arXiv research

New method predicts heat load in thermal grids using latent variables.

Heat demand prediction is a prominent research topic in the area of intelligent energy networks. It has been well recognized that periodicity is one of the important characteristics of heat demand. Seasonal-trend decomposition based on LOESS (STL) algorithm can analyze the periodicity of a heat demand series, and decom…

Novel probabilistic models forecast residential heating and electricity demand at hourly resolution.

Proposes learning manifold implicitly via heat kernel.

New blurring diffusion models bridge heat dissipation and denoising.

This paper proposes an unsupervised learning method to solve heat equations on chips.

Sharp heat kernel estimates on manifolds lead to solutions of the Parabolic Anderson model.

We propose a formally completely integrable extension of heat hierarchy based on the space of symmetries isomorphic to the Weyl algebra $\mathcal{A}_1$. The extended heat hierarchy will be the basic model for the analysis of the extension of KP hierarchy, and other integrable equations.

New model generates images by reversing heat equation, revealing disentanglement.

In this paper, we study the Poisson equation and heat equation in a model matrix geometry $M_n$. Our main results are about the Poisson equation and global behavior of the heat equation on $M_n$. We can show that if $c_0$ is the initial positive definite matrix in $M_n$, then $c(t)$ exists for all time and is positive …

Researchers derived heat kernel expansions for non-compact spaces using Witten deformation.

Study on heat flow across two half-lines with special boundary conditions.

The paper compares heat kernels on manifolds with Robin boundary conditions.

We give a short proof of a strong version of the short time asymptotic expansion of heat kernels associated to Laplace type operators acting on sections of vector bundles over compact Riemannian manifolds, including exponential decay of the difference of the approximate heat kernel and the true heat kernel. We use this…

Study on biharmonic map heat flow with monotonicity formula.

Study on uniquely determining thermal properties from boundary temperature and heat flux measurements.

Understanding the heat usage of customers is crucial for effective district heating operations and management. Unfortunately, existing knowledge about customers and their heat load behaviors is quite scarce. Most previous studies are limited to small-scale analyses that are not representative enough to understand the b…

We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We show explicitly that the obtaine…

The heat kernel for the Cauchy-Riemann subLaplacian on S(2n+1) is derived in a manner which is completely analogous to the classical derivation of elliptic heat kernels. This suggests that the classical hamiltonian construction of elliptic heat kernels, with appropriate modifications, does yield heat kernels for subell…

The paper studies heat kernel asymptotics and proves Morse inequalities.

Derives gradient estimates for CR heat equation on pseudo-Hermitian manifolds.

New heat equation method solves intertwining problems in CR geometry.

The Liouville theorem is proven for V T-harmonic map heat flow.

We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We argue that the obtained formal s…

Paper studies heat flow for maps on manifolds, avoiding singularities.

In this paper, we first give a direct proof for two recurrence relations of the heat kernels for hyperbolic spaces in \cite{DM}. Then, by similar computation, we give two similar recurrence relations of the heat kernels for spheres. Finally, as an application, we compute the diagonal of heat kernels for odd dimensional…

Improved graph-based connectivity estimation using heat modelling.

Formulae connect heat kernels on glued manifolds.

Proves upper bounds for heat kernels evolving on manifolds.

We construct default-free interest rate models in the spirit of the well-known Markov funcional models: our focus is analytic tractability of the models and generality of the approach. We work in the setting of state price densities and construct models by means of the so called propagation property. The propagation pr…

This paper describes results characterizing the range of the time-t heat operator on various manifolds, including Euclidean spaces, spheres, and hyperbolic spaces. The guiding principle behind these results is this: The functions in the range of the heat operator should be, roughly, those functions having an analytic c…

We study the subelliptic heat kernel of the sub-Laplacian on a 2n+1-dimensional anti-de Sitter space H2n+1 which also appears as a model space of a CR Sasakian manifold with constant negative sectional curvature. In particular we obtain an explicit and geometrically meaningful formula for the subelliptic heat kernel. T…

Study on biharmonic heat equation on manifolds with curvature constraints.

Derives properties of heat kernel for Rumin complex on Heisenberg groups.

The paper studies heat kernels on weighted Riemannian manifolds with curvature bounds.

In this paper we give Hamilton's Laplacian estimates for the heat equation on complete noncompact manifolds with nonnegative Ricci curvature. As an application, combining Li-Yau's lower and upper bounds of the heat kernel, we give an estimate on Laplacian form of the heat kernel on complete manifolds with nonnegative R…

Paper studies smoothness of bi-conformal heat flow on 4-manifolds.

Study heat content in sub-Riemannian manifolds, obtaining asymptotic expansion.

In this paper, we study two kind of L^2 norm preserved non-local heat flows on closed manifolds. We first study the global existence, stability and asymptotic behavior to such non-local heat flows. Next we give the gradient estimates of positive solutions to these heat flows.

The paper develops heat kernel comparison theorems and applies them to spectral geometry.

We consider the heat equation associated with a class of second order hypoelliptic Hörmander operators with constant second order term and linear drift. We describe the possible small time heat kernel expansion on the diagonal giving a geometric characterization of the coefficients in terms of the divergence of the dri…

Heat flow fails to preserve concavity in curved spaces.

We develop a new method for the calculation of the heat trace asymptotics of the Laplacian on symmetric spaces that is based on a representation of the heat semigroup in form of an average over the Lie group of isometries and obtain a generating function for the whole sequence of all heat invariants.

Bounds on Hessian of heat equation coupled with Ricci flow.

Study heat flow on collapsing K3 surfaces, handling conic singularities.

We study new invariants of elliptic partial differential operators acting on sections of a vector bundle over a closed Riemannian manifold that we call the relativistic heat trace and the quantum heat traces. We obtain some reduction formulas expressing these new invariants in terms of some integral transforms of the u…

Novel numerical scheme for G-heat equation with uncertainty.

Exponential rate of convergence for harmonic heat flow maps.