A smooth basis for atomistic machine learning

• URL: http://arxiv.org/abs/2209.01948v2
• Date: Tue, 23 May 2023 18:22:43 GMT
• Title: A smooth basis for atomistic machine learning
• Authors: Filippo Bigi, Kevin Huguenin-Dumittan, Michele Ceriotti, David E. Manolopoulos
• Abstract summary: We investigate the basis that results from the solution of the Laplacian eigenvalue problem within a sphere around the atom of interest. We show that this generates the smoothest possible basis of a given size within the sphere. We consider several unsupervised metrics of the quality of a basis for a given dataset, and show that the Laplacian eigenstate basis has a performance that is much better than some widely used basis sets.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighbourhood of each atom in the system. Symmetry considerations support the use of spherical harmonics to expand the angular dependence of this density, but there is as yet no clear rationale to choose one radial basis over another. Here we investigate the basis that results from the solution of the Laplacian eigenvalue problem within a sphere around the atom of interest. We show that this generates the smoothest possible basis of a given size within the sphere, and that a tensor product of Laplacian eigenstates also provides the smoothest possible basis for expanding any higher-order correlation of the atomic density within the appropriate hypersphere. We consider several unsupervised metrics of the quality of a basis for a given dataset, and show that the Laplacian eigenstate basis has a performance that is much better than some widely used basis sets and is competitive with data-driven bases that numerically optimize each metric. In supervised machine learning tests, we find that the optimal function smoothness of the Laplacian eigenstates leads to comparable or better performance than can be obtained from a data-driven basis of a similar size that has been optimized to describe the atom-density correlation for the specific dataset. We conclude that the smoothness of the basis functions is a key and hitherto largely overlooked aspect of successful atomic density representations.

Related papers

• Wigner kernels: body-ordered equivariant machine learning without a basis [0.0]
  We propose a novel density-based method which involves computing Wigner kernels'' Wigner kernels are fully equivariant and body-ordered kernels that can be computed iteratively with a cost that is independent of the radial-chemical basis. We present several examples of the accuracy of models based on Wigner kernels in chemical applications.
  arXiv  Detail & Related papers  (2023-03-07T18:34:55Z)
• Electronic-structure properties from atom-centered predictions of the electron density [0.0]
  electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. We propose a gradient-based approach to minimize the loss function of the regression problem in an optimized and highly sparse feature space. We show that starting from the predicted density a single Kohn-Sham diagonalization step can be performed to access total energy components that carry an error of just 0.1 meV/atom.
  arXiv  Detail & Related papers  (2022-06-28T15:35:55Z)
• Density-Based Clustering with Kernel Diffusion [59.4179549482505]
  A naive density corresponding to the indicator function of a unit $d$-dimensional Euclidean ball is commonly used in density-based clustering algorithms. We propose a new kernel diffusion density function, which is adaptive to data of varying local distributional characteristics and smoothness.
  arXiv  Detail & Related papers  (2021-10-11T09:00:33Z)
• Quantum Optimal Control for Pure-State Preparation Using One Initial State [0.0]
  This paper presents a framework for solving the pure-state preparation problem using numerical optimal control. We consider the case where a number of qubits are dispersively coupled to a readout cavity.
  arXiv  Detail & Related papers  (2021-06-16T21:49:48Z)
• Optimal radial basis for density-based atomic representations [58.720142291102135]
  We discuss how to build an adaptive, optimal numerical basis that is chosen to represent most efficiently the structural diversity of the dataset at hand. For each training dataset, this optimal basis is unique, and can be computed at no additional cost with respect to the primitive basis. We demonstrate that this construction yields representations that are accurate and computationally efficient.
  arXiv  Detail & Related papers  (2021-05-18T17:57:08Z)
• The role of feature space in atomistic learning [62.997667081978825]
  Physically-inspired descriptors play a key role in the application of machine-learning techniques to atomistic simulations. We introduce a framework to compare different sets of descriptors, and different ways of transforming them by means of metrics and kernels. We compare representations built in terms of n-body correlations of the atom density, quantitatively assessing the information loss associated with the use of low-order features.
  arXiv  Detail & Related papers  (2020-09-06T14:12:09Z)
• Bayesian Sparse Factor Analysis with Kernelized Observations [67.60224656603823]
  Multi-view problems can be faced with latent variable models. High-dimensionality and non-linear issues are traditionally handled by kernel methods. We propose merging both approaches into single model.
  arXiv  Detail & Related papers  (2020-06-01T14:25:38Z)
• Graph Neural Network for Hamiltonian-Based Material Property Prediction [56.94118357003096]
  We present and compare several different graph convolution networks that are able to predict the band gap for inorganic materials. The models are developed to incorporate two different features: the information of each orbital itself and the interaction between each other. The results show that our model can get a promising prediction accuracy with cross-validation.
  arXiv  Detail & Related papers  (2020-05-27T13:32:10Z)
• Improved guarantees and a multiple-descent curve for Column Subset Selection and the Nystr\"om method [76.73096213472897]
  We develop techniques which exploit spectral properties of the data matrix to obtain improved approximation guarantees. Our approach leads to significantly better bounds for datasets with known rates of singular value decay. We show that both our improved bounds and the multiple-descent curve can be observed on real datasets simply by varying the RBF parameter.
  arXiv  Detail & Related papers  (2020-02-21T00:43:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.