Stabilizing viscous extensional flows using reinforcement learning.

Area of Science:

• Fluid dynamics
• Machine learning
• Control theory

Background:

• The four-roll mill generates local extensional flows, useful for studying liquid drop deformation.
• Extensional flows are inherently unstable, causing drops at stagnation points to escape.

Purpose of the Study:

• To devise a reinforcement learning algorithm for stabilizing liquid drops in a four-roll mill flow.
• To develop a robust control strategy for maintaining drop position at the flow stagnation point.

Main Methods:

• Modeling the flow as a superposition of rotlets and the drop as a rigid sphere.
• Employing a probabilistic reinforcement learning approach using an actor-critic method.
• Training the algorithm to optimize speed adjustments for stabilization.

Main Results:

• The developed algorithm successfully stabilized the drop, keeping it near the stagnation point.
• The control strategy demonstrated robustness against thermal noise and adaptability to initial positions.
• The algorithm can be adjusted to limit flow extension magnitude near the drop.

Conclusions:

• Reinforcement learning offers an effective method for controlling unstable fluid dynamics, specifically in four-roll mill flows.
• The probabilistic actor-critic approach provides a robust and adaptable control solution for particle stabilization.
• This work highlights the potential of machine learning in advanced fluid mechanics applications.