A novel finite-element-based solution and property construction method for thermal problems fromsparse data

Purpose The purpose of this paper is to propose a method for rapidly estimating full-field solutions and material properties from sparse measurement data. This approach is particularly effective for monitoring and controlling experiments (digital twinning), especially in extreme thermal environments where sparse diagnostic sensor data may be the only available information. Design/methodology/approach This paper addresses this full field solution and material properties construction procedure using an efficient finite-element-based approach combined with a modified optimizing a discrete loss (ODIL) concept. A finite-element specific regularization term is added to the loss function to resolve the ill-posedness. The loss function gradients are calculated analytically. The non-linear material properties are constructed as a piecewise linear function during the temperature change. A sample from fusion energy experimental facility is used as the test case to demonstrate the proposed methodology. Findings The results indicate that the proposed method enables near-real-time construction of solutions and non-linear material properties using sparse temperature measurements. This demonstrates its suitability for digital twinning applications, particularly in high-temperature environments. Originality/value This work presents a novel finite-element-based approach combined with a modified ODIL method, which can be used for full solution construction from sparse measurements. In addition, it enables the construction of non-linear material properties as a piecewise linear function of temperature. Unlike many modern approaches, this method does not rely on machine learning, making it more interpretable and, moreover, it does not require extensive training. The ability to achieve near-real-time solution construction enhances its applicability for monitoring and control (digital twinning) in extreme thermal conditions.