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Experimental designs based on the classical D-optimal criterion minimize the volume of the linear-approximation inference regions for the parameters using local sensitivity coefficients. For nonlinear models, these designs can be unreliable…

Methodology · Statistics 2021-01-22 Hana Sulieman

A common goal throughout science and engineering is to solve optimization problems constrained by computational models. However, in many cases a high-fidelity numerical emulation of systems cannot be optimized due to code complexity and…

Numerical Analysis · Mathematics 2023-05-31 Joseph Hart , Bart van Bloemen Waanders

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…

Numerical Analysis · Mathematics 2016-12-22 John P. Hollkamp , Mihir Sen , Fabio Semperlotti

We consider optimal experimental design (OED) for nonlinear inverse problems within the Bayesian framework. Optimizing the data acquisition process for large-scale nonlinear Bayesian inverse problems is a computationally challenging task…

Numerical Analysis · Mathematics 2024-05-14 Karina Koval , Ruanui Nicholson

We study the problem of selecting $k$ experiments from a larger candidate pool, where the goal is to maximize mutual information (MI) between the selected subset and the underlying parameters. Finding the exact solution is to this…

Machine Learning · Statistics 2024-02-26 Fengyi Li , Ayoub Belhadji , Youssef Marzouk

The design of multiple experiments is commonly undertaken via suboptimal strategies, such as batch (open-loop) design that omits feedback or greedy (myopic) design that does not account for future effects. This paper introduces new…

Methodology · Statistics 2016-04-29 Xun Huan , Youssef M. Marzouk

Response surface designs are usually described as being run under complete randomization of the treatment combinations to the experimental units. In practice, however, it is often necessary or beneficial to run them under some kind of…

Methodology · Statistics 2024-10-25 Luzia A. Trinca , Steven G. Gilmour

Physical design refers to mathematical optimization of a desired objective (e.g. strong light--matter interactions, or complete quantum state transfer) subject to the governing dynamical equations, such as Maxwell's or Schrodinger's…

Optics · Physics 2023-04-03 Shai Gertler , Zeyu Kuang , Colin Christie , Owen D. Miller

We present a method for nonlinear parametric optimization based on algebraic geometry. The problem to be studied, which arises in optimal control, is to minimize a polynomial function with parameters subject to semialgebraic constraints.…

Optimization and Control · Mathematics 2007-05-23 Ioannis A. Fotiou , Philipp Rostalski , Bernd Sturmfels , Manfred Morari

We present a fully Bayesian sequential strategy for predicting the mean response surface of heteroscedastic stochastic simulation functions. Leveraging dual Gaussian processes as the surrogate model and a criterion based on empirical…

Methodology · Statistics 2025-06-12 Yuying Huang , Samuel W. K. Wong

In simulation sciences, it is desirable to capture the real-world problem features as accurately as possible. Methods popular for scientific simulations such as the finite element method (FEM) and finite volume method (FVM) use piecewise…

Numerical Analysis · Mathematics 2023-07-18 Vidhi Zala , Akil Narayan , Robert M Kirby

We propose novel optimal designs for longitudinal data for the common situation where the resources for longitudinal data collection are limited, by determining the optimal locations in time where measurements should be taken. As for all…

Methodology · Statistics 2016-04-20 Hao Ji , Hans-Georg Müller

D-Optimal designs for estimating parameters of response models are derived by maximizing the determinant of the Fisher information matrix. For non-linear models, the Fisher information matrix depends on the unknown parameter vector of…

Methodology · Statistics 2026-01-16 Suvrojit Ghosh , Koulik Khamaru , Tirthankar Dasgupta

In statistics, experimental designs are methods for making efficient experiments. E-optimal designs are the multisets of experimental conditions which minimize the maximum axis of the confidence ellipsoid of estimators. The aim of this…

Statistics Theory · Mathematics 2013-03-20 Takuma Takeuchi , Hiroto Sekido

We consider maximin and Bayesian $D$-optimal designs for nonlinear regression models. The maximin criterion requires the specification of a region for the nonlinear parameters in the model, while the Bayesian optimality criterion assumes…

Statistics Theory · Mathematics 2009-09-29 Dietrich Braess , Holger Dette

A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation. The radial direction and the angular direction of the…

Numerical Analysis · Mathematics 2017-12-27 Yoshihito Kazashi

Bayesian experimental design is a technique that allows to efficiently select measurements to characterize a physical system by maximizing the expected information gain. Recent developments in deep neural networks and normalizing flows…

Quantum Physics · Physics 2023-06-27 Leopoldo Sarra , Florian Marquardt

Nuclear Reaction Analysis with ${}^{3}$He holds the promise to measure Deuterium depth profiles up to large depths. However, the extraction of the depth profile from the measured data is an ill-posed inversion problem. Here we demonstrate…

Accelerator Physics · Physics 2009-11-13 U. von Toussaint , T. Schwarz-Selinger , S. Gori

Generalized linear models (GLMs) have been used widely for modelling the mean response both for discrete and continuous random variables with an emphasis on categorical response. Recently Yang, Mandal and Majumdar (2013) considered full…

Statistics Theory · Mathematics 2013-05-06 Jie Yang , Abhyuday Mandal

Existing works on "black-box" model interpretation use local-linear approximations to explain the predictions made for each data instance in terms of the importance assigned to the different features for arriving at the prediction. These…

Machine Learning · Computer Science 2019-08-28 Kartik Ahuja , William Zame , Mihaela van der Schaar