Fig. 8: Schematic information-flow chart and environmental updates (chronologically following thick brown arrows) of ANN-based bead-specific decentralized decision-making implementing a system-level policy that controls the locomotion of an N-bead microswimmer.
The detailing ANN architecture (inspired by ref. 58) emphasizes an ANN's perception, \({{{{{\bf{p}}}}}}_{{i}_{\nu }}\), of bead i's local neighborhood, ν = −1, 0, 1 (see the “Artificial neural network-based decentralized controllers” subsection of the “Methods”), followed by an embedding, \({{{{{\bf{p}}}}}}_{{i}_{\nu }}\to {\varepsilon }_{{i}_{\nu }}\), and concatenation layer in the sensory module that results in a bead-specific context matrix, \({{{{{\mathcal{C}}}}}}_{i}=({\varepsilon }_{{i}_{-1}},{\varepsilon }_{{i}_{0}},{\varepsilon }_{{i}_{+1}})\), based on which the policy module proposes an action, ai, comprising the proposed force, ϕi, and the cell-state update, Δsi. This step is performed by every bead independently at every successive time step, tk, to induce an update of the state of the microswimmer at times tk + 1 by considering the regularized forces, ϕi→Fi, in the equations of motion of the N-bead hydrodynamic environment, xi(tk)→xi(tk + 1), and performing a noisy (c.f., red wiggly arrow) cell-state update.
