Related papers: An Optimal Projection Framework for Structure-Pres…
We examine some differential geometric approaches to finding approximate solutions to the continuous time nonlinear filtering problem. Our primary focus is a new projection method for the optimal filter infinite dimensional Stochastic…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
This article surveys nonlinear model reduction methods that remain effective in regimes where linear reduced-space approximations are intrinsically inefficient, such as transport-dominated problems with wave-like phenomena and moving…
This paper presents a reduced order approach for transient modeling of multiple moving objects in nonlinear crossflows. The Proper Orthogonal Decomposition method and the Galerkin projection are used to construct a reduced version of the…
State estimation aims at approximately reconstructing the solution $u$ to a parametrized partial differential equation from $m$ linear measurements, when the parameter vector $y$ is unknown. Fast numerical recovery methods have been…
Most model reduction methods reduce the state dimension and then temporally evolve a set of coefficients that encode the state in the reduced representation. In this paper, we instead employ an efficient representation of the entire…
The paper addresses the model reduction problem for linear and nonlinear systems using the notion of least squares moment matching. For linear systems, the main idea is to approximate a transfer function by ensuring that the interpolation…
In this paper, we propose a novel primal-dual inexact gradient projection method for nonlinear optimization problems with convex-set constraint. This method only needs inexact computation of the projections onto the convex set for each…
Projection-based model order reduction on nonlinear manifolds has been recently proposed for problems with slowly decaying Kolmogorov n-width such as advection-dominated ones. These methods often use neural networks for manifold learning…
We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model…
Of all the possible projection methods for solving large-scale Lyapunov matrix equations, Galerkin approaches remain much more popular than minimal-residual ones. This is mainly due to the different nature of the projected problems stemming…
We introduce a model reduction approach for linear time-invariant second order systems based on positive real balanced truncation. Our method guarantees asymptotic stability and passivity of the reduced order model as well as the positive…
We devise a space-time tensor method for the low-rank approximation of linear parabolic evolution equations. The proposed method is a stable Galerkin method, uniformly in the discretization parameters, based on a Minimal Residual…
We present a novel two-view geometry estimation framework which is based on a differentiable robust loss function fitting. We propose to treat the robust fundamental matrix estimation as an implicit layer, which allows us to avoid…
Model instability and poor prediction of long-term behavior are common problems when modeling dynamical systems using nonlinear "black-box" techniques. Direct optimization of the long-term predictions, often called simulation error…
A stochastic gradient method for finite-sum minimization subject to deterministic linear constraints is proposed and analyzed. The procedure presented adapts the projected gradient method on convex set to the use of both a stochastic…
In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…
Persistence-based topological optimization deforms a point cloud $X \subset \mathbb{R}^d$ by minimizing objectives of the form $L(X) = \ell(\mathrm{Dgm}(X))$, where $\mathrm{Dgm}(X)$ is a persistence diagram. In practice, optimization is…
This paper considers optimization problems on the Stiefel manifold $X^{\mathsf{T}}X=I_p$, where $X\in \mathbb{R}^{n \times p}$ is the variable and $I_p$ is the $p$-by-$p$ identity matrix. A framework of constraint preserving update schemes…
We propose a novel gradient-based online optimization framework for solving stochastic programming problems that frequently arise in the context of cyber-physical and robotic systems. Our problem formulation accommodates constraints that…