GTApprox: surrogate modeling for industrial design

We describe GTApprox -- a new tool for medium-scale surrogate modeling in industrial design. Compared to existing software, GTApprox brings several innovations: a few novel approximation algorithms, several advanced methods of automated model selection, novel options in the form of hints. We demonstrate the efficiency of GTApprox on a large collection of test problems. In addition, we describe several applications of GTApprox to real engineering problems. Keywords: 1. Introduction approximation, surrogate model, surrogate-based optimization 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. Preprint submitted to February 23, 2018 Mathematically, the approximation problem can generally be described as follows. A great variety of surrogate modeling methods exist, with different assumptions on the underlying response functions, data sets, and model structure [11].