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Machine learning accurate exchange and correlation functionals of the electronic density.

ABSTRACT: Density functional theory (DFT) is the standard formalism to study the electronic structure of matter at the atomic scale. In Kohn-Sham DFT simulations, the balance between accuracy and computational cost depends on the choice of exchange and correlation functional, which only exists in approximate form. Here, we propose a framework to create density functionals using supervised machine learning, termed NeuralXC. These machine-learned functionals are designed to lift the accuracy of baseline functionals towards that provided by more accurate methods while maintaining their efficiency. We show that the functionals learn a meaningful representation of the physical information contained in the training data, making them transferable across systems. A NeuralXC functional optimized for water outperforms other methods characterizing bond breaking and excels when comparing against experimental results. This work demonstrates that NeuralXC is a first step towards the design of a universal, highly accurate functional valid for both molecules and solids.

SUBMITTER: Dick S

PROVIDER: S-EPMC7360771 | biostudies-literature | 2020 Jul

REPOSITORIES: biostudies-literature

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Machine learning accurate exchange and correlation functionals of the electronic density.

Dick Sebastian S Fernandez-Serra Marivi M

Nature communications 20200714 1

Density functional theory (DFT) is the standard formalism to study the electronic structure of matter at the atomic scale. In Kohn-Sham DFT simulations, the balance between accuracy and computational cost depends on the choice of exchange and correlation functional, which only exists in approximate form. Here, we propose a framework to create density functionals using supervised machine learning, termed NeuralXC. These machine-learned functionals are designed to lift the accuracy of baseline fun ...[more]

PMID: 32665540

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Project description:Researchers carrying out calculations using the DFT method face the problem of the correct choice of the exchange-correlation functional to describe the quantities they are interested in. This article deals with benchmark calculations aimed at testing various exchange-correlation functionals in terms of a reliable description of the electron density distribution in molecules. For this purpose, 30 functionals representing all rungs of Jacob's Ladder are selected and then the values of some QTAIM-based parameters are compared with their reference equivalents obtained at the CCSD/aug-cc-pVTZ level of theory. The presented results show that the DFT method undoubtedly has the greatest problems with a reliable description of the electron density distribution in multiple strongly polar bonds, such as C=O, and bonds associated with large electron charge delocalization. The performance of the tested functionals turned out to be unsystematic. Nevertheless, in terms of a reliable general description of QTAIM-based parameters, the M11, SVWN, BHHLYP, M06-HF, and, to a slightly lesser extent, also BLYP, B3LYP, and X3LYP functionals turned out to be the worst. It is alarming to find the most popular B3LYP functional in this group. On the other hand, in the case of the electron density at the bond critical point, being the most important QTAIM-based parameter, the M06-HF functional is especially discouraged due to the very poor description of the C=O bond. On the contrary, the VSXC, M06-L, SOGGA11-X, M06-2X, MN12-SX, and, to a slightly lesser extent, also TPSS, TPSSh, and B1B95 perform well in this respect. Particularly noteworthy is the overwhelming performance of double hybrids in terms of reliable values of bond delocalization indices. The results show that there is no clear improvement in the reliability of describing the electron density distribution with climbing Jacob's Ladder, as top-ranked double hybrids are also, in some cases, able to produce poor values compared to CCSD.

Project description:BACKGROUND AND PURPOSE:MR imaging-based modeling of tumor cell density can substantially improve targeted treatment of glioblastoma. Unfortunately, interpatient variability limits the predictive ability of many modeling approaches. We present a transfer learning method that generates individualized patient models, grounded in the wealth of population data, while also detecting and adjusting for interpatient variabilities based on each patient's own histologic data. MATERIALS AND METHODS:We recruited patients with primary glioblastoma undergoing image-guided biopsies and preoperative imaging, including contrast-enhanced MR imaging, dynamic susceptibility contrast MR imaging, and diffusion tensor imaging. We calculated relative cerebral blood volume from DSC-MR imaging and mean diffusivity and fractional anisotropy from DTI. Following image coregistration, we assessed tumor cell density for each biopsy and identified corresponding localized MR imaging measurements. We then explored a range of univariate and multivariate predictive models of tumor cell density based on MR imaging measurements in a generalized one-model-fits-all approach. We then implemented both univariate and multivariate individualized transfer learning predictive models, which harness the available population-level data but allow individual variability in their predictions. Finally, we compared Pearson correlation coefficients and mean absolute error between the individualized transfer learning and generalized one-model-fits-all models. RESULTS:Tumor cell density significantly correlated with relative CBV (r = 0.33, P < .001), and T1-weighted postcontrast (r = 0.36, P < .001) on univariate analysis after correcting for multiple comparisons. With single-variable modeling (using relative CBV), transfer learning increased predictive performance (r = 0.53, mean absolute error = 15.19%) compared with one-model-fits-all (r = 0.27, mean absolute error = 17.79%). With multivariate modeling, transfer learning further improved performance (r = 0.88, mean absolute error = 5.66%) compared with one-model-fits-all (r = 0.39, mean absolute error = 16.55%). CONCLUSIONS:Transfer learning significantly improves predictive modeling performance for quantifying tumor cell density in glioblastoma.

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Machine learning accurate exchange and correlation functionals of the electronic density.

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Machine learning accurate exchange and correlation functionals of the electronic density.

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