No abstract

Complex nonlinear dynamics arise in many fields of science and engineering, but uncovering the underlying differential equations directly from observations poses a challenging task. The ability to symbolically model complex networked systems is key to understanding them, an open problem in many disciplines. Here we introduce for the first time a method that can automatically generate symbolic equations for a nonlinear coupled dynamical system directly from time series data. This method is applicable to any system that can be described using sets of ordinary nonlinear differential equations, and assumes that the (possibly noisy) time series of all variables are observable. Previous automated symbolic modeling approaches of coupled physical systems produced linear models or required a nonlinear model to be provided manually. The advance presented here is made possible by allowing the method to model each (possibly coupled) variable separately, intelligently perturbing and destabilizing the system to extract its less observable characteristics, and automatically simplifying the equations during modeling. We demonstrate this method on four simulated and two real systems spanning mechanics, ecology, and systems biology. Unlike numerical models, symbolic models have explanatory value, suggesting that automated ''reverse engineering'' approaches for model-free symbolic nonlinear system identification may play an increasing role in our ability to understand progressively more complex systems in the future.coevolution ͉ modeling ͉ symbolic identification M any branches of science and engineering represent systems that change over time as sets of differential equations, in which each equation describes the rate of change of a single variable as a function of the state of other variables. The structures of these equations are usually determined by hand from first principles, and in some cases regression methods (1-3) are used to identify the parameters of these equations. Nonparametric methods that assume linearity (4) or produce numerical models (5, 6) fail to reveal the full internal structure of complex systems. A key challenge, however, is to uncover the governing equations automatically merely by perturbing and then observing the system in intelligent ways, just as a scientist would do in the presence of an experimental system. Obstacles to achieving this lay in the lack of efficient methods to search the space of symbolic equations and in assuming that precollected data are supplied to the modeling process.Determining the symbolic structure of the governing dynamics of an unknown system is especially challenging when rare yet informative behavior can go unnoticed unless the system is perturbed in very specific ways. Coarse parameter sweeps or random samplings are unlikely to catch these subtleties, and so passive machine learning methods that rely on offline analysis of precollected data may be ineffective. Instead, active learning (7) processes that are able to generate new perturbations or seek out informative part...

Animals sustain the ability to operate after injury by creating qualitatively different compensatory behaviors. Although such robustness would be desirable in engineered systems, most machines fail in the face of unexpected damage. We describe a robot that can recover from such change autonomously, through continuous self-modeling. A four-legged machine uses actuation-sensation relationships to indirectly infer its own structure, and it then uses this self-model to generate forward locomotion. When a leg part is removed, it adapts the self-models, leading to the generation of alternative gaits. This concept may help develop more robust machines and shed light on self-modeling in animals.

Machines powered by artificial intelligence increasingly mediate our social, cultural, economic and political interactions. Understanding the behaviour of artificial intelligence systems is essential to our ability to control their actions, reap their benefits and minimize their harms. Here we argue that this necessitates a broad scientific research agenda to study machine behaviour that incorporates and expands upon the discipline of computer science and includes insights from across the sciences. We first outline a set of questions that are fundamental to this emerging field and then explore the technical, legal and institutional constraints on the study of machine behaviour.

Living systems are more robust, diverse, complex, and supportive of human life than any technology yet created. However, our ability to create novel lifeforms is currently limited to varying existing organisms or bioengineering organoids in vitro. Here we show a scalable pipeline for creating functional novel lifeforms: AI methods automatically design diverse candidate lifeforms in silico to perform some desired function, and transferable designs are then created using a cell-based construction toolkit to realize living systems with the predicted behaviors. Although some steps in this pipeline still require manual intervention, complete automation in future would pave the way to designing and deploying unique, bespoke living systems for a wide range of functions.