Neural Lumped Parameter Differential Equations with Application in Friction-Stir Processing

• URL: http://arxiv.org/abs/2304.09047v1
• Date: Tue, 18 Apr 2023 15:11:27 GMT
• Title: Neural Lumped Parameter Differential Equations with Application in Friction-Stir Processing
• Authors: James Koch, WoongJo Choi, Ethan King, David Garcia, Hrishikesh Das, Tianhao Wang, Ken Ross, Keerti Kappagantula
• Abstract summary: Lumped parameter methods aim to simplify the evolution of spatially-extended or continuous physical systems. We build upon the notion of the Universal Differential Equation to construct data-driven models for reducing dynamics to that of a lumped parameter.
• Score: 2.158307833088858
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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