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Chemical space which encompasses all stable compounds is unfathomably large and its dimension scales linearly with the number of atoms considered. The success of machine learning methods suggests that many physical quantities exhibit…

We propose an efficient residual minimization technique for the nonlinear model-order reduction of parameterized hyperbolic partial differential equations. Our nonlinear approximation space is a span of snapshots evaluated on a shifted…

This work proposes a motion planning algorithm for robotic manipulators that combines sampling-based and search-based planning methods. The core contribution of the proposed approach is the usage of burs of free configuration space…

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

Quantifying robustness in a single measure for the purposes of model selection, development of adversarial training methods, and anticipating trends has so far been elusive. The simplest metric to consider is the number of trainable…

We consider the task of lossy compression of high-dimensional vectors through quantization. We propose the approach that learns quantization parameters by minimizing the distortion of scalar products and squared distances between pairs of…

In applications involving ordinal predictors, common approaches to reduce dimensionality are either extensions of unsupervised techniques such as principal component analysis, or variable selection procedures that rely on modeling the…

Physical models of biological systems can become difficult to interpret when they have a large number of parameters. But the models themselves actually depend on (i.e. are sensitive to) only a subset of those parameters. Rigorously…

Incorporating domain knowledge into the modeling process is an effective way to improve learning accuracy. However, as it is provided by humans, domain knowledge can only be specified with some degree of uncertainty. We propose to…

Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…

This paper focuses on the construction of accurate and predictive data-driven reduced models of large-scale numerical simulations with complex dynamics and sparse training datasets. In these settings, standard, single-domain approaches may…

We consider the reduction of parametric families of linear dynamical systems having an affine parameter dependence that differ from one another by a low-rank variation in the state matrix. Usual approaches for parametric model reduction…

Soft robots achieve functionality through tight coupling among geometry, material composition, and actuation. As a result, effective design optimization requires these three aspects to be considered jointly rather than in isolation. This…

In this work we show that the classification performance of high-dimensional structural MRI data with only a small set of training examples is improved by the usage of dimension reduction methods. We assessed two different dimension…

Effective motion planning in high dimensional spaces is a long-standing open problem in robotics. One class of traditional motion planning algorithms corresponds to potential-based motion planning. An advantage of potential based motion…

Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…

Human-robot collaboration is on the rise. Robots need to increasingly improve the efficiency and smoothness with which they assist humans by properly anticipating a human's intention. To do so, prediction models need to increase their…

Human motion prediction is non-trivial in modern industrial settings. Accurate prediction of human motion can not only improve efficiency in human robot collaboration, but also enhance human safety in close proximity to robots. Among…

Learning from demonstration (LfD) is considered as an efficient way to transfer skills from humans to robots. Traditionally, LfD has been used to transfer Cartesian and joint positions and forces from human demonstrations. The traditional…

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is…