Related papers: Global sensitivity analysis for optimization of th…

Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models. A well-known Achilles' heel of this approach is its computational cost which often renders it unfeasible in practice. An…

High-order tensor methods that employ Taylor-based local models (of degree $p\ge 3$) within adaptive regularization frameworks have been recently proposed for both convex and nonconvex optimization problems. They have been shown to have…

We introduce the concept of {\it generalized reducibility}, which provides a flexible framework for analyzing the long-time behavior of solutions to quadratic quantum Hamiltonians. As an application of this notion, for many prescribed…

We present a general, systematic, and efficient method for decomposing any given exponential operator of bosonic mode operators, describing an arbitrary multi-mode Hamiltonian evolution, into a set of universal unitary gates. Although our…

One of the key applications for quantum computers will be the simulation of other quantum systems that arise in chemistry, materials science, etc, in order to accelerate the process of discovery. It is important to ask: Can this be achieved…

We use sensitivity analysis to design bounding-focused discretization (cutting-surface) methods for the global optimization of nonconvex semi-infinite programs (SIPs). We begin by formulating the optimal bounding-focused discretization of…

In global sensitivity analysis, the well known Sobol' sensitivity indices aim to quantify how the variance in the output of a mathematical model can be apportioned to the different variances of its input random variables. These indices are…

Scatterometry is a fast, indirect and nondestructive optical method for the quality control in the production of lithography masks. Geometry parameters of line gratings are obtained from diffracted light intensities by solving an inverse…

The Doyle-Fuller-Newman model is arguably the most ubiquitous electrochemical model in lithium-ion battery research. Since it is a highly nonlinear model, its input-output relations are still poorly understood. Researchers therefore often…

We derive a general formula of the reduced fidelity susceptibility when the reduced density matrix is $2\times2$ block-diagonal. By using this result and the continuous unitary transformations, we study finite-size scaling of the reduced…

We establish sensitivity analysis on the sphere. We present formulas that allow us to decompose a function $f\colon \mathbb S^d\rightarrow \mathbb R$ into a sum of terms $f_{\boldsymbol u,\boldsymbol \xi}$. The index $\boldsymbol u$ is a…

Suppressing the Trotter error in dynamical quantum simulation typically requires running deeper circuits, posing a great challenge for noisy near-term quantum devices. Studies have shown that the empirical error is usually much smaller than…

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

We present two analytical formulae for estimating the sensitivity -- namely, the gradient or Jacobian -- at given realizations of an arbitrary-dimensional random vector with respect to its distributional parameters. The first formula…

We propose personalized Tucker decomposition (perTucker) to address the limitations of traditional tensor decomposition methods in capturing heterogeneity across different datasets. perTucker decomposes tensor data into shared global…

Black-box global optimization aims at minimizing an objective function whose analytical form is not known. To do so, many state-of-the-art methods rely on sampling-based strategies, where sampling distributions are built in an iterative…

Decomposing complex time series into trend, seasonality, and remainder components is an important task to facilitate time series anomaly detection and forecasting. Although numerous methods have been proposed, there are still many time…

There exist many methods for sensitivity analysis readily available to the practitioner. While each seeks to help the modeler answer the same general question -- How do sources of uncertainty or changes in the model inputs relate to…

Problem decomposition plays a vital role when applying cooperative coevolution (CC) to large scale global optimization problems. However, most learning-based decomposition algorithms either only apply to additively separable problems or…

Global sensitivity analysis (GSA) is a recommended step in the use of computer simulation models. GSA quantifies the relative importance of model inputs on outputs (Factor Ranking), identifies inputs that could be fixed, thus simplifying…