Approximation of Large Stiff Acausal Models

Abstract

Simulations drive mission-critical decision making in many fields, but are prone to computational intractability, which severely limits an engineer’s productivity whilst designing practical systems. In particular, simulating systems with widely separated timescales are prone to computational problem called stiffness. In this thesis, we aim to alleviate these issues by the use of approximate models called surrogates, which match the full system to high fidelity whilst being inexpensive to simulate. In this thesis, we introduce a general data-driven method to generate surrogates, called the Continuous-Time Echo State Networks (CTESN), that can capture multiple widely separated time-scales which is easy to automate. We comment on its implementa- tion and then propose an active learning scheme for adaptively choosing training points. We then present several examples and case studies of stiff high-dimensional acausal systems from diverse domains heating, ventilation and cooling (HVAC) sys- tems, quantitative systems pharmacology models and electrical circuits, where we accelerate their simulation by multiple orders of magnitude. We then deploy these surrogates in the context of many downstream tasks, such as global optimization, predicting non-linear system response, and global sensitivity analysis, accelerating all tasks by two orders of magnitude. Lastly, we also show that our surrogate modeling architecture can also be used as a universal adaptive filter.