Neural Lumped Parameter Differential Equations with Application in Friction-Stir Processing
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.
Code (0)
등록된 구현이 없습니다.
Tasks
FrictionSimilar Papers 제목 키워드 기반
First Contact: Data-driven Friction-Stir Process Control
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…
Linear models of activation cascades: analytical solutions and coarse-graining of delayed signal transduction
Cellular signal transduction usually involves activation cascades, the sequential activation of a series of proteins following the reception of an input signal. Here we study the classic model of weakly activated cascade…
Learning Nonlinear Dynamics in Physical Modelling Synthesis using Neural Ordinary Differential Equations
Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibra…
Reinterpreting PID Controller From the Perspective of State Feedback and Lumped Disturbance Compensation
This paper analyzes the motion of solutions to non-homogeneous linear differential equations. It further clarifies that a proportional-integral-derivative (PID) controller essentially comprises two parts: a homogeneous c…
First-order friction models with bristle dynamics: lumped and distributed formulations
Dynamic models, particularly rate-dependent models, have proven effective in capturing the key phenomenological features of frictional processes, whilst also possessing important mathematical properties that facilitate t…