Related papers: Windowed least-squares model reduction for dynamic…
We provide the first global model recovery results for the IRLS (iteratively reweighted least squares) heuristic for robust regression problems. IRLS is known to offer excellent performance, despite bad initializations and data corruption,…
This article discusses a newly developed online manifold learning method, subspace iteration using reduced models (SIRM), for the dimensionality reduction of dynamical systems. This method may be viewed as subspace iteration combined with a…
This chapter offers a comprehensive introduction to the least-squares neural network (LSNN) method introduced in [14,16], for solving scalar first-order hyperbolic partial differential equations, specifically linear advection-reaction…
Learning under a Wasserstein loss, a.k.a. Wasserstein loss minimization (WLM), is an emerging research topic for gaining insights from a large set of structured objects. Despite being conceptually simple, WLM problems are computationally…
Reconstructing full spatio-temporal dynamics from sparse observations in both space and time remains a central challenge in complex systems, as measurements can be spatially incomplete and can be also limited to narrow temporal windows. Yet…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
This paper presents a generalized weak Galerkin (gWG) finite element method for linear elasticity problems on general polygonal and polyhedral meshes. The proposed framework is flexible and efficient, allowing for the use of nonpolynomial…
Iteratively Re-weighted Least Squares (IRLS) is a method for solving minimization problems involving non-quadratic cost functions, perhaps non-convex and non-smooth, which however can be described as the infimum over a family of quadratic…
If a dynamic system has active constraints on the state vector and they are known, then taking them into account during modeling is often advantageous. Unfortunately, in the constrained discrete-time state-space estimation, the state…
Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…
Partial least squares (PLS) is a simple factorisation method that works well with high dimensional problems in which the number of observations is limited given the number of independent variables. In this article, we show that PLS can…
We derive and analyze a hybridizable discontinuous Galerkin (HDG) method for approximating weak solutions to the equations of time-harmonic linear elasticity on a bounded Lipschitz domain in three dimensions. The real symmetry of the stress…
Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…
We address the problem of sparse recovery in an online setting, where random linear measurements of a sparse signal are revealed sequentially and the objective is to recover the underlying signal. We propose a reweighted least squares (RLS)…
Reduced order models are becoming increasingly important for rendering complex and multiscale spatio-temporal dynamics computationally tractable. The computational efficiency of such surrogate models is especially important for design,…
In this monograph, we review and develop variable projection Gauss-Newton, Levenberg-Marquardt and Newton methods for the Weighted Low-Rank Approximation (WLRA) problem, which has now an increasing number of applications in many scientific…
We present a physics-based fluid control method utilizing localized spacetime windows, extending force-based spacetime control to simulation scales that were previously intractable. Building on the observation that optimal control force…
Reduced-order modeling techniques, including balanced truncation and $\mathcal{H}_2$-optimal model reduction, exploit the structure of linear dynamical systems to produce models that accurately capture the dynamics. For nonlinear systems…
We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-square method is employed to ensure stability of the discrete…
This paper studies the problem of distributed weighted least-squares (WLS) estimation for an interconnected linear measurement network with additive noise. Two types of measurements are considered: self measurements for individual nodes,…