Related papers: Stability of saddle points via explicit coderivati…
We study the parameter estimation for parabolic, linear, second-order, stochastic partial differential equations (SPDEs) observing a mild solution on a discrete grid in time and space. A high-frequency regime is considered where the mesh of…
We study inference on scalar-valued pathwise differentiable targets after adaptive data collection, such as a bandit algorithm. We introduce a novel target-specific condition, directional stability, which is strictly weaker than previously…
Many modern machine learning applications - from online principal component analysis to covariance matrix identification and dictionary learning - can be formulated as minimization problems on Riemannian manifolds, and are typically solved…
The aim of this paper is to investigate the response of this system/scheme in terms of stability in presence of explicitly treated residual terms, as it inevitably occurs in the reality of NWP. This sudy is restricted to the impact of…
In this work we study convergence properties of sparse polynomial approximations for a class of affine parametric saddle point problems. Such problems can be found in many computational science and engineering fields, including the Stokes…
We introduce several notions of generalised principal eigenvalue for a linear elliptic operator on a general unbounded domain, under boundary condition of the oblique derivative type. We employ these notions in the stability analysis of…
By applying some techniques of set-valued and variational analysis, we study solution stability of nonhomogeneous split equality problems and nonhomogeneous split feasibility problems, where the constraint sets need not be convex. Necessary…
This paper primarily considers the robust estimation problem under Wasserstein distance constraints on the parameter and noise distributions in the linear measurement model with additive noise, which can be formulated as an…
We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
In this paper, we study the stability of fractional Sobolev trace inequality within both the functional and critical point settings. In the functional setting, we establish the following sharp estimate:…
Partial differential equations endowed with a Hamiltonian structure, like the Korteweg--de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for…
Gradient descent is a popular algorithm in optimization, and its performance in convex settings is mostly well understood. In non-convex settings, it has been shown that gradient descent is able to escape saddle points asymptotically and…
We consider the inverse problem of recovering stationary coefficients in a class of dynamical Schr\"odinger equations with locally analytic nonlinear terms. Upon treating the well-posedness for small initial data and trivial boundary data,…
In this paper exponential stability of nonlinear fractional order stochastic system with Poisson jumps is studied in finite dimensional space. Existence and uniqueness of solution, stability and exponential stability results are established…
We present a fully discrete stability analysis of the domain-of-dependence stabilization for hyperbolic problems. The method aims to address issues caused by small cut cells by redistributing mass around the neighborhood of a small cut cell…
We consider the steady Swift - Hohenberg partial differential equation. It is a one-parameter family of PDE on the plane, modeling for example Rayleigh - B\'enard convection. For values of the parameter near its critical value, we look for…
Steady states are invaluable in the study of dynamical systems. High-dimensional dynamical systems, due to a separation of time-scales, often evolve towards a lower dimensional manifold $M$. We introduce an approach to locate saddle points…
We present an original study on the numerical stabiliy of explicit schemes solving the incompressible Euler equations on an open domain with slipping boundary conditions. Relying on the skewness property of the non-linear term, we…
This paper presents a mathematical foundation for physical models in nonlinear optics through the lens of evolutionary equations. It focuses on two key concepts: well-posedness and exponential stability of Maxwell equations, with models…