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Airfoil shape design is a classical problem in engineering and manufacturing. In this work, we combine principled physics-based considerations for the shape design problem with modern computational techniques using a data-driven approach.…
High-dimensional data analysis has been an active area, and the main focuses have been variable selection and dimension reduction. In practice, it occurs often that the variables are located on an unknown, lower-dimensional nonlinear…
Retrieving the missing dimension information in acoustic images from 2D forward-looking sonar is a well-known problem in the field of underwater robotics. There are works attempting to retrieve 3D information from a single image which…
The precise reconstruction of 3D objects from a single RGB image in complex scenes presents a critical challenge in virtual reality, autonomous driving, and robotics. Existing neural implicit 3D representation methods face significant…
Periodic and symmetric two-dimensional textures with various cross-sectional profiles have been employed to improve and optimize the physical response of the surfaces such as drag force, superhydrophobicity, and adhesion. While the effect…
Randomized dimensionality reduction is a widely-used algorithmic technique for speeding up large-scale Euclidean optimization problems. In this paper, we study dimension reduction for a variety of maximization problems, including…
Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…
We have deluge of data in time series format for numerous phenomena. The number of snapshots, resolution and many other factors come into play as we look to identify the dynamics in a given problem. The pre-processing and post-processing…
Building on recent advances in representation learning for wireless channels, this work investigates the cost-benefit trade-offs of high-dimensional channel embeddings in practical systems. We benchmark multiple wireless representations:…
A novel interface reconstruction strategy for volume of fluid (VOF) methods is introduced that represents the liquid-gas interface as two planes that co-exist within a single computational cell. In comparison to the piecewise linear…
We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor…
We present a novel approach to address the multi-agent sparse contextual linear bandit problem, in which the feature vectors have a high dimension $d$ whereas the reward function depends on only a limited set of features - precisely $s_0…
We give a dimensionality reduction procedure to approximate the sum of distances of a given set of $n$ points in $R^d$ to any "shape" that lies in a $k$-dimensional subspace. Here, by "shape" we mean any set of points in $R^d$. Our…
Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…
State-of-the-art models rely on massive widths despite exhibiting low Intrinsic Dimension (ID). We posit that this redundancy serves the non-convex optimization search rather than the final representation. We validate this hypothesis by…
Modern data sets, such as those in healthcare and e-commerce, are often derived from many individuals or systems but have insufficient data from each source alone to separately estimate individual, often high-dimensional, model parameters.…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
In aerodynamic design, the use of Computational Fluid Dynamics (CFD) tools has long relied on Reynolds-Averaged Navier-Stokes (RANS) and Unsteady RANS (URANS) turbulence models. However, these methods face limitations in predicting…
Data visualisation helps understanding data represented by multiple variables, also called features, stored in a large matrix where individuals are stored in lines and variable values in columns. These data structures are frequently called…
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…