Certification of Autoencoder-based Models for Dynamical Systems

Deep learning models have emerged as powerful tools for modeling complex dynamical systems, offering data-driven alternatives to traditional identification techniques. Among them, autoencoder-based architectures have gained popularity due to their ability to extract low-dimensional latent representations starting from high-dimensional information. However, a major challenge persists: assessing the reliability of these models, especially in control tasks where prediction errors can have critical consequences. In this work, we propose an optimization-based certification approach to quantify the worst-case prediction error of ReLU-activated autoencoder models of dynamical systems. By formulating a targeted Mixed-Integer Quadratic Programming, our approach identifies data sequences that maximize the deviation between the model’s predicted output and the true system response.