Results 11 to 20 of about 31,410,548 (207)
Operator inference for non-intrusive model reduction with quadratic manifolds [PDF]
Computer Methods in Applied Mechanics and Engineering, 2022 This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models.
Rudy Geelen, S. Wright, K. Willcox
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High-order differentiable autoencoder for nonlinear model reduction [PDF]
ACM Transactions on Graphics, 2021 This paper provides a new avenue for exploiting deep neural networks to improve physics-based simulation. Specifically, we integrate the classic Lagrangian mechanics with a deep autoencoder to accelerate elastic simulation of deformable solids.
Siyuan Shen +6 more
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Model Reduction and Neural Networks for Parametric PDEs [PDF]
SMAI Journal of Computational Mathematics, 2020 We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with ideas from model ...
K. Bhattacharya +3 more
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Learning physics-based models from data: perspectives from inverse problems and model reduction
Acta Numerica, 2021 This article addresses the inference of physics models from data, from the perspectives of inverse problems and model reduction. These fields develop formulations that integrate data into physics-based models while exploiting the fact that many ...
O. Ghattas, K. Willcox
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Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms [PDF]
Computer Methods in Applied Mechanics and Engineering, 2020 This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form.
P. Benner +4 more
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Breaking the Kolmogorov Barrier with Nonlinear Model Reduction
Notices of the American Mathematical Society, 2022 Introduction. Model reduction is ubiquitous in computational science and engineering. It plays a key role in making computationally tractable outer-loop applications that require simulating systems for many scenarios with different parameters and inputs.
B. Peherstorfer
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Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders [PDF]
Journal of Computational Physics, 2018 Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the reduced-basis method ...
Kookjin Lee, K. Carlberg
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Generalized Multiscale Finite Element Method for Elastic Wave Propagation in the Frequency Domain
Computation, 2020 In this work, we consider elastic wave propagation in fractured media. The mathematical model is described by the Helmholtz problem related to wave propagation with specific interface conditions (Linear Slip Model, LSM) on the fracture in the frequency ...
Uygulana Gavrilieva +2 more
doaj +1 more source
Algorithms, 2021 Parameter identification is an important research topic with a variety of applications in industrial and environmental problems. Usually, a functional has to be minimized in conjunction with parameter identification; thus, there is a certain similarity ...
Vasiliy V. Grigoriev +2 more
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Dynamical reduction models [PDF]
Physics Reports, 2003 The report presents an exhaustive review of the recent attempt to overcome the difficulties that standard quantum mechanics meets in accounting for the measurement (or macro-objectification) problem, an attempt based on the consideration of nonlinear and stochastic modifications of the Schroedinger equation.
BASSI, ANGELO, GHIRARDI, GIANCARLO
openaire +3 more sources