# Control of Two-way Coupled Fluid Systems with Differentiable Solvers

arXiv: https://arxiv.org/abs/2206.00342 · HTML: https://mlsanity.com/paper/2206.00342/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 40 references that are in the map.
- First posted on arXiv 1 Jun 2022.

## Builds on (most cited first, 16 of 16)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1708.06850/) (2017)
- [Accelerated Policy Learning with Parallel Differentiable Simulation](https://mlsanity.com/paper/2204.07137/) (2022)
- [Efficient collective swimming by harnessing vortices through deep reinforcement learning](https://mlsanity.com/paper/1802.02674/) (2018)
- [Deep Dynamical Modeling and Control of Unsteady Fluid Flows](https://mlsanity.com/paper/1805.07472/) (2018)
- [Learning Compositional Koopman Operators for Model-Based Control](https://mlsanity.com/paper/1910.08264/) (2019)
- [SPNets: Differentiable Fluid Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1806.06094/) (2018)
- [Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows](https://mlsanity.com/paper/2007.00936/) (2020)
- [Deep Learning-Aided Model Predictive Control of Wind Farms for AGC Considering the Dynamic Wake Effect](https://mlsanity.com/paper/2006.09656/) (2020)

## Built on by (most cited first, 1 of 1)

- [A domain decomposition-based autoregressive deep learning model for unsteady and nonlinear partial differential equations](https://mlsanity.com/paper/2408.14461/) (2024)

## Abstract (arXiv)

We investigate the use of deep neural networks to control complex nonlinear dynamical systems, specifically the movement of a rigid body immersed in a fluid. We solve the Navier Stokes equations with two way coupling, which gives rise to nonlinear perturbations that make the control task very challenging. Neural networks are trained in an unsupervised way to act as controllers with desired characteristics through a process of learning from a differentiable simulator. Here we introduce a set of physically interpretable loss terms to let the networks learn robust and stable interactions. We demonstrate that controllers trained in a canonical setting with quiescent initial conditions reliably generalize to varied and challenging environments such as previously unseen inflow conditions and forcing, although they do not have any fluid information as input. Further, we show that controllers trained with our approach outperform a variety of classical and learned alternatives in terms of evaluation metrics and generalization capabilities.