# Direct shape optimization through deep reinforcement learning

arXiv: https://arxiv.org/abs/1908.09885 · HTML: https://mlsanity.com/paper/1908.09885/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Aug 2019.

## Built on by (most cited first, 28 of 28)

- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Physics-informed Dyna-Style Model-Based Deep Reinforcement Learning for Dynamic Control](https://mlsanity.com/paper/2108.00128/) (2021)
- [Multi-fidelity reinforcement learning framework for shape optimization](https://mlsanity.com/paper/2202.11170/) (2022)
- [Deep reinforcement learning for optimal well control in subsurface systems with uncertain geology](https://mlsanity.com/paper/2203.13375/) (2022)
- [Dynamic Feature-based Deep Reinforcement Learning for Flow Control of Circular Cylinder with Sparse Surface Pressure Sensing](https://mlsanity.com/paper/2307.01995/) (2023)
- [Multi-condition multi-objective optimization using deep reinforcement learning](https://mlsanity.com/paper/2110.05945/) (2021)
- [Sample-Efficient and Surrogate-Based Design Optimization of Underwater Vehicle Hulls](https://mlsanity.com/paper/2304.12420/) (2023)
- [Transfer learning-enhanced deep reinforcement learning for aerodynamic airfoil optimisation subject to structural constraints](https://mlsanity.com/paper/2505.02634/) (2025)
- [Deep learning fluid flow reconstruction around arbitrary two-dimensional objects from sparse sensors using conformal mappings](https://mlsanity.com/paper/2202.03798/) (2022)
- [Enhancing Vehicle Aerodynamics with Deep Reinforcement Learning in Voxelised Models](https://mlsanity.com/paper/2405.11492/) (2024)
- [Investigation of reinforcement learning for shape optimization of profile extrusion dies](https://mlsanity.com/paper/2212.12207/) (2022)
- [A reinforcement learning strategy to automate and accelerate h/p-multigrid solvers](https://mlsanity.com/paper/2407.15872/) (2024)
- [Non-iterative generation of an optimal mesh for a blade passage using deep reinforcement learning](https://mlsanity.com/paper/2209.05280/) (2022)
- [Active Control of Flow over Rotating Cylinder by Multiple Jets using Deep Reinforcement Learning](https://mlsanity.com/paper/2307.12083/) (2023)
- [Physics-Driven ML-Based Modelling for Correcting Inverse Estimation](https://mlsanity.com/paper/2309.13985/) (2023)
- [Design Optimization of Nuclear Fusion Reactor through Deep Reinforcement Learning](https://mlsanity.com/paper/2409.08231/) (2024)
- [Heuristic Learning for Active Flow Control Using Coding Agents](https://mlsanity.com/paper/2607.11565/) (2026)
- [Stabilising viscous extensional flows using Reinforcement Learning](https://mlsanity.com/paper/2110.14677/) (2021)
- [A mechanism-driven reinforcement learning framework for shape optimization of airfoils](https://mlsanity.com/paper/2403.04329/) (2024)
- [Anvil: An integration of artificial intelligence, sampling techniques, and a combined CAD-CFD tool](https://mlsanity.com/paper/2407.02519/) (2024)
- [Deep Reinforcement Learning for the Design of Metamaterial Mechanisms with Functional Compliance Control](https://mlsanity.com/paper/2408.04376/) (2024)
- [Reinforcement learning framework for the mechanical design of microelectronic components under multiphysics constraints](https://mlsanity.com/paper/2504.17142/) (2025)
- [Reinforcement Learning for Accelerated Aerodynamic Shape Optimisation](https://mlsanity.com/paper/2507.17786/) (2025)
- [Oranits: Mission Assignment and Task Offloading in Open RAN-based ITS using Metaheuristic and Deep Reinforcement Learning](https://mlsanity.com/paper/2507.19712/) (2025)
- [Transfer learning strategies for accelerating reinforcement-learning-based flow control](https://mlsanity.com/paper/2510.16016/) (2025)
- [DiffeoMorph: Learning to Morph 3D Shapes Using Differentiable Agent-Based Simulations](https://mlsanity.com/paper/2512.17129/) (2025)
- [BladeSDF : Unconditional and Conditional Generative Modeling of Representative Blade Geometries Using Signed Distance Functions](https://mlsanity.com/paper/2601.13445/) (2026)
- [Large language models for partial differential equation workflows](https://mlsanity.com/paper/2608.03600/) (2026)

## Abstract (arXiv)

Deep Reinforcement Learning (DRL) has recently spread into a range of domains within physics and engineering, with multiple remarkable achievements. Still, much remains to be explored before the capabilities of these methods are well understood. In this paper, we present the first application of DRL to direct shape optimization. We show that, given adequate reward, an artificial neural network trained through DRL is able to generate optimal shapes on its own, without any prior knowledge and in a constrained time. While we choose here to apply this methodology to aerodynamics, the optimization process itself is agnostic to details of the use case, and thus our work paves the way to new generic shape optimization strategies both in fluid mechanics, and more generally in any domain where a relevant reward function can be defined.