相关论文: Convolutional Autoencoders for Reduced-Order Model…

Computational design optimization in fluid dynamics usually requires to solve non-linear partial differential equations numerically. In this work, we explore a Bayesian optimization approach to minimize an object's drag coefficient in…

We formulate a new projection-based reduced-ordered modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov-Galerkin (APG) method, is derived by decomposing the generalized…

Geophysical inversion attempts to estimate the distribution of physical properties in the Earth's interior from observations collected at or above the surface. Inverse problems are commonly posed as least-squares optimization problems in…

We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic linear part that are subject to external forcing with…

We propose a customized convolutional neural network based autoencoder called a hierarchical autoencoder, which allows us to extract nonlinear autoencoder modes of flow fields while preserving the contribution order of the latent vectors.…

Manifold-valued data naturally arises in medical imaging. In cognitive neuroscience, for instance, brain connectomes base the analysis of coactivation patterns between different brain regions on the analysis of the correlations of their…

The aerodynamic optimization process of cars requires multiple iterations between aerodynamicists and stylists. Response Surface Modeling and Reduced-Order Modeling are commonly used to eliminate the overhead due to Computational Fluid…

Data-driven reduced order modeling of chaotic dynamics can result in systems that either dissipate or diverge catastrophically. Leveraging non-linear dimensionality reduction of autoencoders and the freedom of non-linear operator inference…

The present work proposes an inflow turbulence generation strategy using deep learning methods. This is achieved with the help of an autoencoder architecture with two different types of operational layers in the latent-space: a fully…

This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…

Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be…

Data-driven modeling for nonlinear fluid flows using sparse convolution-based mapping into a feature space where the dynamics are Markov linear is explored in this article. The underlying principle of low-order models for fluid systems is…

Fluid-structure interactions are central to many bio-molecular processes, and they impose a great challenge for computational and modeling methods. In this paper, we consider the immersed boundary method (IBM) for biofluid systems, and to…

To describe non-equilibrium transport processes in a quantum device with infinite baths, we propose to formulate the problems as a reduced-order problem. Starting with the Liouville-von Neumann equation for the density-matrix, the…

This work proposes a model-reduction approach for the material point method on nonlinear manifolds. Our technique approximates the $\textit{kinematics}$ by approximating the deformation map using an implicit neural representation that…

This work studies the problem of modeling visual processes by leveraging deep generative architectures for learning linear, Gaussian representations from observed sequences. We propose a joint learning framework, combining a vector…

Our world is full of physics-driven data where effective mappings between data manifolds are desired. There is an increasing demand for understanding combined model-based and data-driven methods. We propose a nonlinear, learned singular…

The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…

Deep learning models for image compression often face practical limitations in hardware-constrained applications. Although these models achieve high-quality reconstructions, they are typically complex, heavyweight, and require substantial…

This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with model…