Related papers: Nonlinear Model Reduction by Probabilistic Manifol…

Recent advancements in multi-modal large language models have propelled the development of joint probabilistic models capable of both image understanding and generation. However, we have identified that recent methods suffer from loss of…

Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…

We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…

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…

The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. This work presents the first nonintrusive implementation…

Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…

Machine learning (ML) is rapidly transforming the way molecular dynamics simulations are performed and analyzed, from materials modeling to studies of protein folding and function. ML algorithms are often employed to learn low-dimensional…

Dynamic Mode Decomposition (DMD) is a data based modeling tool that identifies a matrix to map a quantity at some time instant to the same quantity in future. We design a new version which we call Adaptive Dynamic Mode Decomposition (ADMD)…

In this work, we present a model order reduction technique for nonlinear structures assembled from components.The reduced order model is constructed by reducing the substructures with proper orthogonal decomposition and connecting them by a…

Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data…

In this paper, we present a new nonintrusive reduced basis method when a cheap low-fidelity model and expensive high-fidelity model are available. The method relies on proper orthogonal decomposition (POD) to generate the high-fidelity…

Most models of generative AI for images assume that images are inherently low-dimensional objects embedded within a high-dimensional space. Additionally, it is often implicitly assumed that thematic image datasets form smooth or piecewise…

The investigation of fluid-solid systems is very important in a lot of industrial processes. From a computational point of view, the simulation of such systems is very expensive, especially when a huge number of parametric configurations…

We present a fully non-intrusive parametric reduced-order modeling (PROM) framework for geometrically nonlinear structures subject to geometric variations. The method builds upon equation-driven Galerkin ROMs constructed from vibration…

In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on…

In this work we present an integrated computational pipeline involving several model order reduction techniques for industrial and applied mathematics, as emerging technology for product and/or process design procedures. Its data-driven…

The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by widely disparate time scales. As a result,…

Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps…

In an ever-increasing interest for Machine Learning (ML) and a favorable data development context, we here propose an original methodology for data-based prediction of two-dimensional physical fields. Polynomial Chaos Expansion (PCE),…

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…