Physical Extrapolation of Quantum Observables by Generalization with Gaussian Processes

Vargas-Hernández, Rodrigo A.; Krems, Roman V.

doi:10.1007/978-3-030-40245-7_9

Cited by 3 publications

(5 citation statements)

References 43 publications

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“…As illustrated in Ref. [48], the iterative kernel construction algorithm based on BIC optimization is critical for building models with low generalization error.…”

Section: Discussionmentioning

confidence: 99%

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Gradient domain machine learning with composite kernels: improving the accuracy of PES and force fields for large molecules

Asnaashari,

Krems

2021

Preprint

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The generalization accuracy of machine learning models of potential energy surfaces (PES) and force fields (FF) for large polyatomic molecules can be generally improved either by increasing the number of training points or by improving the models. In order to build accurate models based on expensive high-level ab initio calculations, much of recent work has focused on the latter. In particular, it has been shown that gradient domain machine learning (GDML) models produce accurate results for high-dimensional molecular systems with a small number of ab initio calculations.The present work extends GDML to models with complex kernels built to maximize inference from a small number of molecular geometries. We illustrate that GDML models can be improved by increasing the complexity of underlying kernels through a greedy search algorithm using Bayesian information criterion as the model selection metric. We show that this requires including anisotropy into kernel functions and produces models with significantly smaller generalization errors. The results are presented for ethanol, uracil, malonaldehyde and aspirin. For aspirin, the model with complex kernels trained by forces at 1000 randomly sampled molecular geometries produces a global 57-dimensional PES with the mean absolute accuracy 0.177 kcal/mol (61.9 cm −1 ) and FFs with the mean absolute error 0.457 kcal/mol Å −1 .

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“…As illustrated in Ref. [48], the iterative kernel construction algorithm based on BIC optimization is critical for building models with low generalization error.…”

Section: Discussionmentioning

confidence: 99%

“…As shown previously, complex kernel functions cannot be constructed as random combinations of simple kernels [48]. Instead, the kernel construction algorithm should be guided by a model selection metric.…”

Section: Complex Kernelsmentioning

confidence: 99%

Gradient domain machine learning with composite kernels: improving the accuracy of PES and force fields for large molecules

Asnaashari,

Krems

2021

Preprint

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“…We optimize the functional form of the kernel function using a greedy search algorithm that combines simple functions into linear combinations and products, as was described in [17,18] and used for various applications in [103,108,109,[113][114][115]. The kernel construction algorithm is illustrated in figure 4.…”

Section: Method: Gaussian Process Regression With Variable Kernelsmentioning

confidence: 99%

Efficient interpolation of molecular properties across chemical compound space with low-dimensional descriptors

Mao,

Krems

2024

Mach. Learn.: Sci. Technol.

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We demonstrate accurate data-starved models of molecular properties for interpolation in chemical compound spaces with low-dimensional descriptors. Our starting point is based on three-dimensional, universal, physical descriptors derived from the properties of the distributions of the eigenvalues of Coulomb matrices. To account for the shape and composition of molecules, we combine these descriptors with six-dimensional features informed by the Gershgorin circle theorem. We use the nine-dimensional descriptors thus obtained for Gaussian process regression based on kernels with variable functional form, leading to extremely eﬃcient, low-dimensional interpolation models. The resulting models trained with 100 molecules are able to predict the product of entropy and temperature (S × T ) and zero point vibrational energy (ZPVE) with the absolute error under 1 kcal/mol for > 78 % and under 1.3 kcal/mol for > 92 % of molecules in the test data. The test data comprises 20,000 molecules with complexity varying from three atoms to 29 atoms and the ranges of S × T and ZPVE covering 36 kcal/mol and 161 kcal/mol, respectively. We also illustrate that the descriptors based on the Gershgorin circle theorem yield more accurate models of molecular entropy than those based on graph neural networks that explicitly account for the atomic connectivity of molecules.

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“…This methodology is commonly named as the Bayesian information criterion (BIC). These kernel structure discovery methods have been demonstrated to extrapolate physical observables accurately enough to detect phase transitions 34,35 . Additionally, GPs with complex kernels have shown the possibility to predict accurate energies for PES trained only with low energy points 17,18 .…”

Section: Gaussian Processesmentioning

confidence: 99%

“…The latter quantifies the similarity between a pair of points. If the kernel function can generalize a similarity metric, GPs are efficient regression algorithms that require less training data than NNs 1 , and are also capable of extrapolating functions beyond the training data regime 17,[34][35][36][37] . To achieve more robust kernel functions, once can simply combine different simple kernel functions 38,39 .…”

Section: Introductionmentioning

confidence: 99%

Gaussian Processes with Spectral Delta kernel for higher accurate Potential Energy surfaces for large molecules

Vargas-Hernández,

Gardner

2021

Preprint

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The interpolation of high-dimensional potential energy surfaces (PESs) is commonly done with physicallyinspired deep-neural network models. In this work, we illustrate that Gaussian Processes (GPs) are also capable of interpolating high-dimensional complex physical systems. The accuracy of GPs depends on the robustness of the kernel function, and a boost in the accuracy is achieved by linearly combining kernel functions. In this work, we proposed an alternative route by parametrizing the kernel function through Bochners' theorem. We interpolated the PES of various chemical systems achieving a global accuracy of < 0.06 kcal/mol for Benzene, Malonaldehyde, Ethanol, and protonated Imidazole dimer using only 15 000 training points. Additionally, for Aspirin, we achieved a global error of 0.063 kcal/mol with 20 000 points. Given these results, we believe this kernel function is system-agnostic and could allow GPs to tackle a wider variety of high-dimensional physical systems.

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Physical Extrapolation of Quantum Observables by Generalization with Gaussian Processes

Cited by 3 publications

References 43 publications

Gradient domain machine learning with composite kernels: improving the accuracy of PES and force fields for large molecules

Gradient domain machine learning with composite kernels: improving the accuracy of PES and force fields for large molecules

Efficient interpolation of molecular properties across chemical compound space with low-dimensional descriptors

Gaussian Processes with Spectral Delta kernel for higher accurate Potential Energy surfaces for large molecules

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