Related papers: Learning a Reduced Basis of Dynamical Systems usin…
Modeling the dynamic behavior of deformable objects is crucial for creating realistic digital worlds. While conventional simulations produce high-quality motions, their computational costs are often prohibitive. Subspace simulation…
Disentanglement is a useful property in representation learning which increases the interpretability of generative models such as Variational autoencoders (VAE), Generative Adversarial Models, and their many variants. Typically in such…
Conventional magneto-static finite element analysis of electrical machine design is time-consuming and computationally expensive. Since each machine topology has a distinct set of parameters, design optimization is commonly performed…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
Autoencoders are a widespread tool in machine learning to transform high-dimensional data into a lowerdimensional representation which still exhibits the essential characteristics of the input. The encoder provides an embedding from the…
Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computational domains, etc.…
Embedding techniques allow the approximations of finite dimensional attractors and manifolds of infinite dimensional dynamical systems via subdivision and continuation methods. These approximations give a topological one-to-one image of the…
Data sets that are specified by a large number of features are currently outside the area of applicability for quantum machine learning algorithms. An immediate solution to this impasse is the application of dimensionality reduction methods…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
We use spatially-sparse two, three and four dimensional convolutional autoencoder networks to model sparse structures in 2D space, 3D space, and 3+1=4 dimensional space-time. We evaluate the resulting latent spaces by testing their…
We use invariant manifold results on Banach spaces to conclude the existence of spectral submanifolds (SSMs) in a class of nonlinear, externally forced beam oscillations. SSMs are the smoothest nonlinear extensions of spectral subspaces of…
We investigate how symmetries present in datasets affect the structure of the latent space learned by Variational Autoencoders (VAEs). By training VAEs on data originating from simple mechanical systems and particle collisions, we analyze…
Stochastic dynamical systems with slow or metastable behavior evolve, on long time scales, on an unknown low-dimensional manifold in high-dimensional ambient space. Building a reduced simulator from short-burst ambient ensembles is a…
In the autoencoder based anomaly detection paradigm, implementing the autoencoder in edge devices capable of learning in real-time is exceedingly challenging due to limited hardware, energy, and computational resources. We show that these…
Dictionary learning has recently emerged as a promising approach for mechanistic interpretability of large transformer models. Disentangling high-dimensional transformer embeddings requires algorithms that scale to high-dimensional data…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
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…
Autoencoders, which consist of an encoder and a decoder, are widely used in machine learning for dimension reduction of high-dimensional data. The encoder embeds the input data manifold into a lower-dimensional latent space, while the…
This work concerns control-oriented and structure-preserving learning of low-dimensional approximations of high-dimensional physical systems, with a focus on mechanical systems. We investigate the integration of neural autoencoders in model…
The autoencoder is an unsupervised learning paradigm that aims to create a compact latent representation of data by minimizing the reconstruction loss. However, it tends to overlook the fact that most data (images) are embedded in a…