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SUMMARY:Learning Nonlocal Constitutive PDE Models with Vector-Cloud Neural
  Networks - Jiequn Han (Princeton University)
DTSTART:20211118T163000Z
DTEND:20211118T170000Z
UID:TALK165457@talks.cam.ac.uk
DESCRIPTION:Constitutive models are widely used for modeling complex syste
 ms in science and engineering\, when first-principle-based\, well-resolved
  simulations are prohibitively expensive. For example\, in fluid dynamics\
 , constitutive models are required to describe nonlocal\, unresolved physi
 cs such as turbulence and laminar-turbulent transition. However\, traditio
 nal constitutive models based on PDEs often lack robustness and are too ri
 gid to accommodate diverse calibration datasets. We propose a frame-indepe
 ndent\, nonlocal constitutive model based on a vector-cloud neural network
  that represents the physics of PDEs and meanwhile can be learned with dat
 a. The model predicts the closure variable at a point based on the flow in
 formation in its neighborhood. Such nonlocal information is represented by
  a group of points\, each having a feature vector attached to it\, and thu
 s the input is referred to as vector cloud. The cloud is mapped to the clo
 sure variable through a frame-independent neural network\, invariant both 
 to coordinate translation and rotation and to the ordering of points in th
 e cloud. As such\, the network can deal with any number of arbitrarily arr
 anged grid points and thus is suitable for unstructured meshes in fluid si
 mulations. The merits of the proposed network are demonstrated for scalar 
 transport PDEs on a family of parameterized periodic hill geometries. The 
 vector-cloud neural network is a promising tool not only as nonlocal const
 itutive models and but also as general surrogate models for PDEs on irregu
 lar domains.
LOCATION:Seminar Room 1\, Newton Institute
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