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

arXiv: https://arxiv.org/abs/2510.07549 · HTML: https://mlsanity.com/paper/2510.07549/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 8 Oct 2025.

## Builds on (most cited first, 12 of 12)

- [Data Driven Governing Equations Approximation Using Deep Neural Networks](https://mlsanity.com/paper/1811.05537/) (2018)
- [A Probabilistic Graphical Model Foundation for Enabling Predictive Digital Twins at Scale](https://mlsanity.com/paper/2012.05841/) (2020)
- [Data-Driven Deep Learning of Partial Differential Equations in Modal Space](https://mlsanity.com/paper/1910.06948/) (2019)
- [Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space](https://mlsanity.com/paper/2106.03603/) (2021)
- [Learning Stochastic Dynamical System via Flow Map Operator](https://mlsanity.com/paper/2305.03874/) (2023)
- [Learning reduced systems via deep neural networks with memory](https://mlsanity.com/paper/2003.09451/) (2020)
- [Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarks](https://mlsanity.com/paper/2307.11013/) (2023)
- [Digital twin, physics-based model, and machine learning applied to damage detection in structures](https://mlsanity.com/paper/2005.14360/) (2020)
- [Digital Twins: State of the Art Theory and Practice, Challenges, and Open Research Questions](https://mlsanity.com/paper/2011.02833/) (2020)
- [Modeling Unknown Stochastic Dynamical System via Autoencoder](https://mlsanity.com/paper/2312.10001/) (2023)
- [Deep Learning of Chaotic Systems from Partially-Observed Data](https://mlsanity.com/paper/2205.08384/) (2022)
- [Modeling unknown dynamical systems with hidden parameters](https://mlsanity.com/paper/2202.01858/) (2022)

## Built on by (most cited first, 5 of 5)

- [Neural-POD: A Plug-and-Play Neural Operator Framework for Infinite-Dimensional Functional Nonlinear Proper Orthogonal Decomposition](https://mlsanity.com/paper/2602.15632/) (2026)
- [PIP2 Net: Physics-informed Partition Penalty Deep Operator Network](https://mlsanity.com/paper/2512.15086/) (2025)
- [A Continual Validation, Updating, and Decision-Making Framework for Self-Adaptive Digital Twins via Robust Model Predictive Control: A Case Study in Additive Manufacturing](https://mlsanity.com/paper/2607.18164/) (2026)
- [Modeling Unknown Nonlocal PDE Systems via Flow Map Learning](https://mlsanity.com/paper/2608.00400/) (2026)
- [Data-driven Effective Modeling of Stochastic Chemical Reaction Networks](https://mlsanity.com/paper/2608.25421/) (2026)

## Abstract (arXiv)

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.