Title: Simulation and time series analysis of responsive active Brownian particles (rABPs) with memory

Abstract: To realise the goals of active matter at the micro- and nano-scale, the next generation of microrobots must be capable of autonomously sensing and responding to their environment to carry out pre-programmed tasks. Memory effects are proposed to have a significant effect on the dynamics of responsive robotic systems, drawing parallels to strategies used in nature across all length-scales. Inspired by the integral feedback control mechanism by which E.coli are proposed to sense their environment, we develop a numerical responsive active Brownian particle (rABP) model in which the rABPs continuously react to changes in the physical parameters dictated by their local environment. The resulting generated time series are then used to classify and characterise their response, leading to the identification of conditional heteroscedasticity in their physics. We then train recurrent neural networks (RNNs) capable of quantitatively describing the responsiveness of rABPs using their 2-D trajectories. We believe that our proposed strategy to determine the parameters governing the dynamics of rABPs can be applied to guide the design of microrobots with physical intelligence encoded during their fabrication.