Publication Date

Fall 2024

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Computer Engineering

Advisor

Feruza Amirkulova; Magdalini Eirinaki; Stas Tiomkin

Abstract

Partial Differential Equations (PDEs) serve as fundamental tools in scientific and engineering disciplines, modeling phenomena ranging from material design to climate dynamics. Developing robotic systems capable of controlling PDE-governed systems, particularly when these phenomena are only partially observable, has the potential to drive significant technological advancements. This work presents a framework that leverages physics-informed machine learning (ML) for the control of PDEs. At the core of this approach is an agent equipped with sensors that generate a low-dimensional, physics-informed representation of the environment, enabling the derivation of optimal sparse control policies for the agent’s actuators. The focus is on manipulating wave energy through cylindrical scatterers controlled by a robot. The method presented in this work is evaluated by comparing its control capabilities to a well-known physics-uninformed baseline, demonstrating superior robustness across various scenarios. Additionally, the approach is validated against a gradient-based optimization (GBO) solver, which provides optimal steady-state scatterer configurations. The results show that the method achieves performance comparable to the GBO, while the physics-uninformed approach does not perform as well. This research extends beyond classical robotics challenges by addressing the manipulation of acoustic waves, with applications in the design of artificial materials, ultrasonic tools, and energy harvesting. The data-driven robot learning method efficiently focuses or suppresses scattered acoustic energy depending on the task, outperforming state-of-the-art learning methods in both solution quality and computational efficiency. Furthermore, the method is competitive with classical semi-analytical approaches in acoustics.

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