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We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known compactly supported density g with a finite number…

Proton therapy is a modality in fast development. Characterized by a maximum dose deposition at the end of the proton trajectory followed by a sharp fall-off, proton beams can deliver a highly conformal dose to the tumor while sparing…

Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this work…

Offline optimization is an important task in numerous material engineering domains where online experimentation to collect data is too expensive and needs to be replaced by an in silico maximization of a surrogate of the black-box function.…

Inverse design algorithms are the basis for realizing high-performance, freeform nanophotonic devices. Current methods to enforce geometric constraints, such as practical fabrication constraints, are heuristic and not robust. In this work,…

This paper introduces a practical sampling method for training surrogate models in the context of uncertainty propagation. We propose a heuristic method to uniformly draw samples within highest density regions of the density given by the…

Topology optimization (TO) provides a principled mathematical approach for optimizing the performance of a structure by designing its material spatial distribution in a pre-defined domain and subject to a set of constraints. The majority of…

Mathematical models of the human heart are increasingly playing a vital role in understanding the working mechanisms of the heart, both under healthy functioning and during disease. The aim is to aid medical practitioners diagnose and treat…

In this paper, we focus on developing efficient sensitivity analysis methods for a computationally expensive objective function $f(x)$ in the case that the minimization of it has just been performed. Here "computationally expensive" means…

Accurate surrogate construction for PDE-driven high-dimensional rare-event simulation is challenging when performance evaluations are expensive. Since a globally accurate surrogate may require many high-fidelity evaluations, adaptive…

This work is concerned with optimal control of partial differential equations where the control enters the state equation as a coefficient and should take on values only from a given discrete set of values corresponding to available…

In real-time trajectory planning for unmanned vehicles, on-board sensors, radars and other instruments are used to collect information on possible obstacles to be avoided and pathways to be followed. Since, in practice, observations of the…

Parametric shape optimization aims at minimizing an objective function f(x) where x are CAD parameters. This task is difficult when f is the output of an expensive-to-evaluate numerical simulator and the number of CAD parameters is large.…

Surrogate neural network-based models have been lately trained and used in a variety of science and engineering applications where the number of evaluations of a target function is limited by execution time. In cell phone camera systems,…

Traditionally, systems governed by linear Partial Differential Equations (PDEs) are spatially discretized to exploit their algebraic structure and reduce the computational effort for controlling them. Due to beneficial insights of the PDEs,…

Blocking, a special case of rerandomization, is routinely implemented in the design stage of randomized experiments to balance the baseline covariates. This study proposes a regression adjustment method based on the least absolute shrinkage…

In this paper, we study a fixed-confidence, fixed-tolerance formulation of a class of stochastic bi-level optimization problems, where the upper-level problem selects from a finite set of systems based on a performance metric, and the…

This paper considers structural optimization under a reliability constraint, where the input distribution is only partially known. Specifically, when we only know that the expected value vector and the variance-covariance matrix of the…

Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…

The development of nonlinear optimization algorithms capable of performing reliably in the presence of noise has garnered considerable attention lately. This paper advocates for strategies to create noise-tolerant nonlinear optimization…