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A smooth basis for atomistic machine learning

Publications associées (32)

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Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity

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Let G be either a simple linear algebraic group over an algebraically closed field of characteristic l>0 or a quantum group at an l-th root of unity. The category Rep(G) of finite-dimensional G-modules is non-semisimple. In this thesis, we develop new tech ...

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We prove that under certain mild moment and continuity assumptions, the d-dimensional continuum Gaussian free field is the only stochastic process satisfying the usual domain Markov property and a scaling assumption. Our proof is based on a decomposition o ...

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Slice Estimation in Diffusion MRI of Neonatal and Fetal Brains in Image and Spherical Harmonics Domains Using Autoencoders

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Koopmans Spectral Functionals in Periodic Boundary Conditions

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We introduce HP, an implementation of density-functional perturbation theory, designed to compute Hubbard parameters (on-site U and inter-site V ) in the framework of DFT+U and DFT+U+V. The code does not require the use of computationally expensive superce ...

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Spectral analysis for transmission eigenvalue problems with and without the complementing conditions

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The interior transmission eigenvalue problem is a system of partial differential equations equipped with Cauchy data on the boundary: the transmission conditions. This problem appears in the inverse scattering theory for inhomogeneous media when, for some ...

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Two-dimensional Hubbard model at finite temperature: Weak, strong, and long correlation regimes

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We investigate the momentum-resolved spin and charge susceptibilities, as well as the chemical potential and double occupancy in the two-dimensional Hubbard model as functions of doping, temperature, and interaction strength. Through these quantities, we i ...

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Optimal radial basis for density-based atomic representations

Michele Ceriotti, Sergey Pozdnyakov, Jigyasa Nigam, Félix Benedito Clément Musil, Alexander Jan Goscinski

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations ...

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