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Machine learning is used to approximate the kinetic energy of one dimens...
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Finding Density Functionals with Machine Learning
Machine learning is used to approximate density functionals. For the mod...
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Understanding Machinelearned Density Functionals
Kernel ridge regression is used to approximate the kinetic energy of non...
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DeePKS: a comprehensive datadriven approach towards chemically accurate density functional theory
We propose a general machine learningbased framework for building an ac...
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On overcoming the Curse of Dimensionality in Neural Networks
Let H be a reproducing Kernel Hilbert space. For i=1,...,N, let x_i∈R^d ...
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Stress testing the dark energy equation of state imprint on supernova data
This work determines the degree to which a standard LambdaCDM analysis ...
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MachineLearned Preconditioners for Linear Solvers in Geophysical Fluid Flows
It is tested whether machine learning methods can be used for preconditi...
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Analytical classical density functionals from an equation learning network
We explore the feasibility of using machine learning methods to obtain an analytic form of the classical free energy functional for two model fluids, hard rods and Lennard–Jones, in one dimension . The Equation Learning Network proposed in Ref. 1 is suitably modified to construct free energy densities which are functions of a set of weighted densities and which are built from a small number of basis functions with flexible combination rules. This setup considerably enlarges the functional space used in the machine learning optimization as compared to previous work 2 where the functional is limited to a simple polynomial form. As a result, we find a good approximation for the exact hard rod functional and its direct correlation function. For the Lennard–Jones fluid, we let the network learn (i) the full excess free energy functional and (ii) the excess free energy functional related to interparticle attractions. Both functionals show a good agreement with simulated density profiles for thermodynamic parameters inside and outside the training region.
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