相关论文: Data-Driven Learning of Reduced-order Dynamics for…

Non-intrusive methods have been used since two decades to derive reduced-order models for geometrically nonlinear structures, with a particular emphasis on the so-called STiffness Evaluation Procedure (STEP), relying on the static…

In this work, we consider wave propagation in materials characterized by nonlinear properties or damage. To accelerate the simulations of the resulting high-dimensional problems, we apply model order reduction methods. Depending on the…

In this chapter we examine reduced order techniques for geometrical parametrized heat exchange systems, Poisson, and flows based on Stokes, steady and unsteady incompressible Navier-Stokes and Cahn-Hilliard problems. The full order finite…

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…

This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied…

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…

In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal…

For general nonlinear mechanical systems, we derive closed-form, reduced-order models up to cubic order based on rigorous invariant manifold results. For conservative systems, the reduction is based on Lyapunov Subcenter Manifold (LSM)…

This paper proposes a non-intrusive, data-driven reduced-order modeling framework for stochastic optimal control problems governed by partial differential equations. The control problem is formulated with a quadratic cost functional and…

In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

We consider parameter identification problems in parametrized partial differential equations (PDE). This leads to nonlinear ill-posed inverse problems. One way to solve them are iterative regularization methods, which typically require…

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…

Traditional reduced order modeling techniques such as the reduced basis (RB) method (relying, e.g., on proper orthogonal decomposition (POD)) suffer from severe limitations when dealing with nonlinear time-dependent parametrized PDEs,…

This paper presents a new data-driven non-intrusive reduced-order model(NIROM) that outperforms the traditional Proper orthogonal decomposition (POD) based reducedorder model. This is achieved by using Auto-Encoder(AE) and attention-based…

We propose a nonlinear reduced basis method for the efficient approximation of parametrized partial differential equations (PDEs), exploiting kernel proper orthogonal decomposition (KPOD) for the generation of a reduced-order space and…

In this paper, we consider the learning of a Reduced-Order Linear Parameter-Varying Model (ROLPVM) of a nonlinear dynamical system based on data. This is achieved by a two-step procedure. In the first step, we learn a projection to a lower…

Fluid flow in the transonic regime finds relevance in aerospace engineering, particularly in the design of commercial air transportation vehicles. Computational fluid dynamics models of transonic flow for aerospace applications are…

Generally, reduced order models of fluid flows are obtained by projecting the Navier-Stokes equations onto a reduced subspace spanned by vector functions that carry the meaningful information of the dynamics. A common method to generate…

We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…