Traditional engineering applications rely on physics-based models that are developed and refined over time for specific use cases. These models are typically used to calculate various physical properties such as stresses, velocity profiles, concentrations, etc., and typically require solving multidimensional partial differential equations (PDEs). Common use cases for such physics-based models include process optimization, unknown parameter estimation, and uncertainty analysis.
Machine learning techniques are used to solve or approximate solutions to complex problems arising from physics-based modeling, including problems involving PDEs. The goal of this paper is to demonstrate how an encoder-decoder neural network framework can be used to build low-dimensional models and generate high-fidelity solutions to complex and time-consuming physics-based models using approximate fast solutions from low-fidelity physics-based models.
In this paper, we investigate how machine learning can be used to rapidly predict solutions of high-fidelity complex physical models using simpler physical models. Two different closed-form solutions of advection-diffusion PDEs (AD PDEs), known as the Gaussian plume model and the Gaussian puff model, are typically used to model the atmospheric dispersion of gas emissions. The Gaussian puff model is a more complex physically-based model that requires more computational effort to generate a high-fidelity solution compared to the simpler Gaussian plume model, which involves several assumptions and approximations.
A long short-term memory (LSTM) network encoder-decoder architecture was trained to use solutions of the simpler Gaussian plume model for different leak rates, wind speeds, and directions to predict the solution of the more complex Gaussian puff model. The LSTM model with three LSTM layers with 16 neurons each efficiently simulated concentrations for the entire set of 2014 samples in just 1.34 minutes. This contrasts sharply with the time-consuming simulation process of traditional software, which took 14 hours to achieve similar concentration results in this study. The implementation of the LSTM network improved computational speed by 625.15 times.
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Paper SPE 216003 can be found on OnePetro here.
