# Learning Efficient Navigation in Vortical Flow Fields

arXiv: https://arxiv.org/abs/2102.10536 · HTML: https://mlsanity.com/paper/2102.10536/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 56 references that are in the map.
- First posted on arXiv 21 Feb 2021.

## Builds on (most cited first, 8 of 8)

- [Deep Reinforcement Learning that Matters](https://mlsanity.com/paper/1709.06560/) (2017)
- [Neural Lander: Stable Drone Landing Control using Learned Dynamics](https://mlsanity.com/paper/1811.08027/) (2018)
- [Efficient collective swimming by harnessing vortices through deep reinforcement learning](https://mlsanity.com/paper/1802.02674/) (2018)
- [Remember and Forget for Experience Replay](https://mlsanity.com/paper/1807.05827/) (2018)
- [Flow Navigation by Smart Microswimmers via Reinforcement Learning](https://mlsanity.com/paper/1701.08848/) (2017)
- [Zermelo's problem: Optimal point-to-point navigation in 2D turbulent flows using Reinforcement Learning](https://mlsanity.com/paper/1907.08591/) (2019)
- [GLAS: Global-to-Local Safe Autonomy Synthesis for Multi-Robot Motion Planning with End-to-End Learning](https://mlsanity.com/paper/2002.11807/) (2020)
- [Learning to swim in potential flow](https://mlsanity.com/paper/2009.14280/) (2020)

## Built on by (most cited first, 26 of 26)

- [The transformative potential of machine learning for experiments in fluid mechanics](https://mlsanity.com/paper/2303.15832/) (2023)
- [Leveraging arbitrary mobile sensor trajectories with shallow recurrent decoder networks for full-state reconstruction](https://mlsanity.com/paper/2307.11793/) (2023)
- [A Platform-Agnostic Deep Reinforcement Learning Framework for Effective Sim2Real Transfer towards Autonomous Driving](https://mlsanity.com/paper/2304.08235/) (2023)
- [Navigation in a simplified Urban Flow through Deep Reinforcement Learning](https://mlsanity.com/paper/2409.17922/) (2024)
- [HypeRL: Hypernetwork-Based Reinforcement Learning for Control of Parametrized Dynamical Systems](https://mlsanity.com/paper/2501.04538/) (2025)
- [Discovering Individual Rewards in Collective Behavior through Inverse Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2305.10548/) (2023)
- [Training microrobots to swim by a large language model](https://mlsanity.com/paper/2402.00044/) (2024)
- [Physics-Guided Actor-Critic Reinforcement Learning for Swimming in Turbulence](https://mlsanity.com/paper/2406.10242/) (2024)
- [Chemotaxis of sea urchin sperm cells through deep reinforcement learning](https://mlsanity.com/paper/2209.07407/) (2022)
- [Learning to swim efficiently in a nonuniform flow field](https://mlsanity.com/paper/2212.11482/) (2022)
- [A reinforcement learning path planning approach for range-only underwater target localization with autonomous vehicles](https://mlsanity.com/paper/2301.06863/) (2023)
- [Deep-learning-powered data analysis in plankton ecology](https://mlsanity.com/paper/2309.08500/) (2023)
- [Deep Dive into Model-free Reinforcement Learning for Biological and Robotic Systems: Theory and Practice](https://mlsanity.com/paper/2405.11457/) (2024)
- [Multi-modal Policies with Physics-informed Representations in Complex Fluid Environments](https://mlsanity.com/paper/2410.15250/) (2024)
- [Maximizing Seaweed Growth on Autonomous Farms: A Dynamic Programming Approach for Underactuated Systems Navigating on Uncertain Ocean Currents](https://mlsanity.com/paper/2307.01916/) (2023)
- [Mixing Artificial and Natural Intelligence: From Statistical Mechanics to AI and Back to Turbulence](https://mlsanity.com/paper/2403.17993/) (2024)
- [A critical assessment of reinforcement learning methods for microswimmer navigation in complex flows](https://mlsanity.com/paper/2505.05525/) (2025)
- [Controlling Topological Defects in Polar Fluids via Reinforcement Learning](https://mlsanity.com/paper/2507.19298/) (2025)
- [Smart navigation of a gravity-driven glider with adjustable centre-of-mass](https://mlsanity.com/paper/2510.09250/) (2025)
- [Navigation in a Three-Dimensional Urban Flow using Deep Reinforcement Learning](https://mlsanity.com/paper/2510.25679/) (2025)
- [How do trout regulate patterns of muscle contraction to optimize propulsive efficiency during steady swimming](https://mlsanity.com/paper/2512.01218/) (2025)
- [Khalasi: Energy-Efficient Navigation for Surface Vehicles in Vortical Flow Fields](https://mlsanity.com/paper/2512.06912/) (2025)
- [Emergence of a Flow-Assisted Casting Strategy for Olfactory Navigation via Memory-Augmented Reinforcement Learning](https://mlsanity.com/paper/2605.18881/) (2026)
- [Multi-agent rendezvous in fluid flows via reinforcement learning](https://mlsanity.com/paper/2606.11274/) (2026)
- [Flow-aware Optimal Navigation in Unsteady Flows through Reinforcement Learning](https://mlsanity.com/paper/2607.13553/) (2026)
- [HypEMBER: Hypernetwork-based Ensemble for Robust Policy Learning of Parametrized Dynamical Systems](https://mlsanity.com/paper/2607.19628/) (2026)

## Abstract (arXiv)

Efficient point-to-point navigation in the presence of a background flow field is important for robotic applications such as ocean surveying. In such applications, robots may only have knowledge of their immediate surroundings or be faced with time-varying currents, which limits the use of optimal control techniques for planning trajectories. Here, we apply a novel Reinforcement Learning algorithm to discover time-efficient navigation policies to steer a fixed-speed swimmer through an unsteady two-dimensional flow field. The algorithm entails inputting environmental cues into a deep neural network that determines the swimmer's actions, and deploying Remember and Forget Experience replay. We find that the resulting swimmers successfully exploit the background flow to reach the target, but that this success depends on the type of sensed environmental cue. Surprisingly, a velocity sensing approach outperformed a bio-mimetic vorticity sensing approach by nearly two-fold in success rate. Equipped with local velocity measurements, the reinforcement learning algorithm achieved near 100% success in reaching the target locations while approaching the time-efficiency of paths found by a global optimal control planner.