Guaranteed Error-bounded Surrogate Framework for Solving Process Simulation Problems

Abstract

Process simulation problems often involve systems of nonlinear and nonconvex equations and may run into convergence issues due to the existence of recycle loops within such models. To that end, surrogate models have gained significant attention as an alternative to high-fidelity models as they significantly reduce the computational burden. However, these models do not always provide a guarantee on the prediction accuracy over the domain of interest. To address this issue, we strike a balance between computational complexity by developing a data-driven branch and prune-based framework that progressively leads to a guaranteed solution to the original system of equations. Specifically, we utilize interval arithmetic techniques to exploit Hessian information about the model of interest. Along with checking whether a solution can exist in the domain under consideration, we generate error-bounded convex hull surrogates using the sampled data and Hessian information. When integrated in a branch and prune framework, the branching leads to the domain under consideration becoming smaller, thereby reducing the quantified prediction error of the surrogate, ultimately yielding a solution to the system of equations. In this manner, we overcome the convergence issues that are faced by many simulation packages. We demonstrate the applicability of our framework through several case studies. We first utilize a set of test problems from literature. For each of these test systems, we can find a valid solution. We then demonstrate the efficacy of our framework on real-world process simulation problems.