Digital Twin, Automation, S/W

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Traditional Data Driven Reduced Order Models Data driven surrogate models or proxy models are often required for various purpose in engineering and science. Typical uses include optimization, inverse problems, parameter estimation, sensitivity analysis, uncertainty quantification, where full-fledged simulations (FEM, FVM/CFD, MD, …) are too resource and time intensive to be practical and experiments are also too time consuming and expensive. Such surrogate models are obtained by dimensionality reduction techniques such as PCA/POD/DMD or other machine learning models such as Neural Networks. The deep neural network has gained prominence in the last decade. However, such data driven techniques have some key limitations typically relating to dependence on large volumes of training data. It is not straightforward to quantify the performance of such models when they are evaluated outside the scope of the training data or in regimes where training data does not exist or is impossible to obtain. The Physics Informed Neural Network The physics informed neural network (PINN) has been recently developed to overcome the limitation of traditional data driven models. Figure 2 illustrates this concept, which was developed by Raissi et. al. [1,2] at Brown University. This is part of a general effort to augment the traditional neural network with domain knowledge. The PINN is strongly recommended over the traditional neural network because of its robustness induced by incorporating physics-based domain knowledge into the neural network. The PINN is also more accurate, in general.