Data-driven modeling provides an efficient approach to compute approximate solutions for complex multiphysics parametrized problems such as induction hardening (IH) process. Basically, some physical quantities of interest (QoI) related to the IH process will be evaluated under real-time constraint, without any explicit knowledge of the physical behavior of the system. Hence, computationally expensive finite element models will be replaced by a parametric solution, called metamodel. Two data-driven models for temporal evolution of temperature and austenite phase transformation, during induction heating, were first developed by using the proper orthogonal decomposition based reduced-order model followed by a nonlinear regression method for temperature field and a classification combined with regression for austenite evolution. Then, data-driven and hybrid models were created to predict hardness, after quenching. It is shown that the results of artificial intelligence models are promising and provide good approximations in the low-data limit case.

Finite element modeling (FEM) has recently become the most attractive computational tool to predict and optimize many industrial problems. However, the FEM becomes ineffective as far as complex multi-physics parameterized problems, such as induction heating process, are concerned because of high computational cost. This work aims at studying the possibility of applying a new approach based on the reduced order modeling (ROM) to obtain approximate solutions of a parametric problem. Basically, the effect of induction heating process parameters on some physical quantities of interest (QoI) will be analyzed under the real-time constraint. To achieve this dimensionality reduction, a set of precomputed solutions is first collected, at some sparse points in the space domain and for a properly selected process parameters, by solving the full-order models implemented in the commercial finite element software FORGE®. A Proper Orthogonal Decomposition (POD) based reducedorder model is then applied to the collected data to find a low dimensional space onto which the solution manifold could be projected and an approximated solution for new process parameters could be efficiently computed in real time. Besides, the POD is applied to build a reduced basis and to compute their corresponding modal coefficients. It is then followed by artificial intelligence techniques for regression purpose, such as sparse Proper Generalized Decomposition, to fit the low dimensional POD modal coefficients. Hence, the problem can be solved with a much lower dimension compared to the initial one. It was shown that a good approximation of the QoI was provided, in low-data limit, using a single POD modal coefficient as a response for the regression methods. However, the obtained approximation accuracy needs to be enhanced.

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