Related papers: Frequency-weighted H2-optimal model order reductio…
High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced-order models, which often rely on…
Balanced truncation is one of the most common model order reduction schemes. In this paper, we study finite-frequency model order reduction (FF-MOR) problems of linear continuous-time systems within the framework of balanced truncation…
Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…
Mechanical systems are usually modeled by second-order Ordinary Differential Equations (ODE) which take the form $\ddot{q} = f(t, q, \dot{q})$. While simulation methods tailored to these equations have been studied, using them in direct…
We propose a new methodology to design first-order methods for unconstrained strongly convex problems. Specifically, instead of tackling the original objective directly, we construct a shifted objective function that has the same minimizer…
Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…
In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We…
Finite element based simulation of phenomena governed by partial differential equations is a standard tool in many engineering workflows today. However, the simulation of complex geometries is computationally expensive. Many engineering…
We consider an optimization problem related to semi-active damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use a minimization…
The recent promises of Model Predictive Control in robotics have motivated the development of tailored second-order methods to solve optimal control problems efficiently. While those methods benefit from strong convergence properties,…
It is of great concern to produce numerically efficient methods for moisture diffusion through porous media, capable of accurately calculate moisture distribution with a reduced computational effort. In this way, model reduction methods are…
In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…
In this paper, we investigate the optimal $\mathcal{H}_2$ model reduction problem for single-input single-output (SISO) continuous-time linear time-invariant (LTI) systems. A semi-definite relaxation (SDR) approach is proposed to determine…
Deep learning-based models have demonstrated remarkable success in solving illposed inverse problems; however, many fail to strictly adhere to the physical constraints imposed by the measurement process. In this work, we introduce a…
An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…
Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…
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…
Classical supervised learning via empirical risk (or negative log-likelihood) minimization hinges upon the assumption that the testing distribution coincides with the training distribution. This assumption can be challenged in modern…
Optimal model reduction for large-scale linear dynamical systems is studied. In contrast to most existing works, the systems under consideration are not required to be stable, neither in discrete nor in continuous time. As a consequence,…
We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…