Permutationally invariant polynomial representation of polarizability tensor surfaces for linear regression analysis

Omodemi, Oluwaseun; Kaledin, Martina; Kaledin, Alexey L.

doi:10.1002/jcc.26952

Cited by 5 publications

(10 citation statements)

References 38 publications

(102 reference statements)

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“…Zhang et al proposed a tensorial embedded atom neural network (T-EANN) model to learn molecular polarizability in which the scalar NN outputs or their derivatives are multiplied by atomic coordinate vectors to preserve the rotationally covariant symmetry . Omodemi et al described a linearly functional form for a polarizability tensor surface with permutationally invariant polynomials . Schütt et al proposed message-passing neural networks to predict molecular polarizability tensors with equivariant feature vectors or physically inspired response formalism …”

Section: Introductionmentioning

confidence: 99%

Accurate and Interpretable Dipole Interaction Model-Based Machine Learning for Molecular Polarizability

Feng

Zhang

et al. 2023

J. Chem. Theory Comput.

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Polarizabilities play significant roles in describing dispersive and inductive interactions of the atom and molecular systems. However, an accurate prediction of molecular polarizabilities from first principles is computationally prohibitive. Although physical models or statistical machine learning models have been proposed, either a lack of accurate description of local chemical environments or demanding a large number of samples for training has limited their practical applications. In this study, we combine a physically inspired dipole interaction model and an accurate neural network method for predicting the polarizability tensors of molecules. With the local chemical environment precisely described and the requirement of rotational covariance naturally fulfilled, this hybrid model is proven to give an accurate molecular polarizability prediction, essentially reducing the number of training samples. The atomic polarizabilities are physically interpretable and transferable to larger molecules unseen in the training set. This promising method may find its wide range of applications, such as spectroscopic simulations and the construction of polarizable force fields.

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Section: Introductionmentioning

confidence: 99%

Accurate and Interpretable Dipole Interaction Model-Based Machine Learning for Molecular Polarizability

Feng

Zhang

et al. 2023

J. Chem. Theory Comput.

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“…Following this initial step, we run NVE trajectories, with energies and forces computed on the fly, at each of the E j total energies with zero total angular momentum using the B3LYP functional [64] with aug-cc-pVDZ basis set [65]. As was noted by us recently in applications involving PIP fitting of polarizability tensors [38,39] and discussed by others in different contexts [66,67], augmenting orbital basis sets with diffuse functions plays a very important role in polarizability calculations. In Supporting information we provide the equilibrium geometries (Tables S1, S2), multipole and polarizability tensors (Tables S3, S4, S5) and vibrational frequencies (Table S6).…”

Section: A Pip Representationmentioning

confidence: 99%

“…More advanced methodologies, such as those based on polynomial functions fitted to ab initio data, bring up a family of alternative approaches [32–37]. Representation of the molecular dipole moment and polarizability tensor, as global functions of nuclear coordinates fitted to an extensive set of high quality ab initio data is a rather challenging task; however, recent developments in the permutationally invariant polynomial (PIP) theory have produced some major new advances [32–36, 38–40]. In a related manner, machine leaning techniques, in particular those based on artificial neural networks (ANN) [41], have shown themselves to be competitive in accurate representation of multipole moments and dipole polarizability tensor trained on ab initio derived data [13–16, 42, 43].…”

Section: Introductionmentioning

confidence: 99%

“…In this work we use linear regression by means of the singular value decomposition treatment[61] as implemented in the DGESVD subroutine of the Intel Math Kernel Library[62]. This procedure was done by us previously in similar applications[39].S C H E M E 1 Details of transformation of a nuclear configuration X into an identical configuration X' as a result of a permutation of the identical nuclei 2 and 3. The two-sided arrows indicate the elements being transformed upon the permutation.…”

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confidence: 99%

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Revisiting theN(N + 1)/2‐sites‐type Gaussian charge model for permutationally invariant polynomial fitting of global molecular tensor surfaces

Kudratov

Kaledin

2023

Int J of Quantum Chemistry

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The exact expressions for the dipole, quadrupole, and octupoles of a collection of N point charges involve summations of corresponding tensors over the N sites weighted by their charge magnitudes. When the point charges are atoms (in a molecule) the N‐site formula is an approximation, and one must integrate over the electron density to recover the exact multipoles. In the present work we revisit the N(N + 1)/2‐site point charge density model of Hall (Chem. Phys. Lett. 6, 501, 1973) for the purpose of fitting ab initio derived multipole moment hypersurfaces using permutationally invariant polynomials (PIP). We examine new approaches in PIP‐fitting procedures for the dipole, quadrupole, octupole moments, and polarizability tensor surfaces (DMS, QMS, OMS and PTS, respectively) for a non‐polar CCl4 and a polar CHCl3 and show that compared to the primitive N‐site model the N(N + 1)/2‐site model appreciably improves the relative RMSE of the DMS and does much more substantially so, by an order of magnitude, for the corresponding ones of QMS and OMS. Training datasets are obtained by sampling potential energies up to 18 000 cm−1 above the global minima, generated by molecular dynamics simulations at the DFT B3LYP/aug‐cc‐pVDZ level of theory.

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“…The model is a multivariate model designed based on the support vector method. Multiple indicators can be applied and combined in the analysis of the forecasting process [17][18]. The model has several main components.…”

Section: Support Vector Modelmentioning

confidence: 99%

Linear Regression for Water Pollution Control Planning under Support Vectors

2021

WPPCP

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China is facing a serious situation in water pollution prevention and control, and the uncertainty of regional development should be fully considered when formulating water pollution prevention and control planning, and its scientificity should be improved through effective mathematical methods. Water resources and water environment are closely related to human health, and China has not yet established a comprehensive set of water resources and environment monitoring network, so the water pollution prevention and control planning process is crucial to the implementation of water pollution control planning. Due to the relatively low level of economic development in China, the state attaches less importance to water pollution prevention and control issues, and therefore also has a certain impact on the water environment. In order to reduce the problems caused by water pollution, the Water Resources Management Committee has organised the preparation of water pollution control plans. This paper presents an empirical analysis of the support vector model for water pollution prevention and control planning in China. The results of the study show that the introduction of the support vector approach to water pollution prevention and control planning in China can effectively improve the scientific nature of the planning. This paper firstly introduces the support vector model, which is a multivariate model designed based on the support vector method, and can be used to analyse multiple indicators and conduct comprehensive analysis in the prediction process; finally, the planning scheme should be designed with full consideration of water pollution prevention and control planning to avoid conflicts between different water resources and environmental issues. However, there are many problems with the use of the support vector approach in water pollution prevention and control planning that warrant further research.

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Permutationally invariant polynomial representation of polarizability tensor surfaces for linear regression analysis

Cited by 5 publications

References 38 publications

Accurate and Interpretable Dipole Interaction Model-Based Machine Learning for Molecular Polarizability

Accurate and Interpretable Dipole Interaction Model-Based Machine Learning for Molecular Polarizability

Revisiting theN(N + 1)/2‐sites‐type Gaussian charge model for permutationally invariant polynomial fitting of global molecular tensor surfaces

Linear Regression for Water Pollution Control Planning under Support Vectors

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