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This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue…
Signal integrity (SI) analysis in printed circuit board (PCB) interconnects faces increasing complexity due to diverse integrated circuit (IC) buffer technologies, varying operating conditions, and manufacturing tolerances. Existing machine…
Diffusion and flow-matching have emerged as powerful methodologies for generative modeling, with remarkable success in capturing complex data distributions and enabling flexible guidance at inference time. Many downstream applications,…
Machine learning surrogate emulators are needed in engineering design and optimization tasks to rapidly emulate computationally expensive physics-based models. In micromechanics problems the local full-field response variables are desired…
Surrogate modelling techniques have opened up new possibilities to overcome the limitations of computationally intensive numerical models in various areas of engineering and science. However, while fundamental in many engineering…
Production optimization in stress-sensitive unconventional reservoirs is governed by a nonlinear trade-off between pressure-driven flow and stress-induced degradation of fracture conductivity and matrix permeability. While higher drawdown…
Surrogate modeling for systems with high-dimensional quantities of interest remains challenging, particularly when training data are costly to acquire. This work develops multifidelity methods for multiple-input multiple-output linear…
This paper presents enhancement strategies for the Hermitian and skew-Hermitian splitting method based on gradient iterations. The spectral properties are exploited for the parameter estimation, often resulting in a better convergence. In…
We introduce adaptive sampling methods for stochastic programs with deterministic constraints. First, we propose and analyze a variant of the stochastic projected gradient method where the sample size used to approximate the reduced…
In this work, an adaptive edge element method is developed for an H(curl)-elliptic constrained optimal control problem. We use the lowest-order Nedelec's edge elements of first family and the piecewise (element-wise) constant functions to…
Reliability-based design optimization (RBDO) is an active field of research with an ever increasing number of contributions. Numerous methods have been proposed for the solution of RBDO, a complex problem that combines optimization and…
Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical…
We propose a novel estimator for the principal component (PC) subspace tailored to the high-dimension, low-sample size (HDLSS) context. The method, termed Adaptive Reference-Guided (ARG) estimator, is designed for data exhibiting spiked…
Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order…
The dynamic multi-mode resource-constrained project scheduling problem (DMRCPSP) is of practical importance, as it requires making real-time decisions under changing project states and resource availability. Genetic Programming (GP) has…
We study principal components regression (PCR) in an asymptotic high-dimensional regression setting, where the number of data points is proportional to the dimension. We derive exact limiting formulas for the estimation and prediction…
ReParameterization (RP) Policy Gradient Methods (PGMs) have been widely adopted for continuous control tasks in robotics and computer graphics. However, recent studies have revealed that, when applied to long-term reinforcement learning…
In order to tackle the problem of sampling from heavy tailed, high dimensional distributions via Markov Chain Monte Carlo (MCMC) methods, Yang, Latuszy\'nski, and Roberts (2022) (arXiv:2205.12112) introduces the stereographic projection as…
The offline time of the reduced basis method can be very long given a large training set of parameter samples. This usually happens when the system has more than two independent parameters. On the other hand, if the training set includes…
Hamilton-Jacobi (HJ) reachability analysis is a widely used method for ensuring the safety of robotic systems. Traditional approaches compute reachable sets by numerically solving an HJ Partial Differential Equation (PDE) over a grid, which…