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The bootstrap is a popular data-driven method to quantify statistical uncertainty, but for modern high-dimensional problems, it could suffer from huge computational costs due to the need to repeatedly generate resamples and refit models. We…

We present a new application of model checking which achieves real-time multi-step planning and obstacle avoidance on a real autonomous robot. We have developed a small, purpose-built model checking algorithm which generates plans in situ…

Computer experiments refer to the study of real systems using complex simulation models. They have been widely used as alternatives to physical experiments. Design and analysis of computer experiments have attracted great attention in past…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from…

The bifactor model and its extensions are multidimensional latent variable models, under which each item measures up to one subdimension on top of the primary dimension(s). Despite their wide applications to educational and psychological…

Regression is a fundamental prediction task common in data-centric engineering applications that involves learning mappings between continuous variables. In many engineering applications (e.g.\ structural health monitoring), feature-label…

The task of approximating a function of d variables from its evaluations at a given number of points is ubiquitous in numerical analysis and engineering applications. When d is large, this task is challenged by the so-called curse of…

Modeling processes are the activities of capturing and representing processes and control of their dynamic behavior. Desired features of the model include capture of relevant aspects of a real phenomenon, understandability, and completeness…

Modern distributed systems include a class of applications in which non-functional requirements are important. In particular, these applications include multimedia facilities where real time constraints are crucial to their correct…

For high dimensional particle systems, governed by smooth nonlinearities depending on mutual distances between particles, one can construct low-dimensional representations of the dynamical system, which allow the learning of nearly optimal…

We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…

Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…

Derivative-free algorithms seek the minimum of a given function based only on function values queried at appropriate points. Although these methods are widely used in practice, their performance is known to worsen as the problem dimension…

Graphs are widespread data structures used to model a wide variety of problems. The sheer amount of data to be processed has prompted the creation of a myriad of systems that help us cope with massive scale graphs. The pressure to deliver…

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.…

Time-series analysis is fundamental for modeling and predicting dynamical behaviors from time-ordered data, with applications in many disciplines such as physics, biology, finance, and engineering. Measured time-series data, however, are…

Multivariate spatial data plays an important role in computational science and engineering simulations. The potential features and hidden relationships in multivariate data can assist scientists to gain an in-depth understanding of a…

A linear multiple regression model in function spaces is formulated, under temporal correlated errors. This formulation involves kernel regressors. A generalized least-squared regression parameter estimator is derived. Its asymptotic…

We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the…