Physics-Informed Field Inversion for Sparse Data Assimilation (2509.19160v1)

Abstract: Data-driven methods keep increasing their popularity in engineering applications, given the developments in data analysis techniques. Some of these approaches, such as Field Inversion Machine Learning (FIML), suggest correcting low-fidelity models by leveraging available observations of the problem. However, the solely data-driven field inversion stage of the method generally requires dense observations that limit the usage of sparse data. In this study, we propose a physical loss term addition to the field inversion stage of the FIML technique similar to the physics-informed machine learning applications. This addition embeds the complex physics of the problem into the low-fidelity model, which allows for obtaining dense gradient information for every correction parameter and acts as an adaptive regularization term improving inversion accuracy. The proposed Physics-Informed Field Inversion approach is tested using three different examples and highlights that incorporating physical loss can enhance the reconstruction performance for limited data cases, such as sparse, truncated, and noisy observations. Additionally, this modification enables us to obtain accurate posterior correction parameter distribution with limited realizations, making it data-efficient. The increase in the computational cost caused by the physical loss calculation is at an acceptable level given the relaxed grid and numerical scheme requirements.