Related papers: Data-Driven Nonlinear Model Reduction to Spectral …
In the field of structural health monitoring (SHM), inverse problems which require repeated analyses are common. With the increase in the use of nonlinear models, the development of nonlinear reduced order modelling techniques is of…
A cutting-plane model for a nonsmooth function is the maximum of several first-order expansions centered at different points. Using such a model in a bundle method leads to linear convergence (of serious steps) to a minimum. In smooth…
Passive Non-Line-of-Sight (NLOS) imaging requires to reconstruct objects which cannot be seen in line without using external controllable light sources. It can be widely applied in areas like counter-terrorism, urban-Warfare,…
Supersymmetric orbifold projection of N=1 SQCD with relatively small number of flavors (not larger than the number of colors) is considered. The purpose is to check whether orbifolding commutes with the infrared limit. On the one hand, one…
A method for model reduction in nonlinear ODE systems is demonstrated through computational examples. The method does not require an implicit separation of time-scales in the fine dynamics to be effective. From the computational standpoint,…
It is shown that an explicit oblique projection nonlinear feedback controller is able to stabilize semilinear parabolic equations, with time-dependent dynamics and with a polynomial nonlinearity. The actuators are typically modeled by a…
Recent works have developed new projection-free first-order methods based on utilizing linesearches and normal vector computations to maintain feasibility. These oracles can be cheaper than orthogonal projection or linear optimization…
Mechanical metamaterials utilize geometry to achieve exceptional mechanical properties, including those not typically possible for traditional materials. To achieve these properties, it is necessary to identify the proper structures and…
In this paper, we propose a nonlinear dimensionality reduction algorithm for the manifold of Symmetric Positive Definite (SPD) matrices that considers the geometry of SPD matrices and provides a low dimensional representation of the…
A general, variational approach to derive low-order reduced systems for nonlinear systems subject to an autonomous forcing, is introduced. The approach is based on the concept of optimal parameterizing manifold (PM) that substitutes the…
We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to captureaccurately the solutions without numerically resolving the high frequency oscillations {\em in both space and time}.Such PDE…
We study control systems invariant under a Lie group with application to the problem of nonlinear trajectory planning. A theory of symmetry reduction of exterior differential systems is employed to demonstrate how symmetry reduction and…
We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…
This paper deals with model-order reduction of parametric partial differential equations (PPDE). More specifically, we consider the problem of finding a good approximation subspace of the solution manifold of the PPDE when only partial…
Slow-fast dynamical systems, i.e., singularly or non-singularly perturbed dynamical systems possess slow invariant manifolds on which trajectories evolve slowly. Since the last century various methods have been developed for approximating…
Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…
Deep learning models have gained great success in many real-world applications. However, most existing networks are typically designed in heuristic manners, thus lack of rigorous mathematical principles and derivations. Several recent…
Tracking and acquiring simultaneous optical images of randomly moving targets obscured by scattering media remains a challenging problem of importance to many applications that require precise object localization and identification. In this…
We propose a new model reduction framework for problems that exhibit transport phenomena. As in the moving finite element method (MFEM), our method employs time-dependent transformation operators and, especially, generalizes MFEM to…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…