Inverse modeling of multiphysics problems remains a challenging task due to strong nonlinearity and high computational cost. In coupled electro-thermal simulations, identifying unknown input parameters from observed field responses is particularly difficult since conventional inverse approaches rely on repeated forward analyses.

This study proposes a data-driven inverse modeling framework that integrates coupled electro-thermal simulations with deep learning techniques. Forward simulations are performed using a finite-element-based electro-thermal analysis platform, where quasi-static electric field analysis is followed by Joule heating evaluation and transient heat conduction analysis. These simulations generate spatial distributions of current density and temperature, which serve as observational data for inverse learning.

A dataset is constructed from multiple simulation cases under varying voltage conditions. To ensure computational feasibility, large-scale field outputs are systematically reduced while preserving essential spatial characteristics. Based on this dataset, several learning-based inverse models are investigated, including Multi-Layer Perceptron (MLP), Convolutional Neural Networks (CNN), and Vision Transformers (ViT).

The results demonstrate that learning-based models can successfully infer input voltage levels from electro-thermal field patterns. MLP provides stable regression performance, CNN effectively captures local spatial features, and ViT shows potential for modeling global spatial dependencies when properly regularized. These findings indicate that electro-thermal field responses contain sufficient information for inverse parameter estimation.

The proposed framework offers a computationally efficient alternative to traditional inverse solvers and highlights the potential of data-driven approaches in multiphysics inverse modeling. This work contributes to the development of machine-learning-assisted computational methods for complex coupled systems.