arXiv subjects

Wouter J. Schuttert

Publications and source records attributed to Wouter J. Schuttert.

2 recordsLinked to original sources

arXiv2026

A manifold-aware Neural ODE surrogate model for stochastic induction heating with anisotropic electrical conductivity

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.

cs.CE↗

arXiv2025

Constitutive Manifold Neural Networks

Anisotropic material properties, such as the thermal conductivities of engineering composites, exhibit variability due to inherent material heterogeneity and manufacturing-related uncertainties. Mathematically, these properties are modeled as symmetric positive definite (SPD) tensors, which reside on a curved Riemannian manifold. Extending this description to a stochastic framework requires preserving both the SPD structure and the underlying spatial symmetries of the tensors. This is achieved through the spectral decomposition of tensors, which enables the parameterization of uncertainties into scale (strength) and rotation (orientation) components. To quantify the impact of strength and orientation uncertainties on the thermal behaviour of the composite, the stochastic material tensor must be propagated through a physics-based forward model. This process necessitates computationally efficient surrogate models, for which a feedforward neural network (FNN) is employed. However, conventional FNN architectures are not well-suited for SPD tensors, as directly using tensor components as input features fails to preserve their underlying geometric structure, often leading to suboptimal performance. To address this issue, we introduce the Constitutive Manifold Neural Network (CMNN), which incorporates input layers that map SPD tensors from the curved manifold to the local tangent space-a flat vector space-thus preserving the statistical and geometric information in the dataset. A case study involving steady-state heat conduction with stochastic anisotropic conductivity demonstrates that geometry-preserving neural network significantly enhances learning performance compared to conventional multilayer perceptrons (MLPs). These findings underscore the importance of manifold-aware methods when working with tensor-valued data in engineering applications.

cs.CE↗