Novel physics-informed optimization framework for complex multi-physics problems: Implementation for a sweeping gas membrane distillation module

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The application of advanced machine learning algorithms such as deep learning is limited for the surrogate-based process optimization of complex multi-physics problems because high-quality experimental and numerical training samples required for deep-learning model training are expensive and scarce. To address this issue, in this study, a novel physics-informed process optimization (PIPO) framework was introduced. In the first step, surrogate models based on conventional neural networks (NN) were trained using a few available high-quality training samples. In the second step, the trained NN models were coupled to the process optimization solver in which the loss of physical laws was added to the optimizer’s objective function to find optimal design points that satisfy the laws of physics. As a result, the generalization performance of the framework was greatly improved for design targets outside the training range of NN models. PIPO is substantially different from the physics-informed neural networks where the loss of physics is added to the loss function used during NN model training. The PIPO framework was used to optimize a sweeping gas membrane distillation (SGMD) module. Eight input design variables, including process and geometrical parameters, were optimized for different challenging targets to achieve the best SGMD performance in terms of ammonia recovery ratio and concentration. It was shown that for noticeably few training samples of 68 experiments, the proposed framework was able to achieve the optimization targets within a reasonable computational cost. The optimum designs were verified and analyzed in detail by high-resolution computational fluid dynamics models.