일시: 2025년 3월 24일 (월) 15:30 - 17:20

장소: 27동 116호

강연 1 (15:30 - 16:20)

- 강연자: Michael Schuster (FAU-Erlangen)

- 제목:  Probabilistic Constrained Optimization with ODEs and PDEs

- 초록: Uncertainty often plays an important role in gas transport and probabilistic constraints are an excellent modeling tool to obtain controls and other quantities that are robust against perturbations. To efficiently evaluate the probabilistic constraint, we present an approach based on kernel density estimation, such that the probabilistic constrained optimization problem can be considered as classical nonlinear problem, allowing us to apply classical nonlinear optimization theory. As an application, we consider and analyze the steady state and the transient gas flow in pipeline networks. We introduce the modelling based on the isothermal Euler equations including random boundary data, leading to optimal control problems with probabilistic constraints.

강연 2 (16:30 - 17:20)

- 강연자: Ilias Ftouhi (FAU-Erlangen)

- 제목:  Placement of sensors via a Varadhan's result

- 초록: The optimal placement and design of sensors is commonly encountered in industrial and applied problems, such as urban planning and the supervision of temperature and pressure in gas networks. In essence, sensors are considered optimally designed when they ensure the highest level of observation for the specific phenomenon in question. Typically, this design process is guided by specific objectives and is subject to constraints commonly defined by an appropriate partial differential equation (PDE), taking into account the underlying physics of the process. In this talk, we will focus on the optimal placement of a finite number of sensors inside a given region. Here, we address the problem in a purely geometric setting, without involving a specific PDE model. We consider a simple and natural geometric criterion of performance, based on distance functions. But, as we shall see, tackling it will require to employ geometric analysis methods combined with a classical result of S. R. Srinivasa Varadhan which provides an efficient approximation of the distance function via the solution of a simple elliptic PDE. The talk is based on works in collaboration with Enrique Zuazua (FAU, Germany)