# Physical Design using Differentiable Learned Simulators

arXiv: https://arxiv.org/abs/2202.00728 · HTML: https://mlsanity.com/paper/2202.00728/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 77 references that are in the map.
- First posted on arXiv 1 Feb 2022.

## Builds on (most cited first, 30 of 35)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Training Deep Nets with Sublinear Memory Cost](https://mlsanity.com/paper/1604.06174/) (2016)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Generalisation in humans and deep neural networks](https://mlsanity.com/paper/1808.08750/) (2018)
- [Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids](https://mlsanity.com/paper/1810.01566/) (2018)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Embodied Intelligence via Learning and Evolution](https://mlsanity.com/paper/2102.02202/) (2021)
- [Benchmarking Model-Based Reinforcement Learning](https://mlsanity.com/paper/1907.02057/) (2019)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [PHYRE: A New Benchmark for Physical Reasoning](https://mlsanity.com/paper/1908.05656/) (2019)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [Learned Coarse Models for Efficient Turbulence Simulation](https://mlsanity.com/paper/2112.15275/) (2021)
- [SPNets: Differentiable Fluid Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1806.06094/) (2018)
- [Rapid trial-and-error learning with simulation supports flexible tool use and physical reasoning](https://mlsanity.com/paper/1907.09620/) (2019)
- [On the role of planning in model-based deep reinforcement learning](https://mlsanity.com/paper/2011.04021/) (2020)
- [An End-to-End Differentiable Framework for Contact-Aware Robot Design](https://mlsanity.com/paper/2107.07501/) (2021)

## Built on by (most cited first, 30 of 37)

- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [MultiScale MeshGraphNets](https://mlsanity.com/paper/2210.00612/) (2022)
- [Operator Learning with Neural Fields: Tackling PDEs on General Geometries](https://mlsanity.com/paper/2306.07266/) (2023)
- [Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformers](https://mlsanity.com/paper/2302.10803/) (2023)
- [Learning to Accelerate Partial Differential Equations via Latent Global Evolution](https://mlsanity.com/paper/2206.07681/) (2022)
- [Learning Neural PDE Solvers with Parameter-Guided Channel Attention](https://mlsanity.com/paper/2304.14118/) (2023)
- [Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformer](https://mlsanity.com/paper/2312.12467/) (2023)
- [Swarm Reinforcement Learning For Adaptive Mesh Refinement](https://mlsanity.com/paper/2304.00818/) (2023)
- [Grounding Graph Network Simulators using Physical Sensor Observations](https://mlsanity.com/paper/2302.11864/) (2023)
- [MMGP: a Mesh Morphing Gaussian Process-based machine learning method for regression of physical problems under non-parameterized geometrical variability](https://mlsanity.com/paper/2305.12871/) (2023)
- [A review of graph neural network applications in mechanics-related domains](https://mlsanity.com/paper/2407.11060/) (2024)
- [Drag-guided diffusion models for vehicle image generation](https://mlsanity.com/paper/2306.09935/) (2023)
- [3D-IntPhys: Towards More Generalized 3D-grounded Visual Intuitive Physics under Challenging Scenes](https://mlsanity.com/paper/2304.11470/) (2023)
- [Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systems](https://mlsanity.com/paper/2211.01873/) (2022)
- [Thermodynamics of learning physical phenomena](https://mlsanity.com/paper/2207.12749/) (2022)
- [VLMgineer: Vision Language Models as Robotic Toolsmiths](https://mlsanity.com/paper/2507.12644/) (2025)
- [OmniArch: Building Foundation Model For Scientific Computing](https://mlsanity.com/paper/2402.16014/) (2024)
- [Latent Intuitive Physics: Learning to Transfer Hidden Physics from A 3D Video](https://mlsanity.com/paper/2406.12769/) (2024)
- [Learning to Design and Use Tools for Robotic Manipulation](https://mlsanity.com/paper/2311.00754/) (2023)
- [Graph Neural Network Based Surrogate Model of Physics Simulations for Geometry Design](https://mlsanity.com/paper/2302.00557/) (2023)
- [Inverse analysis of granular flows using differentiable graph neural network simulator](https://mlsanity.com/paper/2401.13695/) (2024)
- [Up-sampling-only and Adaptive Mesh-based GNN for Simulating Physical Systems](https://mlsanity.com/paper/2409.04740/) (2024)
- [RobotSmith: Generative Robotic Tool Design for Acquisition of Complex Manipulation Skills](https://mlsanity.com/paper/2506.14763/) (2025)
- [SURFSUP: Learning Fluid Simulation for Novel Surfaces](https://mlsanity.com/paper/2304.06197/) (2023)
- [Diffusion Generative Inverse Design](https://mlsanity.com/paper/2309.02040/) (2023)
- [Learning Effective Dynamics across Spatio-Temporal Scales of Complex Flows](https://mlsanity.com/paper/2502.07990/) (2025)
- [A Design Co-Pilot for Task-Tailored Manipulators](https://mlsanity.com/paper/2509.13077/) (2025)
- [Accelerating PDE-Constrained Optimization by the Derivative of Neural Operators](https://mlsanity.com/paper/2506.13120/) (2025)

## Abstract (arXiv)

Designing physical artifacts that serve a purpose - such as tools and other functional structures - is central to engineering as well as everyday human behavior. Though automating design has tremendous promise, general-purpose methods do not yet exist. Here we explore a simple, fast, and robust approach to inverse design which combines learned forward simulators based on graph neural networks with gradient-based design optimization. Our approach solves high-dimensional problems with complex physical dynamics, including designing surfaces and tools to manipulate fluid flows and optimizing the shape of an airfoil to minimize drag. This framework produces high-quality designs by propagating gradients through trajectories of hundreds of steps, even when using models that were pre-trained for single-step predictions on data substantially different from the design tasks. In our fluid manipulation tasks, the resulting designs outperformed those found by sampling-based optimization techniques. In airfoil design, they matched the quality of those obtained with a specialized solver. Our results suggest that despite some remaining challenges, machine learning-based simulators are maturing to the point where they can support general-purpose design optimization across a variety of domains.