Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Understanding Machine-learned Density Functionals   Kernel ridge regression is used to approximate the kinetic energy of
non-interacting fermions in a one-dimensional box as a functional of their
density. The properties of different kernels and methods of cross-validation
are explored, and highly accurate energies are achieved. Accurate {\em
constrained optimal densities} are found via a modified Euler-Lagrange
constrained minimization of the total energy. A projected gradient descent
algorithm is derived using local principal component analysis. Additionally, a
sparse grid representation of the density can be used without degrading the
performance of the methods. The implications for machine-learned density
functional approximations are discussed.

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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: math
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph