The authors present generalized finite-volume-based discretized loss functions integrated into pressure-linked algorithms for physics-based unsupervised training of neural networks (NNs). In contrast to automatic differentiation-based counterparts, discretized loss functions leverage well-developed numerical schemes of computational fluid dynamics (CFD) for tailoring NN training specific to the flow problems. For validation, neural network-based solvers (NN solvers) are trained by posing equations such as the Poisson equation, energy equation, and Spalart–Allmaras model as loss functions. The predictions from the trained NNs agree well with the solutions from CFD solvers while also providing solution time speed-ups of up to seven times. Another application of unsupervised learning is the novel hybrid loss functions presented in this study. Hybrid learning combines the information from sparse or partial observations with a physics-based loss to train the NNs accurately and provides training speed-ups of up to five times compared with a fully unsupervised method. Also, to properly utilize the potential of discretized loss functions, they are formulated in a machine learning (ML) framework (TensorFlow) integrated with a CFD solver (OpenFOAM). The ML-CFD framework created here infuses versatility into the training by giving loss functions access to the different numerical schemes of the OpenFOAM. In addition, this integration allows for offloading the CFD programming to OpenFOAM, circumventing bottlenecks from manually coding new flow conditions in a solely ML-based framework like TensorFlow.
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