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Data-Driven Model Reduction, Scientific Frontiers, and Applications

Ishan Bajaj, Artie McFerrin Department of Chemical Engineering
Computational Experience with Different Reduced Models for Derivative-Free Optimization


  • Ishan Bajaj
  • M. M. Faruque Hasan


Many problems in engineering, computational biology, chemistry, medicine, and operations research are black-box with unknown algebraic form of the underlying model. Black-box optimization problems are becoming widespread due to development of high-fidelity simulations such as computational fluid dynamics (CFD). This has led to the growing importance of derivative-free optimization (DFO) methods. Typically, model-based methods proceed by performing simulations, fitting an inexpensive reduced model to approximate the original function and optimizing the reduced model. This procedure is repeated in an iterative framework until some convergence criteria is satisfied. Since DFO methods generally deal with computationally expensive simulations, it is critical to obtain optima using few function evaluations. Choosing an appropriate reduced model and derivative-free framework are key to the convergence of a DFO method. In this work, we present a derivative-free framework: UNIPOPT (UNIvariate Projection-based OPTimization) based on projecting all the samples onto a univariate space defined by summation of the decision variables. UNIPOPT also allows for incorporating different reduced models for approximation. Quadratic, polynomial, radial basis function, kriging, artificial neural networks are generally used in the literature for approximation. It has been established in the literature that quadratic, radial basis function and kriging satisfy the fully-linear property. This property is needed to establish the convergence of an algorithm to a stationary point. In this presentation, the performance of UNIPOPT incorporating different reduced models will be shown on a large test suite of black-box problems.