Related papers: Finding Density Functionals with Machine Learning

In this work, we propose new objective functions to train deep neural network based density ratio estimators and apply it to a change point detection problem. Existing methods use linear combinations of kernels to approximate the density…

We present a review of the basic ideas and techniques of the spectral density functional theory which are currently used in electronic structure calculations of strongly-correlated materials where the one-electron description breaks down.…

The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…

In recent years impressive progress has been made in the development of highly accurate energy density functionals, which allow to treat medium-heavy nuclei. In this approach one tries to describe not only the ground state but also the…

Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…

Current meta-learning approaches focus on learning functional representations of relationships between variables, i.e. on estimating conditional expectations in regression. In many applications, however, we are faced with conditional…

The number of electrified powertrains is ever increasing today towards a more sustainable future; thus, it is essential that unwanted failures are prevented, and a reliable operation is secured. Monitoring the internal temperatures of…

Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type…

The diffusion of large databases collecting different kind of material properties from high-throughput density functional theory calculations has opened new paths in the study of materials science thanks to data mining and machine learning…

Nonsmoothness is often a curse for optimization; but it is sometimes a blessing, in particular for applications in machine learning. In this paper, we present the specific structure of nonsmooth optimization problems appearing in machine…

Many machine/deep learning artificial neural networks are trained to simply be interpolation functions that map input variables to output values interpolated from the training data in a linear/nonlinear fashion. Even when the input/output…

RNA function crucially depends on its structure. Thermodynamic models currently used for secondary structure prediction rely on computing the partition function of folding ensembles, and can thus estimate minimum free-energy structures and…

Using an end-to-end differentiable implementation of the Kohn-Sham self-consistent field equations, we obtain an accurate neural network-based exchange and correlation (XC) functional of the electronic density. The functional is optimized…

Generative networks implicitly approximate complex densities from their sampling with impressive accuracy. However, because of the enormous scale of modern datasets, this training process is often computationally expensive. We cast…

Estimating expected polynomials of density functions from samples is a basic problem with numerous applications in statistics and information theory. Although kernel density estimators are widely used in practice for such functional…

High-throughput density-functional calculations of solids are extremely time consuming. As an alternative, we here propose a machine learning approach for the fast prediction of solid-state properties. To achieve this, LSDA calculations are…

Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…

Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual…

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing…

Learning with limited data is one of the biggest problems of machine learning. Current approaches to this issue consist in learning general representations from huge amounts of data before fine-tuning the model on a small dataset of…