دانلود رایگان مقاله مدل سازی جایگزین برای طراحی صنعتی با GTApprox

1. Introduction

Approximation problems (also known as regression problems) arise quite often in industrial design, and solutions of such problems are conventionally referred to as surrogate models [1]. The most common application of surrogate modeling in engineering is in connection to engineering optimization [2]. Indeed, on the one hand, design optimization plays a central role in the industrial design process; on the other hand, a single optimization step typically requires the optimizer to create or refresh a model of the response function whose optimum is sought, to be able to come up with a reasonable next design candidate. The surrogate models used in optimization range from simple local linear regression employed in the basic gradient-based optimization [3] to complex global models employed in the so-called Surrogate-Based Optimization (SBO) [4]. Aside from optimization, surrogate modeling is used in dimension reduction [5,6], sensitivity analysis [7–10], and for visualization of response functions. Mathematically, the approximation problem can generally be described as follows. We assume that we are given a finite sample of pairs (xn, yn)N n=1 (the “training data”), where xn ∈ Rdin , yn ∈ Rdout . These pairs represent sampled inputs and outputs of an unknown response function y = f(x). Our goal is to construct a function (a surrogate model) f : Rdin → Rdout which should be as close as possible to the true function f.

6. Conclusion

We have described GTApprox — a new tool for medium-scale surrogate modeling in industrial design – and its novel features that make it convenient for surrogate modeling, especially for applications in engineering and for use by non-experts in data analysis. The tool contains some entirely new approximation algorithms (e.g., Tensor Approximation with arbitrary factors and incomplete Tensor Approximation) as well as novel model selection metaalgorithms. In addition, GTApprox supports multiple novel “nontechnical” options and features allowing the user to more easily express the desired properties of the model or some domainspecific properties of a data. When compared to scikit-learn algorithms in the default mode on a collection of test problems, GTApprox shows a superior accuracy. This is achieved at the cost of longer training times that, nevertheless, remain moderate for medium-scale problems. We have also briefly described a few applications of GTApprox to real engineering problems where a crucial role was played by the tool’s distinctive elements (the new algorithms MoA and iTA, automated model selection, built-in availability of gradients).