Related papers: A fast surrogate cross validation algorithm for me…
Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…
Surrogate models for computational simulations are input-output approximations that allow computationally intensive analyses, such as uncertainty propagation and inference, to be performed efficiently. When a simulation output does not…
The performance of most evolutionary metaheuristic algorithms relays on various operatives. One of them is the crossover operator, which is divided into two types: application dependent and application independent crossover operators. These…
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…
This paper describes a simple, but effective sampling method for optimizing and learning a discrete approximation (or surrogate) of a multi-dimensional function along a one-dimensional line segment of interest. The method does not rely on…
Algorithmic verification of realistic systems to satisfy safety and other temporal requirements has suffered from poor scalability of the employed formal approaches. To design systems with rigorous guarantees, many approaches still rely on…
Surrogate models are widely used in mechanical design and manufacturing process optimization, where high-fidelity computational models may be unavailable or prohibitively expensive. Their effectiveness, however, is often limited by data…
Cross-validation (CV) is one of the most popular tools for assessing and selecting predictive models. However, standard CV suffers from high computational cost when the number of folds is large. Recently, under the empirical risk…
A surrogate model approximates the outputs of a solver of Partial Differential Equations (PDEs) with a low computational cost. In this article, we propose a method to build learning-based surrogates in the context of parameterized PDEs,…
Verifying the correctness of Bayesian computation is challenging. This is especially true for complex models that are common in practice, as these require sophisticated model implementations and algorithms. In this paper we introduce…
We present an approximation scheme for support vector machine models that use an RBF kernel. A second-order Maclaurin series approximation is used for exponentials of inner products between support vectors and test instances. The…
High-speed flight vehicles, which travel much faster than the speed of sound, are crucial for national defense and space exploration. However, accurately predicting their behavior under numerous, varied flight conditions is a challenge and…
We describe an efficient method for the approximation of functions using radial basis functions (RBFs), and extend this to a solver for boundary value problems on irregular domains. The method is based on RBFs with centers on a regular grid…
The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…
The tritium breeding ratio (TBR) is an essential quantity for the design of modern and next-generation D-T fueled nuclear fusion reactors. Representing the ratio between tritium fuel generated in breeding blankets and fuel consumed during…
Meshfree radial basis function (RBF) methods are popular tools used to numerically solve partial differential equations (PDEs). They take advantage of being flexible with respect to geometry, easy to implement in higher dimensions, and can…
Approximation of scattered geometric data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This method is useful for…
We introduce a novel procedure for obtaining cross-validated predictive estimates for Bayesian hierarchical regression models (BHRMs). Bayesian hierarchical models are popular for their ability to model complex dependence structures and…
Scattered data fitting is a frequently encountered problem for reconstructing an unknown function from given scattered data. Radial basis function (RBF) methods have proven to be highly useful to deal with this problem. We describe two…
[Abridged] We propose a solution to the problem of quickly and accurately predicting gravitational waveforms within any given physical model. The method is relevant for both real-time applications and in more traditional scenarios where the…