Investigation of Physics-Informed Deep Learning for the Prediction of Parametric, Three-Dimensional Flow Based on Boundary Data

Abstract

The placement of temperature sensitive and safety-critical components is crucial in the automotive industry. It is therefore inevitable, even at the design stage of new vehicles that these components are assessed for potential safety issues. However, with increasing number of design proposals, risk assessment quickly becomes expensive. We therefore present a parameterized surrogate model for the prediction of three-dimensional flow fields in aerothermal vehicle simulations. The proposed physics-informed neural network (PINN) design is aimed at learning families of flow solutions according to a geometric variation. In scope of this work, we could show that our nondimensional, multivariate scheme can be efficiently trained to predict the velocity and pressure distribution for different design scenarios and geometric scales. The proposed algorithm is based on a parametric minibatch training which enables the utilization of large datasets necessary for the three-dimensional flow modeling. Further, we introduce a continuous resampling algorithm that allows to operate on one static dataset. Every feature of our methodology is tested individually and verified against conventional CFD simulations. Finally, we apply our proposed method in context of an exemplary real-world automotive application.

Prediction of numerical homogenization using deep learning for the Richards equation

“…Across the training set on coarse grid, the relative l 2 error, that is, the root mean square error (RMSE) [59,66,68,37] is as stated in [56]:…”

Shape‐optimization of extrusion‐dies via parameterized physics‐informed neural networks

“…The choice of the PINN architecture has an important influence on the quality of the results. Here, we adhere to the structure proposed by Rao et al [11], which has also been used in Heger et al [15]. The advantage of this approach is that no longer second derivatives of the velocity are required and that the continuity equation is enforced automatically, for details please refer to Rao et al [11].…”

“…As suggested in Rao et al [11], the first output variable is the stream function 𝚿. The functional relationship between the stream function and the velocity is shown in the following formula for the 2D and 3D cases, respectively [15]:…”

“…For example, in Refs. [14,15], the positioning of individual edges is parameterized and integrated into the PINN model. Further, Refs.…”

Stiff-PDEs and Physics-Informed Neural Networks

“…4 and 5, we investigated these problems with a number of PINN frameworks from Table 1 and compared the results with the FEM solution. PINNs are also known for solving parametric PDEs [41][42][43][44]. In Sect.…”