Traditional engineering applications rely on physics-based models that have been developed and refined over time for specific use cases. These models typically are used for calculating different physical properties such as stress, velocity profiles, and concentration and usually involve solving multidimensional partial differential equations (PDEs). Some typical examples of uses of such physics-based models are in process optimization, unknown parameter estimation, and uncertainty analysis.
Machine learning techniques are used to solve or approximate the solutions of complex problems that arise from physics-based modeling, including problems involving PDEs. The objective of this paper is to demonstrate the use of machine learning to build reduced-order models, using an encoder/decoder neural-network framework, to generate the high-fidelity solutions of a complex, time-consuming, physics-based model using the approximate, fast solutions from low-fidelity physics-based model.
This paper investigates the use of machine learning to rapidly predict the solutions of a high-fidelity, complex physics model using a simpler physics model. Two different closed-form solutions of the advection/diffusion PDE (A-D PDE), known as the Gaussian plume model and Gaussian puff model, are typically used to model the atmospheric dispersion of gas emission. The Gaussian puff model is a more complex physics-based model that requires more computational effort to generate the high-fidelity solutions, as compared with the simpler Gaussian plume model that has several assumptions and approximations.
An encoder/decoder architecture of a long short-term memory (LSTM) network is trained to predict the solutions of the more complex Gaussian puff model using the solutions of the simpler Gaussian plume model for various leak rate, wind speed, and wind direction. The LSTM model, with three LSTM layers with 16 neurons each, efficiently simulated the concentrations of the entire set of 2014 samples in a mere 1.34 minutes. This presents a significant contrast to traditional software’s time-consuming simulation process, which took 14 hours to achieve similar concentration outcomes in this study. The implementation of LSTM network has achieved a computational speed up of 625.15 times.