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

Author

Listed:
  • 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)

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.

Suggested Citation

  • James Koch & WoongJo Choi & Ethan King & David Garcia & Hrishikesh Das & Tianhao Wang & Ken Ross & Keerti Kappagantula, 2025. "Neural lumped parameter differential equations with application in friction-stir processing," Journal of Intelligent Manufacturing, Springer, vol. 36(2), pages 1111-1121, February.
  • Handle: RePEc:spr:joinma:v:36:y:2025:i:2:d:10.1007_s10845-023-02271-5
    DOI: 10.1007/s10845-023-02271-5
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