Exploring Digital Twins of Nonlinear Systems through Meta-Modeling with Echo State Networks

Abstract

monitoring, and control rely on precise dynamic models that can capture the inherent nonlinearities of chemical systems. However, rigorous modeling of complex industrial processes can be computationally demanding. Meta modeling using machine learning methodologies offers a viable approach to generate computationally efficient surrogate representations. Specifically, Echo State Networks (ESNs) are a promising neural network approach for meta-modeling nonlinear dynamical systems. ESNs simplify training through fixed input weights while they focus learning on output weights. This study explores the development of ESN-based digital twins for a nonlinear dynamic process. An ESN is employed to construct a meta-model of a simulated continuously stirred tank reactor with biochemical kinetic. The network was trained on input-output data obtained from the simulation of an ordinary differential equation system, and the performance was evaluated both in-sample and out-of-sample. The results indicate that the ESN meta-model can successfully approximate the underlying dynamics, accurately capturing temporal evolution. A closed-loop digital twin deployment using the ESN surrogate also showed reliable behavior. This work presents initial steps toward developing digital twins of chemical processes using ESN-driven meta-modeling. The findings suggest ESNs can effectively generate computationally efficient surrogate representations of nonlinear dynamical systems. Such digital twins hold promise for online process monitoring and optimized control of industrial plants.

Keywords

• echo state networks
• dynamic systems
• digital twins