Piecewise Affine

Piecewise affine (PWA) functions, which are composed of multiple affine segments, are increasingly used to model complex systems exhibiting abrupt changes in behavior. Current research focuses on efficient algorithms for approximating and learning PWA functions, including iterative methods, tailored neural network architectures (like max-out networks), and specialized solvers for optimization problems involving PWA systems. These advancements are impacting diverse fields, from improving the efficiency and robustness of neural network training and control systems for robotics to enabling more accurate modeling of hybrid dynamical systems and enhancing the interpretability of neural network models. The development of efficient and robust methods for handling PWA systems is crucial for advancing numerous applications across science and engineering.