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Wide accessibility of imaging and profile sensors in modern industrial systems created an abundance of high-dimensional sensing variables. This led to a a growing interest in the research of high-dimensional process monitoring. However,…
A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical…
A data-driven framework is developed to represent chaotic dynamics on an inertial manifold (IM), and applied to solutions of the Kuramoto-Sivashinsky equation. A hybrid method combining linear and nonlinear (neural-network) dimension…
This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…
Integrating physics models within machine learning models holds considerable promise toward learning robust models with improved interpretability and abilities to extrapolate. In this work, we focus on the integration of incomplete physics…
Dynamical Systems (DS) are an effective and powerful means of shaping high-level policies for robotics control. They provide robust and reactive control while ensuring the stability of the driving vector field. The increasing complexity of…
The manifold hypothesis states that high-dimensional data can be modeled as lying on or near a low-dimensional, nonlinear manifold. Variational Autoencoders (VAEs) approximate this manifold by learning mappings from low-dimensional latent…
Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains…
Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…
Deep Learning is having a remarkable impact on the design of Reduced Order Models (ROMs) for Partial Differential Equations (PDEs), where it is exploited as a powerful tool for tackling complex problems for which classical methods might…
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…
The dynamics of a turbulent flow tend to occupy only a portion of the phase space at a statistically stationary regime. From a dynamical systems point of view, this portion is the attractor. The knowledge of the turbulent attractor is…
Discrete latent spaces in variational autoencoders have been shown to effectively capture the data distribution for many real-world problems such as natural language understanding, human intent prediction, and visual scene representation.…
We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds. We redevelop the VAE framework…
We propose K-Deep Simplex(KDS) which, given a set of data points, learns a dictionary comprising synthetic landmarks, along with representation coefficients supported on a simplex. KDS employs a local weighted $\ell_1$ penalty that…
Data-efficient learning remains a central challenge in autonomous driving due to the high cost and safety risks of large-scale real-world interaction. Although world-model-based reinforcement learning enables policy optimization through…
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a…
This paper takes a step towards temporal reasoning in a dynamically changing video, not in the pixel space that constitutes its frames, but in a latent space that describes the non-linear dynamics of the objects in its world. We introduce…
We present a method for learning latent stochastic differential equations (SDEs) from high-dimensional time series data. Given a high-dimensional time series generated from a lower dimensional latent unknown It\^o process, the proposed…
Compressed sensing techniques enable efficient acquisition and recovery of sparse, high-dimensional data signals via low-dimensional projections. In this work, we propose Uncertainty Autoencoders, a learning framework for unsupervised…