Related papers: Nonlinear Balanced Truncation: Part 2 -- Model Red…
We introduce an iterative importance truncation scheme which aims at reducing the dimension of the model space of configuration interaction approaches by an a priori selection of the physically most relevant basis states. Using an…
To implement deep learning models on edge devices, model compression methods have been widely recognized as useful. However, it remains unclear which model compression methods are effective for Structured State Space Sequence (S4) models…
We propose a non-intrusive Deep Learning-based Reduced Order Model (DL-ROM) capable of capturing the complex dynamics of mechanical systems showing inertia and geometric nonlinearities. In the first phase, a limited number of high fidelity…
Forced response curves (FRCs) of nonlinear systems can exhibit complex behaviors, including hardening/softening behavior and bifurcations. Although topology optimization holds great potential for tuning these nonlinear dynamic responses,…
We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…
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…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
Motion planning under uncertainty is essential for reliable robot operation. Despite substantial advances over the past decade, the problem remains difficult for systems with complex dynamics. Most state-of-the-art methods perform search…
In this work, we develop reduced order models (ROMs) to predict solutions to a multiscale kinetic transport equation with a diffusion limit under the parametric setting. When the underlying scattering effect is not sufficiently strong, the…
This paper introduces the Non-linear Partition of Unity Method, a novel technique integrating Radial Basis Function interpolation and Weighted Essentially Non-Oscillatory algorithms. It addresses challenges in high-accuracy approximations,…
The Carleman linearization is one of the mainstream approaches to lift a finite-dimensional nonlinear dynamical system into an infinite-dimensional linear system with the promise of providing accurate approximations of the original…
This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…
We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications,…
In this paper, we consider model order reduction (MOR) methods for problems with slowly decaying Kolmogorov $n$-widths as, e.g., certain wave-like or transport-dominated problems. To overcome this Kolmogorov barrier within MOR, nonlinear…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
Digital twins have emerged as a key technology for optimizing the performance of engineering products and systems. High-fidelity numerical simulations constitute the backbone of engineering design, providing an accurate insight into 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…
When using a finite difference method to solve an initial--boundary--value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze…
Structural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications…
Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions --- computed for properly chosen parameters, using a full-order…