相关论文: Deep Invertible Autoencoders for Dimensionality Re…

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real-time and many-query evaluations…

A big mystery in deep learning continues to be the ability of methods to generalize when the number of model parameters is larger than the number of training examples. In this work, we take a step towards a better understanding of the…

The use of deep learning has become increasingly popular in reduced-order models (ROMs) to obtain low-dimensional representations of full-order models. Convolutional autoencoders (CAEs) are often used to this end as they are adept at…

In the early stages of aerospace design, reduced order models (ROMs) are crucial for minimizing computational costs associated with using physics-rich field information in many-query scenarios requiring multiple evaluations. The intricacy…

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…

In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…

Inverse problems often involve matching observational data using a physical model that takes a large number of parameters as input. These problems tend to be under-constrained and require regularization to impose additional structure on the…

In recent years, numerical methods in industrial applications have evolved from a pure predictive tool towards a means for optimization and control. Since standard numerical analysis methods have become prohibitively costly in such…

Nonintrusive projection-based reduced order models (ROMs) are essential for dynamics prediction in multi-query applications where access to the source of the underlying full order model (FOM) is unavailable; that is, FOM is a black-box.…

A variational autoencoder (VAE) is a probabilistic machine learning framework for posterior inference that projects an input set of high-dimensional data to a lower-dimensional, latent space. The latent space learned with a VAE offers…

This study investigates the use of non-linear unsupervised dimensionality reduction techniques to compress a music dataset into a low-dimensional representation which can be used in turn for the synthesis of new sounds. We systematically…

A common strategy for the dimensionality reduction of nonlinear partial differential equations relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics…

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…

Proper orthogonal decomposition (POD) allows reduced-order modeling of complex dynamical systems at a substantial level, while maintaining a high degree of accuracy in modeling the underlying dynamical systems. Advances in machine learning…

Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional…

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…

In situations where the solution of a high-fidelity dynamical system needs to be evaluated repeatedly, over a vast pool of parametric configurations and in absence of access to the underlying governing equations, data-driven model reduction…

Using the information theory, this study provides insights into how the construction of latent space of autoencoder (AE) using deep neural network (DNN) training finds a smooth low-dimensional manifold in the stiff dynamical system. Our…

We propose a new concept of rateless auto-encoders (RL-AEs) that enable a flexible latent dimensionality, which can be seamlessly adjusted for varying distortion and dimensionality requirements. In the proposed RL-AEs, instead of a…

This paper presents a nonlinear reduced-order modeling (ROM) framework that leverages deep learning and manifold learning to predict compressible flow fields with complex nonlinear features, including shock waves. The proposed DeepManifold…