Document Type


Date of Award


Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Yuan N. Young

Second Advisor

On Shun Pak

Third Advisor

Jonathan H.C. Luke

Fourth Advisor

Michael Siegel

Fifth Advisor

David Shirokoff


This dissertation summarizes computational results from applying reinforcement learning and deep neural network to the designs of artificial microswimmers in the inertialess regime, where the viscous dissipation in the surrounding fluid environment dominates and the swimmer’s inertia is completely negligible. In particular, works in this dissertation consist of four interrelated studies of the design of microswimmers for different tasks: (1) a one-dimensional microswimmer in free-space that moves towards the target via translation, (2) a one-dimensional microswimmer in a periodic domain that rotates to reach the target, (3) a two-dimensional microswimmer that switches gaits to navigate to the designated targets in a plane, and (4) a two-dimensional microswimmer trained to navigate in a non-stationary environment.

The first and second studies focus on how reinforcement learning (specifically model-free, off-policy Q-learning) can be applied to generate one-dimensional translation (part 1) or net rotation (part 2) in low Reynolds number fluids. Through the interaction with the surrounding viscous fluid, the swimmer learns to break the time-reversal symmetry of Stokes flow in order to achieve the maximum displacement (reward) either in free-space or in a periodic domain.

In the third part of the dissertation, a deep reinforcement learning approach (proximal policy optimization) is utilized to train a two-dimensional swimmer to develop complex strategies such as run-and-tumble to navigate through environments and move towards specific targets. Proximal policy optimization contains actor-critic model, the critic estimates the value function, the actor updates the policy distribution in the direction suggested by the critic. Results show the artificial trained swimmer can develop effective policy (gaits) such as translation and rotation, and the swimmer can move to specific targets by combining these gaits in an intelligent way. The simulation results also show that without being explicitly programmed, the trained swimmer is able to perform target navigation even under flow perturbation.

Finally, in the last part of the dissertation, a generalized step-up reinforcement method with deep learning is developed for an environment that changes in time. In this work, the traditional reinforcement learning is combined with a high confidence context detection, allowing the swimmer to be trained to navigate amphibious non-stationary environments that consist of two distinct regions. Computational results show that the swimmer trained by this algorithm adapts to the environments faster, while developing more effective locomotory strategies in both environments, than traditional reinforcement learning approaches. Furthermore, the effective policies with traditional strategies are compared and analyzed. This work illustrates how deep reinforcement learning method can be conveniently adapted to a broader class of problems such as a microswimmer in a non-stationary environment. Results from this part highlight a powerful alternative to current traditional methods for applications in unpredictable, complex fluid environments and open a route towards future designs of “smart” microswimmers with trainable artificial intelligence.



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