Model predictive control (MPC), widely used for real-time control of complex dynamical systems, operates by repeatedly solving an optimization problem over a receding time horizon. Its success hinges on dynamical models that are accurate yet efficient enough for rapid online computation. Frequently, the governing models of complex systems are either unknown or computationally inefficient, forcing MPC to rely on data-driven surrogate models. Echo state networks (ESNs), a class of recurrent neural networks trained through computationally efficient ridge regression, are well-suited for this role and have demonstrated strong forecasting capabilities in chaotic dynamical systems. Their architecture naturally supports rapid training and flexible adaptation to varying control inputs. In this work, we demonstrate that ESNs serve as effective data-driven surrogates for system dynamics under diverse control scenarios, outperforming competing architectures such as long short-term memory (LSTM) networks. On challenging control benchmarks, including the Lorenz system with control and fluid flow past a cylinder, MPC with ESN surrogates consistently achieves the control objective, whereas the next-best considered architecture, LSTM-based MPC, frequently fails. Even in cases where LSTM-based MPC succeeds, ESN-based MPC reduces average control cost by up to 10% and decreases variability by as much as 85%. Beyond performance, ESNs are significantly more sample-efficient and train over an order of magnitude faster than LSTMs. These results establish ESNs as accurate, efficient architectures for scalable data-driven MPC in complex systems with limited training data and unknown dynamics.

Topological data analysis (TDA) has emerged as one of the most promising techniques to reconstruct the unknown shapes of high-dimensional spaces from observed data samples. TDA, thus, yields key shape descriptors in the form of persistent topological features that can be used for any supervised or unsupervised learning task, including multi-way classification. Sparse sampling, on the other hand, provides a highly efficient technique to reconstruct signals in the spatial-temporal domain from just a few carefully-chosen samples. Here, we present a new method, referred to as the Sparse-TDA algorithm, that combines favorable aspects of the two techniques. This combination is realized by selecting an optimal set of sparse pixel samples from the persistent features generated by a vector-based TDA algorithm. These sparse samples are selected from a low-rank matrix representation of persistent features using QR pivoting. We show that the Sparse-TDA method demonstrates promising performance on three benchmark problems related to human posture recognition and image texture classification.