Related papers: Hierarchical model reduction of nonlinear partial …
We propose an efficient residual minimization technique for the nonlinear model-order reduction of parameterized hyperbolic partial differential equations. Our nonlinear approximation space is a span of snapshots evaluated on a shifted…
In many applications throughout science and engineering, model reduction plays an important role replacing expensive large-scale linear dynamical systems by inexpensive reduced order models that capture key features of the original, full…
The focus of this work is on the development of an error-driven isogeometric framework, capable of automatically performing an adaptive simulation in the context of second- and fourth-order, elliptic partial differential equations defined…
Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…
We investigate new developments of the combined Reduced-Basis and Empirical Interpolation Methods (RB-EIM) for parametrized nonlinear parabolic problems. In many situations, the cost of the EIM in the offline stage turns out to be…
We develop a structure-preserving parametric model reduction approach for linearized swing equations where parametrization corresponds to variations in operating conditions. We employ a global basis approach to develop the parametric…
Based on neural network and adaptive subspace approximation method, we propose a new machine learning method for solving partial differential equations. The neural network is adopted to build the basis of the finite dimensional subspace.…
This work presents a novel and efficient nonlinear programming framework that tightly integrates hierarchical decision-making with whole-body inverse kinematic planning and control. Decision-making plays a central role in many aspects of…
Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…
Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current…
We present a novel numerical scheme to approximate the solution map $s\mapsto u(s) := \mathcal{L}^{-s}f$ to partial differential equations involving fractional elliptic operators. Reinterpreting $\mathcal{L}^{-s}$ as interpolation operator…
We focus on the numerical modelling of water waves by means of depth averaged models. We consider in particular PDE systems which consist in a nonlinear hyperbolic model plus a linear dispersive perturbation involving an elliptic operator.…
An adaptive parametric reduced-order modeling method based on interpolating poles of reduced-order models is proposed in this paper. To guarantee correct interpolation, a pole-matching process is conducted to determine which poles of two…
To be feasible for computationally intensive applications such as parametric studies, optimization and control design, large-scale finite element analysis requires model order reduction. This is particularly true in nonlinear settings that…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
The last two decades have seen major developments in interpolatory methods for model reduction of large-scale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at modest cost; refined…
We investigate mathematically a nonlinear approximation type approach recently introduced in [A. Ammar et al., J. Non-Newtonian Fluid Mech., 2006] to solve high dimensional partial differential equations. We show the link between the…
This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control…
A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced in [Balabanov and Nouy 2019, Part I]. Following this framework, we here construct…
This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…