2023, Bianconi, Ginestra, Arenas, Alex, Biamonte, Jacob, Carr, Lincoln D, Kahng, Byungnam, Kertesz, Janos, Kurths, Jürgen, Lü, Linyuan, Masoller, Cristina, Motter, Adilson E, Perc, Matjaž, Radicchi, Filippo, Ramaswamy, Ramakrishna, Rodrigues, Francisco A, Sales-Pardo, Marta, San Miguel, Maxi, Thurner, Stefan, Yasseri, Taha

The 2021 Nobel Prize in Physics recognized the fundamental role of complex systems in the natural sciences. In order to celebrate this milestone, this editorial presents the point of view of the editorial board of JPhys Complexity on the achievements, challenges, and future prospects of the field. To distinguish the voice and the opinion of each editor, this editorial consists of a series of editor perspectives and reflections on few selected themes. A comprehensive and multi-faceted view of the field of complexity science emerges. We hope and trust that this open discussion will be of inspiration for future research on complex systems.

2021, Gelbrecht, Maximilian, Boers, Niklas, Kurths, Jürgen

When predicting complex systems one typically relies on differential equation which can often be incomplete, missing unknown influences or higher order effects. By augmenting the equations with artificial neural networks we can compensate these deficiencies. We show that this can be used to predict paradigmatic, high-dimensional chaotic partial differential equations even when only short and incomplete datasets are available. The forecast horizon for these high dimensional systems is about an order of magnitude larger than the length of the training data.