Publications Server of the Weierstrass Institute for Applied Analysis and Stochastics
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Strong Stationarity Conditions for the Optimal Control of a Cahn-Hilliard-Navier-Stokes System
No full textThis paper is concerned with the distributed optimal control of a time-discrete Cahn–Hilliard–Navier–Stokes system with variable densities. It focuses on the double-obstacle potential which yields an optimal control problem for a variational inequality of fourth order and the Navier–Stokes equation. The existence of solutions to the primal system and of optimal controls is established. The Lipschitz continuity of the constraint mapping is derived and used to characterize the directional derivative of the constraint mapping via a system of variational inequalities and partial differential equations. Finally, strong stationarity conditions are presented following an approach from Mignot and Puel
Frequency noise characterization of narrow-linewidth lasers: A Bayesian approach
Get PDFWe describe a Bayesian estimation approach to infer on the frequency noise characteristics of narrow-linewidth semiconductor lasers from delayed self-heterodyne beat note measurements. Our technique is grounded in a statistical model of the measurement process that accounts for both the impact of the interferometer and the detector noise. The approach yields accurate results, even in scenarios where the intrinsic linewidth plateau is obscured by detector noise. The analysis is carried out using a Markov-chain Monte Carlo method in the frequency domain and exploits prior knowledge about the statistical distribution of the data. The method is validated using simulated time series data from a stochastic laser rate equation model incorporating 1/f -type non-Markovian noise
Strong stationarity conditions for optimal control problems governed by a rate-independent evolution variational inequality
No full textWe prove strong stationarity conditions for optimal control problems that are governed by a prototypical rate-independent evolution variational inequality, i.e., first-order necessary optimality conditions in the form of a primal-dual multiplier system that are equivalent to the purely primal notion of Bouligand stationarity. Our analysis relies on recent results on the Hadamard directional differentiability of the scalar stop operator and a new concept of temporal polyhedricity that generalizes classical ideas of Mignot. The established strong stationarity system is compared with known optimality conditions for optimal control problems governed by elliptic obstacle-type variational inequalities and stationarity systems obtained by regularization
Estimation Beyond Data Reweighting: Kernel Method of Moments
No full textMoment restrictions and their conditional counterparts emerge in many areas of machine learning and statistics ranging from causal inference to reinforcement learning. Estimators for these tasks, generally called methods of moments, include the prominent generalized method of moments (GMM) which has recently gained attention in causal inference. GMM is a special case of the broader family of empirical likelihood estimators which are based on approximating a population distribution by means of minimizing a φ-divergence to an empirical distribution. However, the use of φ-divergences effectively limits the candidate distributions to reweightings of the data samples. We lift this long-standing limitation and provide a method of moments that goes beyond data reweighting. This is achieved by defining an empirical likelihood estimator based on maximum mean discrepancy which we term the kernel method of moments (KMM). We provide a variant of our estimator for conditional moment restrictions and show that it is asymptotically first-order optimal for such problems. Finally, we show that our method achieves competitive performance on several conditional moment restriction tasks
Damage in viscoelastic materials at finite strains
No full textThis contribution reports on an ongoing work in progress dedicated to the mathematical analysis of a model for the evolution of damage in viscoelastic materials with physical and geometrical nonlinearities and under the influence of dynamic effects due to the propagation of elastic waves
MaRDI: Building Research Data Infrastructures for Mathematics and the Mathematical Sciences
No full textMaRDI is building a research data infrastructure for mathematics and be-yond based on semantic technologies (metadata, ontologies, knowledge graphs) anddata repositories. Focusing on the algorithms, models and workflows, the MaRDI in-frastructure will connect with other disciplines and NFDI consortia on data processingmethods, solving real world problems and support mathematicians on research datamanagement
NUSOD 2023
No full textThe 23rd International NUSOD Conference welcomes researchers hailing from 21 countries who present a total of 60 papers, including 6 invited talks. The conference sessions cover a wide range of topics, including integrated devices and systems, laser diodes and VCSELs, photodetectors and solar cells, alongside novel materials and numerical methods. After three years of virtual gatherings due to the global pandemic, we are finally back together in person. This year we are hosted by Politecnico di Torino, one of Italy's oldest and most prestigious technical universities, with a rich history dating back to its establishment in 1859. Throughout its history, Politecnico di Torino has been a leading institution in the fields of engineering, architecture, and applied sciences. It has played a significant role in shaping the industrial and technological landscape of Italy and Europe. At present, Politecnico di Torino has over 36.000 students, 2.000 employees, and offers more than 50 bachelor’s and master’s degree programs. Politecnico di Torino has a consolidated tradition in the field of photonics, covering fundamental research on optoelectronic materials and devices to their application to optical communications, sensing, and imaging. The NUSOD Conference was started at the University of California at Santa Barbara in 2001 and the participation was far beyond expectations - which provided the motivation to make this meeting an annual event circulating the globe. NUSOD is now seen as a key conference in the field of optoelectronics, providing a platform for networking and discussions on the latest challenges and developments in device simulation and design. We wish you a stimulating and enjoyable experience at NUSOD 2023
Rough Volatility
No full textVolatility underpins financial markets by encapsulating uncertainty about prices, individual behaviors, and decisions and has traditionally been modeled as a semimartingale, with consequent scaling properties. The mathematical description of the volatility process has been an active topic of research for decades; however, driven by empirical estimates of the scaling behavior of volatility, a new paradigm has emerged, whereby paths of volatility are rougher than those of semimartingales. According to this perspective, volatility behaves as a fractional Brownian motion with a small Hurst parameter