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Targeted Digital Twin via Flow Map Learning and Its Application to Fluid Dynamics

Qifan Chen, Zhongshu Xu, Jinjin Zhang, Dongbin Xiu

TL;DR

The proposed approach employs memory-based flow map learning to develop a data-driven model of the QoIs using short bursts of trajectory data generated through repeated executions of the full DT, rendering the construction of the FML-based tDT an entirely offline computational process.

Abstract

We present a numerical framework for constructing a targeted digital twin (tDT) that directly models the dynamics of quantities of interest (QoIs) in a full digital twin (DT). The proposed approach employs memory-based flow map learning (FML) to develop a data-driven model of the QoIs using short bursts of trajectory data generated through repeated executions of the full DT. This renders the construction of the FML-based tDT an entirely offline computational process. During online simulation, the learned tDT can efficiently predict and analyze the long-term dynamics of the QoIs without requiring simulations of the full DT system, thereby achieving substantial computational savings. After introducing the general numerical procedure, we demonstrate the construction and predictive capability of the tDT in a computational fluid dynamics (CFD) example: two-dimensional incompressible flow past a cylinder. The QoIs in this problem are the hydrodynamic forces exerted on the cylinder. The resulting tDTs are compact dynamical systems that evolve these forces without explicit knowledge of the underlying flow field. Numerical results show that the tDTs yield accurate long-term predictions of the forces while entirely bypassing full flow simulations.

Targeted Digital Twin via Flow Map Learning and Its Application to Fluid Dynamics

TL;DR

The proposed approach employs memory-based flow map learning to develop a data-driven model of the QoIs using short bursts of trajectory data generated through repeated executions of the full DT, rendering the construction of the FML-based tDT an entirely offline computational process.

Abstract

We present a numerical framework for constructing a targeted digital twin (tDT) that directly models the dynamics of quantities of interest (QoIs) in a full digital twin (DT). The proposed approach employs memory-based flow map learning (FML) to develop a data-driven model of the QoIs using short bursts of trajectory data generated through repeated executions of the full DT. This renders the construction of the FML-based tDT an entirely offline computational process. During online simulation, the learned tDT can efficiently predict and analyze the long-term dynamics of the QoIs without requiring simulations of the full DT system, thereby achieving substantial computational savings. After introducing the general numerical procedure, we demonstrate the construction and predictive capability of the tDT in a computational fluid dynamics (CFD) example: two-dimensional incompressible flow past a cylinder. The QoIs in this problem are the hydrodynamic forces exerted on the cylinder. The resulting tDTs are compact dynamical systems that evolve these forces without explicit knowledge of the underlying flow field. Numerical results show that the tDTs yield accurate long-term predictions of the forces while entirely bypassing full flow simulations.

Paper Structure

This paper contains 24 sections, 38 equations, 16 figures.

Table of Contents

  1. Introduction
  2. Targeted Digital Twin
  3. Full Digital Twin
  4. Quantity-of-Interest
  5. Targeted Digital Twin
  6. Preliminary: Flow Map Learning
  7. Targeted Digital Twin Construction
  8. Mathematical Motivation
  9. Numerical Procedure for tDT
  10. Full DT Model Simulation
  11. FML tDT Model Construction
  12. System Analysis via tDT
  13. Application to Fluid Dynamics
  14. The Full Digital Twin
  15. The Quantity-of-Interest
  16. ...and 9 more sections

Figures (16)

  • Figure 1.1: PDDP (physical-to-digital-digital-to-physical) data flow for Digital Twin (XiuTartakovsky_PDDP).
  • Figure 3.1: DNN structure for FML targeted Digital Twin model.
  • Figure 4.1: Setup for the flow past cylinder simulation. Left: computational domain; Right: computational mesh.
  • Figure 4.2: Illustration of $10$ training data sampled from a single full DT simulation trajectory for $t\in[0, 200]$ at $Re=1997.055$. Note that the $Re$ number is not recorded.
  • Figure 4.3: Illustration of $10$ training data sampled from a single full DT simulation trajectory for $t\in[0, 200]$ at $Re=195.763$. Note that the $Re$ number is not recorded.
  • ...and 11 more figures

Theorems & Definitions (1)

  • Definition 2.1