arXiv research

In this paper, we analyzed the physical meaning of scalar curvatures for a generalized Riemannian space. It is developed the Madsen's formulae for pressures and energy-densities with respect to the corresponding energy-momentum tensors. After that, the energy-momentum tensors, pressures, energy-densities and state-para…

Neural density estimators are flexible families of parametric models which have seen widespread use in unsupervised machine learning in recent years. Maximum-likelihood training typically dictates that these models be constrained to specify an explicit density. However, this limitation can be overcome by instead using …

Quantum vacuum energy (Casimir energy) is reviewed for a mathematical audience as a topic in spectral theory. Then some one-dimensional systems are solved exactly, in terms of closed classical paths and periodic orbits. The relations among local spectral densities, energy densities, global eigenvalue densities, and tot…

Efficiently samples and learns densities with symmetries using equivariant methods.

The paper classifies biharmonic quadratic maps between spheres, proving their energy density properties.

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 densitie…

We show that the energy density of critical points of a class of conformally invariant variational problems with small energy on the unit 2-disk B_1 lies in the local Hardy space h^1(B_1). As a corollary we obtain a new proof of the energy convexity and uniqueness result for weakly harmonic maps with small energy on B_…

Stable solutions to a specific equation are one-dimensional.

A new training method for normalizing flows without samples.

New method trains deep neural networks for non-interacting kinetic-energy functionals in DFT.

We prove that capillary surfaces converge to a specific energy density as the angle approaches zero.

iEFM trains CNF models from unnormalized densities efficiently.

Proves density and mass theorems for specific initial data sets.

The study shows how energy density of harmonic maps dominates in $n$-Fuchsian fibers, leading to unique minimal surfaces.

We give a derivation of the Einstein equation for gravity which employs a definition of the local energy density of the gravitational field as a symmetric second rank tensor whose value for each observer gives the trace of the spatial part of the energy-stress tensor as seen by that observer. We give a physical motivat…

Study on the $L^p$ behavior of helix curves' energy density.

RNE provides a flexible framework for diffusion models, enabling inference-time control and energy-based training.

iDEM generates samples from Boltzmann densities without data.

Adaptive multi-stage density ratio estimation improves learning of latent space EBM.

For Ginzburg-Landau vortices, energy quantization holds only when density is less than 2.

When working with asymptotically hyperbolic initial data sets for general relativity it is convenient to assume certain simplifying properties. We prove that the subset of initial data sets with such properties is dense in the set of physically reasonable asymptotically hyperbolic initial data sets. More specifically, …

The Möbius energy, defined by O'Hara, is one of the knot energies, and named after the Möbius invariant property which was shown by Freedman-He-Wang. The energy can be decomposed into three parts, each of which is Möbius invariant, proved by Ishizeki-Nagasawa. Several discrete versions of Möbius energy, that is, corres…

In this paper, we introduce a new energy density function $\mathscr Y$ on the projective bundle $\mathbb{P}(T_M)\>M$ for a smooth map $f:(M,h)\>(N,g)$ between Riemannian manifolds $\mathscr Y=g_{ij}f^i_αf^j_β\frac{W^αW^β}{\sum h_{γδ} W^γW^δ}.$ We get new Hessian estimates to this energy density and obtain various new…

Bidirectional bounds stabilize training of energy-based models.

Researchers created an accurate kinetic energy functional for materials modeling.

Derives continuum model from discrete $\varepsilon$-graphs with connectivity functional.

Differential conservation laws in Lagrangian field theory are usually related to symmetries of a Lagrangian density and are obtained if the Lie derivative of a Lagrangian density by a certain class of vector fields on a fiber bundle vanishes. However, only two field models meet this property in fact. In gauge theory of…

A new method predicts electron density accurately from atom-centered models.

Unified framework for OOD detection using class ratio estimation.

Improves GANs by sampling from an energy-based model induced by discriminator scores.

We study a variational problem for piecewise-smooth hypersurfaces in the (n+1)-dimensional Euclidean space with an anisotropic energy. An anisotropic energy is the integral of an energy density that depends on the normal at each point over the considered hypersurface. The minimizer of such an energy among all closed hy…

Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields, ranging from materials science to biochemistry to astrophysics. Machine learning holds the promise of learning the kinetic energy functional …

The paper proposes a new method for probabilistic load forecasting using Bernstein-Polynomial Normalizing Flows.

Persistently trained EBMs generate images and estimate complex densities.

Neural network predicts daily power consumption with high accuracy.

Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of non-interacting fermions in 1d, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with fewer than 100 training densities. A predictor identifies if a test density is …

An anisotropic surface energy is the integral of an energy density that depends on the normal at each point over the considered surface, and it is a generalization of surface area. The minimizer of such an energy among all closed surfaces enclosing the same volume is unique and it is (up to rescaling) so-called the Wul…

The study classifies biharmonic submanifolds in a sphere using specific eigenmaps.

New method trains EBMs using NFs for more accurate likelihood estimation.

Given a data set and a subset of labels the problem of semi-supervised learning on point clouds is to extend the labels to the entire data set. In this paper we extend the labels by minimising the constrained discrete $p$-Dirichlet energy. Under suitable conditions the discrete problem can be connected, in the large da…

Extends Penrose's method to null shells with pressure and energy flux.

CEBMs learn flexible latent mappings from data.

We introduce multiscale invariant dictionaries to estimate quantum chemical energies of organic molecules, from training databases. Molecular energies are invariant to isometric atomic displacements, and are Lipschitz continuous to molecular deformations. Similarly to density functional theory (DFT), the molecule is re…

FNFs model parameter-dependent densities by combining a fixed flow with a polynomial parameter-dependent transformation.

Density estimation is a fundamental problem in statistical learning. This problem is especially challenging for complex high-dimensional data due to the curse of dimensionality. A promising solution to this problem is given here in an inference-free hierarchical framework that is built on score matching. We revisit the…

New optimization method for sampling from unknown density measures.

The paper studies geometric properties of hydrodynamical density manifolds.

Equivariant graph neural networks predict electron density for molecules, liquids, and solids.