# Deep Dynamical Modeling and Control of Unsteady Fluid Flows

arXiv: https://arxiv.org/abs/1805.07472 · HTML: https://mlsanity.com/paper/1805.07472/

## Key facts

- Cited by 68 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2018.

## Built on by (most cited first, 30 of 68)

- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [Operator Learning: Algorithms and Analysis](https://mlsanity.com/paper/2402.15715/) (2024)
- [Solving PDE-constrained Control Problems Using Operator Learning](https://mlsanity.com/paper/2111.04941/) (2021)
- [Meta-Learning Dynamics Forecasting Using Task Inference](https://mlsanity.com/paper/2102.10271/) (2021)
- [gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification](https://mlsanity.com/paper/2204.12005/) (2022)
- [Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics](https://mlsanity.com/paper/2210.06036/) (2022)
- [Physics vs Distributions: Pareto Optimal Flow Matching with Physics Constraints](https://mlsanity.com/paper/2506.08604/) (2025)
- [The transformative potential of machine learning for experiments in fluid mechanics](https://mlsanity.com/paper/2303.15832/) (2023)
- [Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operators](https://mlsanity.com/paper/2402.12365/) (2024)
- [Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks](https://mlsanity.com/paper/2504.02843/) (2025)
- [Multifactor Sequential Disentanglement via Structured Koopman Autoencoders](https://mlsanity.com/paper/2303.17264/) (2023)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Learning invariant representations of time-homogeneous stochastic dynamical systems](https://mlsanity.com/paper/2307.09912/) (2023)
- [Solving Inverse Physics Problems with Score Matching](https://mlsanity.com/paper/2301.10250/) (2023)
- [Physics-informed active learning with simultaneous weak-form latent space dynamics identification](https://mlsanity.com/paper/2407.00337/) (2024)
- [An Operator Theoretic Approach for Analyzing Sequence Neural Networks](https://mlsanity.com/paper/2102.07824/) (2021)
- [Model reduction for the material point method via an implicit neural representation of the deformation map](https://mlsanity.com/paper/2109.12390/) (2021)
- [Koopman-Assisted Reinforcement Learning](https://mlsanity.com/paper/2403.02290/) (2024)
- [Neural Koopman prior for data assimilation](https://mlsanity.com/paper/2309.05317/) (2023)
- [Consistent Long-Term Forecasting of Ergodic Dynamical Systems](https://mlsanity.com/paper/2312.13426/) (2023)
- [Innovations Autoencoder and its Application in One-class Anomalous Sequence Detection](https://mlsanity.com/paper/2106.12382/) (2021)
- [Physics-Guided Discovery of Highly Nonlinear Parametric Partial Differential Equations](https://mlsanity.com/paper/2106.01078/) (2021)
- [Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectories](https://mlsanity.com/paper/2209.09977/) (2022)
- [CKNet: A Convolutional Neural Network Based on Koopman Operator for Modeling Latent Dynamics from Pixels](https://mlsanity.com/paper/2102.10205/) (2021)
- [Phi-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilation](https://mlsanity.com/paper/2209.15609/) (2022)
- [Leveraging Neural Koopman Operators to Learn Continuous Representations of Dynamical Systems from Scarce Data](https://mlsanity.com/paper/2303.06972/) (2023)
- [Latent Neural PDE Solver: a reduced-order modelling framework for partial differential equations](https://mlsanity.com/paper/2402.17853/) (2024)
- [Stochastic Adversarial Koopman Model for Dynamical Systems](https://mlsanity.com/paper/2109.05095/) (2021)
- [Half-Inverse Gradients for Physical Deep Learning](https://mlsanity.com/paper/2203.10131/) (2022)

## Abstract (arXiv)

The design of flow control systems remains a challenge due to the nonlinear nature of the equations that govern fluid flow. However, recent advances in computational fluid dynamics (CFD) have enabled the simulation of complex fluid flows with high accuracy, opening the possibility of using learning-based approaches to facilitate controller design. We present a method for learning the forced and unforced dynamics of airflow over a cylinder directly from CFD data. The proposed approach, grounded in Koopman theory, is shown to produce stable dynamical models that can predict the time evolution of the cylinder system over extended time horizons. Finally, by performing model predictive control with the learned dynamical models, we are able to find a straightforward, interpretable control law for suppressing vortex shedding in the wake of the cylinder.