Abstract
Abstract 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.
Highlights
Physics-based simulation has been an integral part of product development and design as a cheaper alternative to physical prototyping
For the investigation of different architectures, we focus on using multilayer perceptron (MLP) and Runge–Kutta neural network (NN) (RKNN) to learn and predict with constant time step
In Section 5.2.3, we further study the capability of Euler NN (EENN) and RKNNs to learn from the snapshots sampled on the coarse time grids and to predict on the fine time grids
Summary
Physics-based simulation has been an integral part of product development and design as a cheaper alternative to physical prototyping. Available, enabling “edge computing,” that is deploying compact computing devices in factories and smart buildings to enable data analysis The existence of such hardware opens up the possibility of transferring the physics-based models from design phase into the operation phase. Apart from these, we would like to point out the numerical-integration-based NN models such as explicit Euler NN (EENN; (Pan and Duraisamy, 2018) and Runge–Kutta NN (RKNN; Wang and Lin, 1998) specialize in nonintrusively modeling the solution of ordinary differential equation (ODE) or partial differential equation (PDE) These networks can efficiently learn the time information in the training data and be more flexible to the time stepping strategy.
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