FlowGINO: Continuous Reconstruction from Sparse Observations along with Aleatoric and Epistemic Uncertainty Estimation

Mapping out physical fields in continuous domain from sparse sensor data observations is a difficult challenge and an active research endeavor in many scientific fields. Since the processes that create this data are often not fully understood, there is increasing interest in leveraging deep neural networks to address this problem. Despite significant progress in using deep learning methods like Implicit Neural Representations (INRs) and Fourier Neural Operators (FNOs) for reconstructing physical fields, there remains a notable gap in research on quantifying the uncertainty of these reconstructions. For high-stakes applications, such as climate modeling, it is critically important to estimate and disentangle the two types of uncertainty: reducible Epistemic Uncertainty and irreducible Aleatoric Uncertainty. Effectively quantifying and separating these uncertainties is essential for the reliable application of deep learning models across scientific domains. We introduce Flow-matching Geometry Informed Neural Operator (FlowGINO) which is not only capable of reconstructing continuous physical fields but also capable of estimating both epistemic and aleatoric uncertainty in a disentangled manner.