Partial Differential Equations' Solver Using Physics Informed Neural Networks
Committee membersBernard, Ghanem
Permanent link to this recordhttp://hdl.handle.net/10754/676833
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AbstractComputational fluid dynamics (CFD) is the analytical process of predicting fluid flow, mass transfer, chemical reactions, and other related phenomena during the design or manufacturing process. Aggressive use of CFD provides drastic reductions in wind tunnel time and lowers the number of experimental rig tests. CFD saves hundreds of millions of dollars for industries, governments, and national laboratories, offering the potential to deliver superior understanding and insight into the critical physical phenomena limiting component performance. Thus, CFD opens new frontiers in many fields, especially vehicle design. One key strength of CFD is its ability to produce simulations useful in inverse design and optimization problems. However, a simulation in a conventional solver is considerably time-consuming to converge. To enable more efficient and scalable CFD simulations, we leverage the universal approximation property of machine learning using deep neural networks (DNNs) to estimate a surrogate solution to the CFD simulation. We present an implementation of this idea in two different models, one representing the eulerian model for compressible viscous flows and another representing the compressible Navier–Stokes equations. Lastly, we discuss the compressible Navier–Stokes network’s performance by implementing an inverse design problem to know if a gradient descent step of the model w.r.t the shape would grant the optimal solution. After training, predictions from these networks are faster than conventional solvers. The network predicts the flow fields hundreds of times faster than current conventional CFD solvers while maintaining good accuracy. Using the network’s predicted solutions to initialize a CFD solver sufficiently speeds up the simulation.
CitationAlhuwaider, S. (2022). Partial Differential Equations' Solver Using Physics Informed Neural Networks. KAUST Research Repository. https://doi.org/10.25781/KAUST-5ONUV