Related papers: Observability for heat equations with time-depende…
In control theory, understanding the observability property of a system is crucial for effectively managing and controlling dynamical systems. This property empowers us to deduce the internal state of a system from its outputs over time,…
Our goal is to study controllability and observability properties of the 1D heat equation with internal control (or observation) set $\omega_{\varepsilon}=(x_{0}-\varepsilon, x_{0}+\varepsilon )$, in the limit $\varepsilon\rightarrow 0$,…
This paper considers the relevance of the concepts of observability and computability in physical theory. Observability is related to verifiability which is essential for effective computing and as physical systems are computational systems…
In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time…
This paper analyzes heat equation with memory in the case of kernels that are linear combinations of Gamma distributions. In this case, it is possible to rewrite the non-local equation as a local system of partial differential equations of…
This paper presents a new observability estimate for parabolic equations in $\Omega\times(0,T)$, where $\Omega$ is a convex domain. The observation region is restricted over a product set of an open nonempty subset of $\Omega$ and a subset…
This paper is mainly concerned with the observability inequalities for heat equations with time-dependent Lipschtiz potentials. The observability inequality for heat equations asserts that the total energy of a solution is bounded above by…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
This paper studies by means of standard analytic tools the small time behavior of the heat content over a bounded Lebesgue measurable set of finite perimeter by working with the set covariance function and by imposing conditions on the heat…
Regression problems with time-series predictors are common in banking and many other areas of application. In this paper, we use multi-head attention networks to develop interpretable features and use them to achieve good predictive…
Energy systems modeling frequently relies on time series data, whether observed or forecast. This is particularly the case, for example, in capacity planning models that use hourly production and load data forecast to occur over the coming…
We propose a method to probe time dependent correlations of non trivial observables in many-body ultracold lattice gases. The scheme uses a quantum non-demolition matter-light interface, first, to map the observable of interest on the many…
Shape memory alloys are remarkable 'smart' materials used in a broad spectrum of applications, ranging from aerospace to robotics, thanks to their unique thermomechanical coupling capabilities. Given the complex properties of shape memory…
Adaptive spatial meshing has proven invaluable for the accurate, efficient computation of solutions of time dependent partial differential equations. In a DA context the use of adaptive spatial meshes addresses several factors that place…
In this work, we propose an unsupervised method for learning dense correspondences between shapes using a recent deep functional map framework. Instead of depending on ground-truth correspondences or the computationally expensive geodesic…
In this paper, we investigate the pointwise time analyticity of three differential equations. They are the biharmonic heat equation, the heat equation with potentials and some nonlinear heat equations with power nonlinearity of order $p$.…
This paper studies the state observation problems for the semilinear heat equation in R^n. We derive observation estimates for the equation using the logarithmic convexity property of the frequency function (see [12]). As an application, we…
Memory effects can lead to history-dependent behavior of a system, and they are ubiquitous in our daily life and have broad applications. Here we explore possibilities of generating memory effects in simple isolated quantum systems. By…
Advanced machine learning models have recently achieved high predictive accuracy for weather and climate prediction. However, these complex models often lack inherent transparency and interpretability, acting as "black boxes" that impede…
Partial Differential Equations are infinite dimensional encoded representations of physical processes. However, imbibing multiple observation data towards a coupled representation presents significant challenges. We present a fully…