Neural lumped parameter differential equations with application in friction-stir processing

James Koch (), WoongJo Choi, Ethan King, David Garcia, Hrishikesh Das, Tianhao Wang, Ken Ross and Keerti Kappagantula
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James Koch: Pacific Northwest National Laboratory
WoongJo Choi: Pacific Northwest National Laboratory
Ethan King: Pacific Northwest National Laboratory
David Garcia: Pacific Northwest National Laboratory
Hrishikesh Das: Pacific Northwest National Laboratory
Tianhao Wang: Pacific Northwest National Laboratory
Ken Ross: Pacific Northwest National Laboratory
Keerti Kappagantula: Pacific Northwest National Laboratory

Journal of Intelligent Manufacturing, 2025, vol. 36, issue 2, No 17, 1121 pages

Abstract: 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 physics simulations. 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.

Keywords: Machine learning; Lumped parameter method; Neural ordinary differential equations; Friction stir processing; Data-driven modeling (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10845-023-02271-5

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