Evolution must explain both its ability to produce beneficial innovations as well as preserve organisms’ existing functional adaptedness to their environment. A proposed mechanism which resolves this tension is the concept of neutral networks, wherein mutations are not strictly beneficial or deleterious but neutral in their effect on organisms’ adaptedness. Neutral networks have been shown to be both prevalent and vast at multiple levels of biological organization. Additionally, there is much philosophical debate regarding how information flows between and across these levels of organization in reality. However, how to pragmatically engineer systems with multiscale structure to harness the inherent robustness that neutral networks confer remains largely unexplored. Here we show that, in hierarchical neural cellular automata (HNCA), various inter-scale connectivity architectures support mutational robustness and evolvability through the formation of neutral networks, wherein similar functional outcomes (e.g., morphogenesis, homeostasis) are achievable through diverse pathways of multiscale interactions. These findings can help inform the way we engineer artificial multiscale systems, e.g. hierarchical arrangements of robots. Operationalizing these insights may offer new ways of designing and engineering intelligent, robust, and adaptive machines. Additionally, the connection structures we explore have philsophical implications which may inform discussions of causal emergence in complex systems.

Using soft materials to build robots is becoming increasingly popular as the importance of morphological complexity in robot design becomes apparent. Additionally, physics simulators which are differentiable are increasingly being used to optimize robot morphologies and controllers over e.g. evolutionary algorithms due to the computational efficiency of gradient descent. One of the most commonly used methods to simulate soft materials is the Material Point Method (MPM), and soft roboticists have implemented the MPM in differentiable robotics simulations and successfully transferred their optimized designs to the real world, validating this approach for real-world soft robot design. However, choosing parameters for MPM that render it stable in a differentiable simulator are non-obvious. For this reason, here we introduce for the first time a set of best practices for employing the MPM to design and optimize soft robots using differentiable physics engines. We perform grid searches over many of the parameters involved in MPM to determine simulation stability ranges and performant parameter choices for a displacement task. This will allow newcomers to MPM simulation to rapidly iterate to find parameters for their application.