Related papers: Robustness of dynamically gradient multivalued dyn…
The existence of adversarial data examples has drawn significant attention in the deep-learning community; such data are seemingly minimally perturbed relative to the original data, but lead to very different outputs from a deep-learning…
ONE of the main goals in the development of theory of chaotic dynamical system has been to make progress in understanding of turbulence. The attempts to related turbulence to chaotic motion got strong impetus from the celebrated paper by…
We survey recent results in the mathematical literature on the equations of incompressible fluid dynamics, highlighting common themes and how they might contribute to the understanding of some phenomena in the theory of fully developed…
This paper studies robustness of MIMO control systems with parametric uncertainties, and establishes a lower dimensional robust stability criterion. For control systems with interval transfer matrices, we identify the minimal testing set…
In this work we study the stability, convergence, and pressure-robustness of discretization methods for incompressible flows with hybrid velocity and pressure. Specifically, focusing on the Stokes problem, we identify a set of assumptions…
We study discrete time linear constrained switching systems with additive disturbances, in which the switching may be on the system matrices, the disturbance sets, the state constraint sets or a combination of the above. In our general…
We introduce the Morse parametric qualification condition for bilevel programming. Generic semi-algebraic functions are Morse parametric in a piecewise sense. Thus, bilevel programs with a Morse parametric lower level constitute a relevant…
A two-dimensional extension of a recently developed formalism for slow-fast quasilinear (QL) systems subject to fast instabilities is derived. Prior work has demonstrated that the emergent dynamics of these systems is characterized by a…
We study evolution equations on metric graphs with reservoirs, that is graphs where a one-dimensional interval is associated to each edge and, in addition, the vertices are able to store and exchange mass with these intervals. Focusing on…
The equations of stationary compressible flows of active liquid crystals are considered in a bounded three-dimensional domain. The system consists of the stationary Navier-Stokes equations coupled with the equation of Q-tensors and the…
Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these…
In this paper we present three multiphase flow models suitable for the study of the dynamics of compressible dispersed multiphase flows. We adopt the Eulerian approach because we focus our attention to dispersed (concentration smaller than…
The Immersed Boundary method has evolved into one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to suffer from a severe timestep stability…
We study generalized fixed-point equations over idempotent semirings and provide an efficient algorithm for the detection whether a sequence of Kleene's iterations stabilizes after a finite number of steps. Previously known approaches…
We provide a complexity classification of four variants of robust integer programming when the underlying Graver basis is given. We discuss applications to robust multicommodity flows and multidimensional transportation, and describe an…
This work presents new tools for studying reachability and set invariance for continuous-time mixed-monotone dynamical systems subject to a disturbance input. The vector field of a mixed-monotone system is decomposable via a decomposition…
Accurate and efficient prediction of multi-scale flows remains a formidable challenge. Constructing theoretical models and numerical methods often involves the design and optimization of parameters. While gradient descent methods have been…
The pursuit of robustness has recently been a popular topic in reinforcement learning (RL) research, yet the existing methods generally suffer from efficiency issues that obstruct their real-world implementation. In this paper, we introduce…
We consider two-dimensional nonstationary Navier-Stokes shear flow with multivalued and nonmonotone boundary conditions on a part of the boundary of the flow domain. We prove the existence of global in time solutions of the considered…
Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…