Fish in schooling formations navigate complex flow fields replete with mechanical energy in the vortex wakes of their companions. Their schooling behavior has been associated with evolutionary advantages including energy savings, yet the underlying physical mechanisms remain unknown. We show that fish can improve their sustained propulsive efficiency by placing themselves in appropriate locations in the wake of other swimmers and intercepting judiciously their shed vortices. This swimming strategy leads to collective energy savings and is revealed through a combination of high-fidelity flow simulations with a deep reinforcement learning (RL) algorithm. The RL algorithm relies on a policy defined by deep, recurrent neural nets, with long-short-term memory cells, that are essential for capturing the unsteadiness of the two-way interactions between the fish and the vortical flow field. Surprisingly, we find that swimming in-line with a leader is not associated with energetic benefits for the follower. Instead, "smart swimmer(s)" place themselves at off-center positions, with respect to the axis of the leader(s) and deform their body to synchronize with the momentum of the oncoming vortices, thus enhancing their swimming efficiency at no cost to the leader(s). The results confirm that fish may harvest energy deposited in vortices and support the conjecture that swimming in formation is energetically advantageous. Moreover, this study demonstrates that deep RL can produce navigation algorithms for complex unsteady and vortical flow fields, with promising implications for energy savings in autonomous robotic swarms.

https://www.pnas.org/content/pnas/115/23/5849.full.pdf

Efficient collective swimming by harnessing vortices through deep reinforcement learning.

The availability of large datasets has boosted the application of machine learning in many fields and is now starting to shape active-matter research as well. Machine learning techniques have already been successfully applied to active-matter data—for example, deep neural networks to analyse images and track objects, and recurrent nets and random forests to analyse time series. Yet machine learning can also help to disentangle the complexity of biological active matter, helping, for example, to establish a relation between genetic code and emergent bacterial behaviour, to find navigation strategies in complex environments, and to map physical cues to animal behaviours. In this Review, we highlight the current state of the art in the application of machine learning to active matter and discuss opportunities and challenges that are emerging. We also emphasize how active matter and machine learning can work together for mutual benefit. This Review surveys machine learning techniques that are currently developed for a range of research topics in biological and artificial active matter and also discusses challenges and exciting opportunities. This research direction promises to help disentangle the complexity of active matter and gain fundamental insights for instance in collective behaviour of systems at many length scales from colonies of bacteria to animal flocks.

https://www.nature.com/articles/s42256-020-0146-9.pdf?proof=t

Machine learning for active matter

Two deep learning (DL) models addressing the super-resolution (SR) reconstruction of turbulent flows from low-resolution coarse flow field data are developed. One is the static convolutional neural network (SCNN), and the other is the novel multiple temporal paths convolutional neural network (MTPC). The SCNN model takes instantaneous snapshots as an input, while the MTPC model takes a time series of velocity fields as an input, and it includes spatial and temporal information simultaneously. Three temporal paths are designed in the MTPC to fully capture features in different time ranges. A weight path is added to generate pixel-level weight maps of each temporal path. These models were first applied to forced isotropic turbulence. The corresponding high-resolution flow fields were reconstructed with high accuracy. The MTPC seems to be able to reproduce many important features as well, such as kinetic energy spectra and the joint probability density function of the second and third invariants of the velocity gradient tensor. As a further evaluation, the SR reconstruction of anisotropic channel flow with the DL models was performed. The SCNN and MTPC remarkably improve the spatial resolution in various wall regions and potentially grasp all the anisotropic turbulent properties. It is also shown that the MTPC supplements more under-resolved details than the SCNN. The success is attributed to the fact that the MTPC can extract extra temporal information from consecutive fluid fields. The present work may contribute to the development of the subgrid-scale model in computational fluid dynamics and enrich the application of SR technology in fluid mechanics.

Deep learning methods for super-resolution reconstruction of turbulent flows

Soft slender structures are ubiquitous in natural and artificial systems, in active and passive settings and across scales, from polymers and flagella, to snakes and space tethers. In this paper, we demonstrate the use of a simple and practical numerical implementation based on the Cosserat rod model to simulate the dynamics of filaments that can bend, twist, stretch and shear while interacting with complex environments via muscular activity, surface contact, friction and hydrodynamics. We validate our simulations by solving a number of forward problems involving the mechanics of passive filaments and comparing them with known analytical results, and extend them to study instabilities in stretched and twisted filaments that form solenoidal and plectonemic structures. We then study active filaments such as snakes and other slender organisms by solving inverse problems to identify optimal gaits for limbless locomotion on solid surfaces and in bulk liquids.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.171628

Forward and inverse problems in the mechanics of soft filaments

The coordinated motion by multiple swimmers is a fundamental component in fish schooling. The flow field induced by the motion of each self-propelled swimmer implies non-linear hydrodynamic interactions among the members of a group. How do swimmers compensate for such hydrodynamic interactions in coordinated patterns? We provide an answer to this riddle though simulations of two, self-propelled, fish-like bodies that employ a learning algorithm to synchronise their swimming patterns. We distinguish between learned motion patterns and the commonly used a-priori specified movements, that are imposed on the swimmers without feedback from their hydrodynamic interactions. First, we demonstrate that two rigid bodies executing pre-specified motions, with an alternating leader and follower, can result in substantial drag-reduction and intermittent thrust generation. In turn, we study two self-propelled swimmers arranged in a leader-follower configuration, with a-priori specified body-deformations. These two self-propelled swimmers do not sustain their tandem configuration. The follower experiences either an increase or decrease in swimming speed, depending on the initial conditions, while the swimming of the leader remains largely unaffected. This indicates that a-priori specified patterns are not sufficient to sustain synchronised swimming. We then examine a tandem of swimmers where the leader has a steady gait and the follower learns to synchronize its motion, to overcome the forces induced by the leader's vortex wake. The follower employs reinforcement learning to adapt its swimming-kinematics so as to minimize its lateral deviations from the leader's path. Swimming in such a sustained synchronised tandem yields up to [Formula: see text] reduction in energy expenditure for the follower, in addition to a [Formula: see text] increase in its swimming-efficiency. The present results show that two self-propelled swimmers can be synchronised by adapting their motion patterns to compensate for flow-structure interactions. Moreover, swimmers can exploit the vortical structures of their flow field so that synchronised swimming is energetically beneficial.

https://iopscience.iop.org/article/10.1088/1748-3190/aa6311/pdf

Synchronisation through learning for two self-propelled swimmers.

Schooling, an archetype of collective behavior, emerges from the interactions of fish responding to visual and other informative cues mediated by their aqueous environment. In this context, a fundamental and largely unexplored question concerns the role of hydrodynamics. Here, we investigate schooling by modeling swimmers as vortex dipoles whose interactions are governed by the Biot-Savart law. When we enhance these dipoles with behavioral rules from classical agent based models we find that they do not lead robustly to schooling due to flow mediated interactions. In turn, we present dipole swimmers equipped with adaptive decision-making that learn, through a reinforcement learning algorithm, to adjust their gaits in response to non-linearly varying hydrodynamic loads. The dipoles maintain their relative position within a formation by adapting their strength and school in a variety of prescribed geometrical arrangements. Furthermore, we identify schooling patterns that minimize the individual and the collective swimming effort, through an evolutionary optimization. The present work suggests that the adaptive response of individual swimmers to flow-mediated interactions is critical in fish schooling.

Learning to school in the presence of hydrodynamic interactions

/pdf/optimal-schooling-formations-using-a-potential-flow-model-9d69l05r1z.pdf

Alexia de Brauer

Papers

Learning to school in the presence of hydrodynamic interactions

Optimal schooling formations using a potential flow model