Ethan King

James Koch, WoongJo Choi, Ethan King et al.

Lumped parameter methods aim to simplify the evolution of spatially-extended or continuous physical systems to that of a "lumped" element representative of the physical scales of the modeled system. For systems where the definition of a lumped element or its associated physics may be unknown, modeling tasks may be restricted to full-fidelity simulations of the physics of a system. In this work, we consider data-driven modeling tasks with limited point-wise measurements of otherwise continuous systems. We build upon the notion of the Universal Differential Equation (UDE) to construct data-driven models for reducing dynamics to that of a lumped parameter and inferring its properties. The flexibility of UDEs allow for composing various known physical priors suitable for application-specific modeling tasks, including lumped parameter methods. The motivating example for this work is the plunge and dwell stages for friction-stir welding; specifically, (i) mapping power input into the tool to a point-measurement of temperature and (ii) using this learned mapping for process control.

James Kotary, Himanshu Sharma, Ethan King et al.

Learning to Optimize (L2O) is a subfield of machine learning (ML) in which ML models are trained to solve parametric optimization problems. The general goal is to learn a fast approximator of solutions to constrained optimization problems, as a function of their defining parameters. Prior L2O methods focus almost entirely on single-level programs, in contrast to the bilevel programs, whose constraints are themselves expressed in terms of optimization subproblems. Bilevel programs have numerous important use cases but are notoriously difficult to solve, particularly under stringent time demands. This paper proposes a framework for learning to solve a broad class of challenging bilevel optimization problems, by leveraging modern techniques for differentiation through optimization problems. The framework is illustrated on an array of synthetic bilevel programs, as well as challenging control system co-design problems, showing how neural networks can be trained as efficient approximators of parametric bilevel optimization.

James Koch, Ethan King, WoongJo Choi et al.

This study validates the use of Neural Lumped Parameter Differential Equations for open-loop setpoint control of the plunge sequence in Friction Stir Processing (FSP). The approach integrates a data-driven framework with classical heat transfer techniques to predict tool temperatures, informing control strategies. By utilizing a trained Neural Lumped Parameter Differential Equation model, we translate theoretical predictions into practical set-point control, facilitating rapid attainment of desired tool temperatures and ensuring consistent thermomechanical states during FSP. This study covers the design, implementation, and experimental validation of our control approach, establishing a foundation for efficient, adaptive FSP operations.