Related papers: ParaDime: A Framework for Parametric Dimensionalit…

Quantum embedding methods enable the study of large, strongly correlated quantum systems by (usually self-consistent) decomposition into computationally manageable subproblems, in the spirit of divide-and-conquer methods. Among these,…

Visual analytics now plays a central role in decision-making across diverse disciplines, but it can be unreliable: the knowledge or insights derived from the analysis may not accurately reflect the underlying data. In this dissertation, we…

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…

Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. Traditionally, this involves using dimensionality reduction (DR) methods to project data onto lower-dimensional spaces or…

In this poster, we present a new VR-CAD framework, allowing user to modify parametric CAD data with 3D interaction in an immersive environment. With this framework, users can implicitly modify parameter values of CAD data with co-localized…

In this paper, we present a Mirroring Neural Network architecture to perform non-linear dimensionality reduction and Object Recognition using a reduced lowdimensional characteristic vector. In addition to dimensionality reduction, the…

The task of dimensionality reduction and visualization of high-dimensional datasets remains a challenging problem since long. Modern high-throughput technologies produce newer high-dimensional datasets having multiple views with relatively…

We propose a neural network-based approach that computes a stable and generalizing metric (LSiM) to compare data from a variety of numerical simulation sources. We focus on scalar time-dependent 2D data that commonly arises from motion and…

Nonlinear dimensionality reduction methods are a popular tool for data scientists and researchers to visualize complex, high dimensional data. However, while these methods continue to improve and grow in number, it is often difficult to…

Efficient and high-fidelity prior sampling and inversion for complex geological media is still a largely unsolved challenge. Here, we use a deep neural network of the variational autoencoder type to construct a parametric low-dimensional…

This paper presents a novel paradigm in simulation-based engineering sciences by introducing a new framework called Generative Parametric Design (GPD). The GPD framework enables the generation of new designs along with their corresponding…

It has become standard to use gradient-based dimensionality reduction (DR) methods like tSNE and UMAP when explaining what AI models have learned. This makes sense: these methods are fast, robust, and have an uncanny ability to find…

Due to the curse of dimensionality, solving high dimensional parabolic partial differential equations (PDEs) has been a challenging problem for decades. Recently, a weak adversarial network (WAN) proposed in (Y.Zang et al., 2020) offered a…

High-Resolution three-dimensional (3D) radio maps (RMs) provide rich information about the radio landscape that is essential to a myriad of wireless applications in the future wireless networks. Although deep learning (DL) methods have…

Similarity matching and join of time series data streams has gained a lot of relevance in today's world that has large streaming data. This process finds wide scale application in the areas of location tracking, sensor networks, object…

Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral…

The study of parameter-dependent partial differential equations (parametric PDEs) with countably many parameters has been actively studied for the last few decades. In particular, it has been well known that a certain type of parametric…

Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…

Solving and optimising Partial Differential Equations (PDEs) in geometrically parameterised domains often requires iterative methods, leading to high computational and time complexities. One potential solution is to learn a direct mapping…

Surrogate models provide compact relations between user-defined input parameters and output quantities of interest, enabling the efficient evaluation of complex parametric systems in many-query settings. Such capabilities are essential in a…