Intelligent modeling with physics-informed machine learning for petroleum engineering problems

The advancement in big data and artificial intelligence has enabled a novel exploration mode for the study of petroleum engineering. Unlike theory-based solution methods, the data-driven intelligent approaches demonstrate superior flexibility, computational efficiency and accuracy for dealing with complex multi-scale, and multi-physics problems. However, these intelligent models often disregard physical laws in pursuit of error minimization, which leads to certain uncertainties. Therefore, physics-informed machine learning approaches have been developed based on data, guided by physics, and supported by machine learning models. This study summarizes four embedding mechanisms for introducing physical information into machine learning models, including input data-based embedding, model architecture-based embedding, loss function-based embedding, and model optimization-based embedding mechanism. These "data + physics" dual-driven intelligent models not only exhibit higher prediction accuracy while adhering to physic laws, but also accelerate the convergence to improve computational efficiency. This paradigm will facilitate the guide developments in solving petroleum engineering problems toward a more comprehensive and efficient direction.