A manifold-aware Neural ODE surrogate model for stochastic induction heating with anisotropic electrical conductivity
2026-08-03 • Computational Engineering, Finance, and Science
Computational Engineering, Finance, and Science
AI summaryⓘ
The authors study how induction welding works for making lightweight parts from fiber-reinforced plastics. They focus on how variations in the material's electrical conductivity, caused by fiber placement, affect the heating process. To model this variability, they create a new mathematical approach that respects the material's physical properties and use simulations to understand its impact on heating. Then, they train specialized neural networks that follow these mathematical rules to predict temperature changes efficiently over time. Different methods for simulating the time aspect are also tested and compared.
Induction weldingFiber-reinforced thermoplastic compositesElectrical conductivity tensorStochastic material modelPositive-definite matrixMonte Carlo simulationSurrogate modelConstitutive Manifold Neural NetworkNeural Ordinary Differential Equation
Authors
Wouter J. Schuttert, Mohammed Iqbal Abdul Rasheed, Bojana Rosić
Abstract
Induction welding plays a central role in enabling lightweight, integrated structures made from fibre-reinforced thermoplastic composites. From a modelling perspective, the induction welding process can be approximated by one-way coupled electromagnetic and heat-transfer equations. In practice, material parameters such as electrical conductivity vary significantly resulting from the deviations in the placement of fibres and hence the fibre-fibre contacts in the mesostructure are governed by consolidation quality of the material. Explicit representation of this variability on the macroscopic scale is essential to capture the closed current loops required for the induction heating process. To address this, a stochastic material model is introduced that respects the symmetric positive-definite (SPD) nature of the conductivity tensor and separates scaling and orientation uncertainties, forming the basis of a surrogate framework. The resulting stochastic conductivity model is first used to quantify the uncertainty in the induction heating process through extensive Monte Carlo simulations, providing detailed insight into the induced currents and the resulting temperature field. Subsequently, to enable efficient uncertainty propagation, SPD-aware surrogate models are trained with a subset of the simulation data, consisting of labelled material states and temperature fields. The surrogates are formulated as Constitutive Manifold Neural Networks (CMNNs) that explicitly respect the underlying SPD manifold structure and are integrated with a Neural Ordinary Differential Equation (NODE) framework to capture temporal dynamics. Several NODE integration schemes are evaluated and compared.