Related papers: An integrated data-driven computational pipeline w…

Data-Driven Computational Mechanics is a novel computing paradigm that enables the transition from standard data-starved approaches to modern data-rich approaches. At this early stage of development, one can distinguish two mainstream…

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…

While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented…

The understanding of nonlinear, high dimensional flows, e.g, atmospheric and ocean flows, is critical to address the impacts of global climate change. Data Assimilation techniques combine physical models and observational data, often in a…

Direct numerical simulation of dynamical systems is of fundamental importance in studying a wide range of complex physical phenomena. However, the ever-increasing need for accuracy leads to extremely large-scale dynamical systems whose…

The structural properties of mechanical metamaterials are typically studied with two-scale methods based on computational homogenization. Because such materials have a complex microstructure, enriched schemes such as second-order…

In this paper, we propose an efficient data-driven predictive control approach for general nonlinear processes based on a reduced-order Koopman operator. A Kalman-based sparse identification of nonlinear dynamics method is employed to…

Materials informatics offers a promising pathway towards rational materials design, replacing the current trial-and-error approach and accelerating the development of new functional materials. Through the use of sophisticated data analysis…

Theory and methods to obtain parametric reduced-order models by moment matching are presented. The definition of the parametric moment is introduced, and methods (model-based and data-driven) for the approximation of the parametric moment…

The simulation of electric rotating machines is both computationally expensive and memory intensive. To overcome these costs, model order reduction techniques can be applied. The focus of this contribution is especially on machines that…

Efficiently estimating system dynamics from data is essential for minimizing data collection costs and improving model performance. This work addresses the challenge of designing future control inputs to maximize information gain, thereby…

Mathematical models are crucial for optimizing and controlling chemical processes, yet they often face significant limitations in terms of computational time, algorithm complexity, and development costs. Hybrid models, which combine…

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,…

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…

We propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic…

In applied mathematics and related disciplines, the modeling-simulation-optimization workflow is a prominent scheme, with mathematical models and numerical algorithms playing a crucial role. For these types of mathematical research data,…

For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…

In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…

In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…

Due to the wide diffusion of 3D printing technologies, geometric algorithms for Additive Manufacturing are being invented at an impressive speed. Each single step, in particular along the Process Planning pipeline, can now count on dozens…