Zoom https://cwi-nl.zoom.us/j/82092307174?pwd=aDcyaFBvWU52eHgySHhXY2ZPRWZLUT09
Meeting ID: 820 9230 7174
Passcode: 618359
Heng Xiao, Professor of Data-Driven Fluid Dynamics, University of Stuttgart.
An Equivariant Neural Operator for Developing Nonlocal Tensorial Constitutive Models
Developing robust constitutive (or closure) models is a fundamental problem for accelerating the simulation of complicated physics such as turbulent flows. Traditional constitutive models based on partial differential equations (PDEs) often lack robustness and are too rigid to accommodate diverse calibration datasets. We propose a frame-independent, nonlocal constitutive model based on a vector-cloud neural network that can be learned from unstructured data. The model predicts the closure variable at a point based on a collection of neighboring points (referred to as a “cloud"). The cloud is mapped to the closure variable through a neural network that is invariant both to coordinate translation and rotation and to the ordering of points in the cloud. The merits of the proposed network are demonstrated for scalar and tensor transport PDEs on a family of parameterized periodic hill geometries. The vector-cloud neural network is a promising tool not only as nonlocal constitutive models and but also as general surrogate models for PDEs on irregular domains.
