A Framework for Data-Driven Simulation of Electrical Circuits Based on Discrete-Continuous Optimization

In this work, we present and investigate a new framework for the data-driven simulation of electrical circuits based on discrete-continuous optimization. For such an end, we provide a formal derivation of the data-driven discrete forward-dynamics problem and for its recursive solution, we adopt a strategy relying on an alternating direction method. Even when we focus primarily on capacitive elements (i.e., the relation between charges and voltages in the capacitive elements is completely replaced by an experimental and probably incomplete data set) and circuits of extremely simple topology, the approach has great potential for its generalization. Finally, we study several examples of increasing complexity and show through their analysis, the very promising features of this novel approach. In particular, we investigate the precision of the resulting numerical method, the ability to deal with nonlinearity contained in the data sets, the ability to handle data sets of varying size and the robustness with respect to noisy data. Where the last two, represent key features to establish data-driven digital twins.