“…The training of random feature map networks only requires linear least-square regression and it was proven rigorously that random feature maps enjoy the so called universal approximation property which states that they can approximate any continuous function arbitrarily close (Park and Sandberg, 1991;Cybenko, 1989;Barron, 1993). The framework of random feature maps was extended to include internal dynamics in so called echo-state networks and reservoir computers with remarkable success in forecasting dynamical systems (Maass et al, 2002;Jaeger, 2002;Jaeger and Haas, 2004;Pathak et al, 2018a;Algar et al, 2019;Nadiga, 2020;Bollt, 2021;Gauthier et al, 2021;Platt et al, 2021).…”