arXiv research

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

Methane is considered being a good choice as a propellant for future reusable launch systems. However, the heat transfer prediction for supercritical methane flowing in cooling channels of a regeneratively cooled combustion chamber is challenging. Because accurate heat transfer predictions are essential to design relia…

LGAC enhances heat transfer in turbulent boundary layers using slot jets.

Estimates heat equation on shrinking Ricci solitons with uniform bounds.

A new method trains physics-constrained neural networks more efficiently.

Introduce a thermodynamically informed, temperature-transferable MLCG framework for proteins.

Proposes learning manifold implicitly via heat kernel.

Physics-based framework improves building energy forecasting.

New example of manifolds with monotonic heat kernels found.

Formulae connect heat kernels on glued manifolds.

We present two initial graphs over the entire $\mathbb{R}^n$, $n \geq 2$ for which the mean curvature flow behaves differently from the heat flow. In the first example, the two flows stabilize at different heights. With our second example, the mean curvature flow oscillates indefinitely while the heat flow stabilizes. …

CTS machines improve screen development in printing industries, reducing costs and increasing profitability.

Study on heat content for submanifolds in sub-Riemannian geometry.

We construct the biharmonic heat kernel for a suitable self-adjoint extension of the bi-Laplacian on a manifold with incomplete edge singularities. We employ a microlocal description of the biharmonic heat kernel to establish mapping properties of the corresponding biharmonic heat operator on certain Banach spaces. Thi…

We compute explicitly, and without any extra regularity assumptions, the large time limit of the fibrewise heat operator for Bismut-Lott type superconnections in the L^2-setting. This is motivated by index theory on certain non-compact spaces (families of manifolds with cocompact group action) where the convergence of …

In this paper, we study the large time behavior of the heat kernel on complete Riemannian manifolds with nonnegative Ricci curvature, which was studied by P. Li with additional maximum volume growth assumption. Following Y. Ding's original strategy, by blowing down the metric, using Cheeger and Colding's theory about l…

The paper (in French) exemplifies graphically a solution of the heat equation which is a 1-dimensional unfolding of an elliptic umbilic catastrophe. The example is due to James Damon and adapts Thom-Mather's singularity theory to multiscale models of scale-space analysis in image processing.

We consider the heat equation associated with a class of hypoelliptic operators of Kolmogorov-Fokker-Planck type in dimension two. We explicitly compute the first meaningful coefficient of the small time asymptotic expansion of the heat kernel on the diagonal, and we interpret it in terms of curvature-like invariants o…

Study shows global oscillatory solutions for Yang-Mills heat flow in 4D space.

This paper classifies symmetries of biharmonic heat equations on surfaces of revolution.

This paper explores how the generalization of substitute classifiers affects the success of black-box adversarial attacks.

The book explores stochastic areas and heat kernels on manifolds.

The heat coefficients related to the Laplace-Beltrami operator defined on the hyperbolic compact manifold $H^3/\Ga$ are evaluated in the case in which the discrete group $\Ga$ contains elliptic and hyperbolic elements. It is shown that while hyperbolic elements give only exponentially vanishing corrections to the trace…

Graphs prove curvature condition with modified heat equation.

The paper explores transferability of adversarial examples between convex and 01 loss models, finding non-transferability due to different decision boundaries caused by outliers.

Deep learning algorithms have increasingly been shown to lack robustness to simple adversarial examples (AdvX). An equally troubling observation is that these adversarial examples transfer between different architectures trained on different datasets. We investigate the transferability of adversarial examples between m…

In this thesis we deal with spectral invariants for polygons and closed orbisurfaces of constant Gaussian curvature. In each case our method is to study the heat kernel and the asymptotic expansion of the heat trace. First, we investigate hyperbolic polygons, i.e. relatively compact domains in the hyperbolic plane with…

Adversarial perturbations fool wearable sensor systems, showing transferability across different systems.

Adversarial examples are maliciously perturbed inputs designed to mislead machine learning (ML) models at test-time. They often transfer: the same adversarial example fools more than one model. In this work, we propose novel methods for estimating the previously unknown dimensionality of the space of adversarial inputs…

This paper discusses the existence of gradient estimates for second order hypoelliptic heat kernels on manifolds. It is now standard that such inequalities, in the elliptic case, are equivalent to a lower bound on the Ricci tensor of the Riemannian metric. For hypoelliptic operators, the associated "Ricci curvature" ta…

This paper explores the connection between adversarial and knowledge transferability.

We show that in dimension 4 and above, the lifespan of Ricci flows depends on the relative smallness of the Ricci curvature compared to the Riemann curvature on the initial manifold. We can generalize this lifespan estimate to the local Ricci flow, using which we prove the short-time existence of Ricci flow solutions o…

In this paper we investigate the small time heat kernel asymptotics on the cut locus on a class of surfaces of revolution, which are the simplest 2-dimensional Riemannian manifolds different from the sphere with non trivial cut-conjugate locus. We determine the degeneracy of the exponential map near a cut-conjugate poi…

Neural networks are vulnerable to adversarial examples, malicious inputs crafted to fool trained models. Adversarial examples often exhibit black-box transfer, meaning that adversarial examples for one model can fool another model. However, adversarial examples are typically overfit to exploit the particular architectu…

Study heat profiles and eigenfunctions using Brownian motion.

We give a counter example to a conjecture of E. Bueler stating the equality between the DeRham cohomology of complete Riemannian manifold and a weighted $L^2$ cohomology where the weight is the heat kernel.

Skip connections make adversarial examples more transferable in ResNets.

Neural networks are vulnerable to adversarial examples, malicious inputs crafted to fool trained models. Adversarial examples often exhibit black-box transfer, meaning that adversarial examples for one model can fool another model. However, adversarial examples may be overfit to exploit the particular architecture and …

Deep learning models are vulnerable to adversarial examples crafted by applying human-imperceptible perturbations on benign inputs. However, under the black-box setting, most existing adversaries often have a poor transferability to attack other defense models. In this work, from the perspective of regarding the advers…

Transfer learning improves model robustness against adversarial attacks.

We establish dimension-independent estimates related to heat operators e^{tL} on manifolds. We first develop a very general contractivity result for Markov kernels which can be applied to diffusion semigroups. Second, we develop estimates on the norm behavior of harmonic and non-negative subharmonic functions. We apply…

Study of geometric analysis on asymmetric metric spaces, including heat flow and Sobolev spaces.

Research has shown that widely used deep neural networks are vulnerable to carefully crafted adversarial perturbations. Moreover, these adversarial perturbations often transfer across models. We hypothesize that adversarial weakness is composed of three sources of bias: architecture, dataset, and random initialization.…

SAM minimizes loss sharpness, improving adversarial transferability.

In this paper, we study global existence and blow up properties to $L^p$ norm preserving non-local heat flows. We first study two kinds of $L^p$ norm preserving non-local flows and prove that these flows have the global solutions. Finally, we give a example to show that one kind of this heat flow may blow up in $L^{\in…

State-of-the-art deep neural networks are known to be vulnerable to adversarial examples, formed by applying small but malicious perturbations to the original inputs. Moreover, the perturbations can \textit{transfer across models}: adversarial examples generated for a specific model will often mislead other unseen mode…

New method improves adversarial transferability from Bayesian neural networks.

Synthetic Ricci flows defined for metric measure spaces.