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We present a method to design driving protocols that achieve fast thermal equilibration of a system of interest using techniques inspired by machine learning training algorithms. For example, consider a Brownian particle manipulated by…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
The problem of thermally activated escape over a potential barrier is solved by means of path integrals for one-dimensional reaction dynamics with very general time dependences. For a suitably chosen but still quite simple static potential…
This paper presents a unified optimization framework for phase change material (PCM) based cooling systems. Thermal management is critical in applications such as photovoltaic (PV) modules, battery packs, and power electronics, where…
Density-based topology optimization has become a powerful method for automatically generating optimized designs in a wide variety of applications. However, it comes with a large computational cost when solving the physical model requires…
We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…
Simulation of thermal dynamics in city-scale district energy grids often becomes computationally prohibitive for long simulation runs. Current model order reduction methods offer limited interpretability with regards to the non-reduced…
The new method is considered for identifying the perfect (optimal) scenario of climate engineering operations based on the optimal control theory. The application of this approach is demonstrated using zero-dimensional energy-balance…
In this paper, we investigate the problem of minimizing the long-term total cost (i.e., the sum of energy cost and thermal discomfort cost) associated with a Heating, Ventilation, and Air Conditioning (HVAC) system of a multizone commercial…
We are concerned with the optimal control problem of the well known nonlocal thermistor problem, i.e., in studying the heat transfer in the resistor device whose electrical conductivity is strongly dependent on the temperature. Existence of…
We introduce a time-implicit, finite-element based space-time discretization scheme for the backward stochastic heat equation, and for the forward-backward stochastic heat equation from stochastic optimal control, and prove strong rates of…
Thermoelectric efficiency is defined as the ratio of power delivered to the load of a device to the rate of heat flow from the source. Till date, it has been studied in presence of thermodynamic constraints set by the Onsager reciprocal…
Partial differential equation (PDE)-constrained optimization arises in many scientific and engineering domains, such as energy systems, fluid dynamics and material design. In these problems, the decision variables (e.g., control inputs or…
In this paper we consider a geothermal energy storage in which the spatio-temporal temperature distribution is modeled by a heat equation with a convection term. Such storages often are embedded in residential heating systems and control…
Virtual Data Center (VDC) embedding has drawn significant attention recently because of growing need for efficient and flexible means of Data Center (DC) resource allocation. Existing studies on VDC embedding mainly focus on improving DCs'…
Optimal (reversible) processes in thermodynamics can be modelled as step-by-step processes, where the system is successively thermalized with respect to different Hamiltonians by an external thermal bath. However, in practice interactions…
We consider the problem of planning the aggregate energy consumption for a set of thermostatically controlled loads for demand response, accounting price forecast trajectory and thermal comfort constraints. We address this as a…
This article is concerned with the solution of a time-dependent shape identification problem. Specifically we consider the heat equation in a domain, which contains a time-dependent inclusion of zero temperature. The objective is to detect…
Decarbonizing the global energy supply requires more efficient heating and cooling systems. Model predictive control enhances the operation of cooling and heating systems but depends on accurate system models, often based on control…
We consider two optimization problems in thermal insulation: in both cases the goal is to find a thin layer around the boundary of the thermal body which gives the best insulation. The total mass of the insulating material is prescribed..…