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In a recent work, we proposed a graph-based manifold learning scheme for the nonlinear Galerkin-reduction of quasi-static solid mechanical problems [1]. The resulting nonlinear approximation spaces can closely and flexibly represent…

A non-intrusive reduced order model based on convolutional autoencoders (NIROM-CAEs) is proposed as a data-driven tool to build an efficient nonlinear reduced-order model for stochastic spatio-temporal large-scale physical problems. The…

In this paper, we investigate tensor based nonintrusive reduced-order models (ROMs) for parametric cross-diffusion equations. The full-order model (FOM) consists of ordinary differential equations (ODEs) in matrix or tensor form resulting…

Parametric high-fidelity simulations are of interest for a wide range of applications. But the restriction of computational resources renders such models to be inapplicable in a real-time context or in multi-query scenarios. Model order…

In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…

We demonstrate that system identification techniques can provide a basis for effective, non-intrusive model order reduction (MOR) for common circuits that are key building blocks in microelectronics. Our approach is motivated by the…

We present two elegant solutions for modeling continuous-time dynamics, in a novel model-based reinforcement learning (RL) framework for semi-Markov decision processes (SMDPs), using neural ordinary differential equations (ODEs). Our models…

We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…

Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…

Model predictive controllers use dynamics models to solve constrained optimal control problems. However, computational requirements for real-time control have limited their use to systems with low-dimensional models. Nevertheless,…

Computing reduced-order models using non-intrusive methods is particularly attractive for systems that are simulated using black-box solvers. However, obtaining accurate data-driven models can be challenging, especially if the underlying…

The objective of this paper is to develop a global non-intrusive Parametric Model Order Reduction (PMOR) methodology for the problem of changing well locations in an oil field, that can eventually be used for well placement optimization to…

Model Order Reduction (MOR) methods enable the generation of real-time-capable digital twins, which can enable various novel value streams in industry. While traditional projection-based methods are robust and accurate for linear problems,…

Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…

In this paper we discuss a projection model order reduction (MOR) method for a class of parametric linear evolution PDEs, which is based on the application of the Laplace transform. The main advantage of this approach consists in the fact…

An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…

Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural…

We investigate the use of reduced-order modelling to run discrete element simulations at higher speeds. Taking a data-driven approach, we run many offline simulations in advance and train a model to predict the velocity field from the mass…

Though high-performance computing enables high-fidelity simulations of complex engineering systems, accurately resolving multi-scale physics for real-world problems remains computationally prohibitive, particularly in many-query…