Model order reduction (MOR) methods enable the generation of real-time-capable digital twins, with the potential to unlock various novel value streams in industry. While traditional projection-based methods are robust and accurate for linear problems, incorporating machine learning to deal with nonlinearity becomes a new choice for reducing complex problems. These kinds of methods are independent to the numerical solver for the full order model and keep the nonintrusiveness of the whole workflow. Such methods usually consist of two steps. The first step is the dimension reduction by a projection-based method, and the second is the model reconstruction by a neural network (NN). In this work, we apply some modifications for both steps respectively and investigate how they are impacted by testing with three different simulation models. In all cases Proper orthogonal decomposition is used for dimension reduction. For this step, the effects of generating the snapshot database with constant input parameters is compared with time-dependent input parameters. For the model reconstruction step, three types of NN architectures are compared: multilayer perceptron (MLP), explicit Euler NN (EENN), and Runge–Kutta NN (RKNN). The MLPs learn the system state directly, whereas EENNs and RKNNs learn the derivative of system state and predict the new state as a numerical integrator. In the tests, RKNNs show their advantage as the network architecture informed by higher-order numerical strategy.

Model order reduction (MOR) can provide low-dimensional numerical models for fast simulation. Unlike intrusive methods, nonintrusive methods are attractive because they can be applied even without access to full order models (FOMs). Since nonintrusive MOR methods strongly rely on snapshots of the FOMs, constructing good snapshot sets becomes crucial. In this work, we propose a novel active-learning-based approach for use in conjunction with nonintrusive MOR methods. It is based on two crucial novelties. First, our approach uses joint space sampling to prepare a data pool of the training data. The training data are selected from the data pool using a greedy strategy supported by an error estimator based on Gaussian process regression. Second, we introduce a case-independent validation strategy based on probably approximately correct learning. While the methods proposed here can be applied to different MOR methods, we test them here with artificial neural networks and operator inference.

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