The field of machine learning in physical systems is rapidly advancing, with a growing focus on developing innovative models that can accurately predict complex phenomena. A key direction in this field is the integration of physical constraints and equations into machine learning architectures, enabling more robust and reliable predictions. This approach has shown promise in various applications, including fluid dynamics and thermophysical property prediction. Notably, the development of interactive web interfaces and open-source models is increasing the accessibility of these advanced methods. In the area of fluid dynamics, novel physics-informed neural network architectures are being developed to improve the accuracy and stability of predictions. These models leverage the discretization of physical equations to provide robust long-term predictions. In addition, score-based generative models are being explored for reservoir simulation, allowing for the reconstruction of spatially varying permeability and saturation fields from sparse observations. Some noteworthy papers in this area include:

• MLPROP, which provides an interactive web interface for predicting thermophysical properties using machine learning models.
• PINP, which proposes a physics-informed neural predictor with latent estimation of fluid flows, demonstrating state-of-the-art performance in spatiotemporal prediction.
• Well2Flow, which introduces a novel methodology for reconstructing reservoir states using score-based generative models, showing strong generalization capabilities across varying geological scenarios.