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.

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.

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.

Robot swarms have, to date, been constructed from artificial materials. Motile biological constructs have been created from muscle cells grown on precisely shaped scaffolds. However, the exploitation of emergent self-organization and functional plasticity into a self-directed living machine has remained a major challenge. We report here a method for generation of in vitro biological robots from frog (Xenopus laevis) cells. These xenobots exhibit coordinated locomotion via cilia present on their surface. These cilia arise through normal tissue patterning and do not require complicated construction methods or genomic editing, making production amenable to high-throughput projects. The biological robots arise by cellular self-organization and do not require scaffolds or microprinting; the amphibian cells are highly amenable to surgical, genetic, chemical, and optical stimulation during the self-assembly process. We show that the xenobots can navigate aqueous environments in diverse ways, heal after damage, and show emergent group behaviors. We constructed a computational model to predict useful collective behaviors that can be elicited from a xenobot swarm. In addition, we provide proof of principle for a writable molecular memory using a photoconvertible protein that can record exposure to a specific wavelength of light. Together, these results introduce a platform that can be used to study many aspects of self-assembly, swarm behavior, and synthetic bioengineering, as well as provide versatile, soft-body living machines for numerous practical applications in biomedicine and the environment.