Sci. Technol.

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Kernel models of potential energy surfaces (PES) for polyatomic molecules are often restricted by a specific choice of the kernel function.This can be avoided by optimizing the complexity of the kernel function. For regression problems with very expensive data, the functional form of the model kernels can be optimized in the Gaussian process (GP) setting through compositional function search guided by the Bayesian information criterion. However, the compositional kernel search is computationally demanding and relies on greedy strategies, which may yield sub-optimal kernels. An alternative strategy of increasing complexity of GP kernels treats a GP as a Bayesian neural network (NN) with a variable number of hidden layers, which yields NNGP models. Here, we present a direct comparison of GP models with composite kernels and NNGP models for applications aiming at the construction of global PES for polyatomic molecules. We show that NNGP models of PES can be trained much more efficiently and yield better generalization accuracy without relying on any specific form of the kernel function. We illustrate that NNGP models trained by distributions of energy points at low energies produce accurate predictions of PES at high energies. We also illustrate that NNGP models can extrapolate in the input variable space by building the free energy surface of the Heisenberg model trained in the paramagnetic phase and validated in the ferromagnetic phase. By construction, composite kernels yield more accurate models than kernels with a fixed functional form. Therefore, by illustrating that NNGP models outperform GP models with composite kernels, our work suggests that NNGP models should be a preferred choice of kernel models for PES.

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Section: Gp Models With Complex Kernelsmentioning

confidence: 91%

Neural network Gaussian processes as efficient models of potential energy surfaces for polyatomic molecules

Dai,

Krems

2023

Mach. Learn.: Sci. Technol.

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“…The main challenge in constructing multi-dimensional PESs is to represent the function between the potential energies and the molecular nuclear coordinates based on the discrete ab initio data. Fitting PESs with machine learning models has been gaining popularity in recent years, and using an artificial neural network (NN) [ 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 ] or a Gaussian process (GP) [ 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 ] are the two most common approaches. GP is a kernel-based supervised statistical learning method [ 71 ], which has been widely used to solve physical chemistry problems such as mapping high-dimensional PESs and simulating quantum scattering dynamics.…”

Section: Ground-state Lina 2 Pesmentioning

confidence: 99%

Globally Accurate Gaussian Process Potential Energy Surface and Quantum Dynamics Studies on the Li(2S) + Na2 → LiNa + Na Reaction at Low Collision Energies

et al. 2023

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The LiNa2 reactive system has recently received great attention in the experimental study of ultracold chemical reactions, but the corresponding theoretical calculations have not been carried out. Here, we report the first globally accurate ground-state LiNa2 potential energy surface (PES) using a Gaussian process model based on only 1776 actively selected high-level ab initio training points. The constructed PES had high precision and strong generalization capability. On the new PES, the quantum dynamics calculations on the Li(2S) + Na2(v = 0, j = 0) → LiNa + Na reaction were carried out in the 0.001–0.01 eV collision energy range using an improved time-dependent wave packet method. The calculated results indicate that this reaction is dominated by a complex-forming mechanism at low collision energies. The presented dynamics data provide guidance for experimental research, and the newly constructed PES could be further used for ultracold reaction dynamics calculations on this reactive system.

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“…Given the intrinsic quantum nature of the PES, it is natural to believe that quantum algorithms may indeed help [17,18]. Through the implementation of a supervised learning setup where the role of the classical NN is played by a parameterized quantum circuit (PQC), the authors of [19][20][21] provided the first evidence that quantum ML (QML) routines may offer improved and more accurate PES predictions.…”

Section: Introductionmentioning

confidence: 99%

Quantum extreme learning of molecular potential energy surfaces and force fields

Lo Monaco,

Bertini,

Lorenzo

et al. 2024

Mach. Learn.: Sci. Technol.

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Quantum machine learning algorithms are expected to play a pivotal role in quantum chemistry simulations in the immediate future. One of such key applications is the training of a quantum neural network to learn the potential energy surface and force field of molecular systems. We address this task by using the quantum extreme learning machine paradigm. This particular supervised learning routine allows for a resource efficient training, consisting of a simple linear regression performed on a classical computer. We have tested a setup that can be used to study molecules of any dimension and optimized for immediate use on NISQ devices with a limited number of native gates. We have applied this setup to three case studies: lithium hydride, water, and formamide, carrying out both noiseless simulations and actual implementation on IBM quantum hardware. Compared to other supervised learning routines, the proposed setup requires minimal quantum resources, making it feasible for direct implementation on quantum platforms, while still achieving a high level of predictive accuracy compared to simulations. Our encouraging results pave the way towards the future application to more complex molecules, being the proposed setup scalable.

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Quantum Gaussian process model of potential energy surface for a polyatomic molecule

Cited by 5 publications

References 77 publications

Neural network Gaussian processes as efficient models of potential energy surfaces for polyatomic molecules

Neural network Gaussian processes as efficient models of potential energy surfaces for polyatomic molecules

Globally Accurate Gaussian Process Potential Energy Surface and Quantum Dynamics Studies on the Li(2S) + Na2 → LiNa + Na Reaction at Low Collision Energies

Quantum extreme learning of molecular potential energy surfaces and force fields

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