# Metamizer: a versatile neural optimizer for fast and accurate physics simulations

arXiv: https://arxiv.org/abs/2410.19746 · HTML: https://mlsanity.com/paper/2410.19746/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 53 references that are in the map.
- First posted on arXiv 10 Oct 2024.

## Builds on (most cited first, 30 of 32)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [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)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks](https://mlsanity.com/paper/1906.05747/) (2019)
- [Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems](https://mlsanity.com/paper/2107.12146/) (2021)
- [Generalized Inner Loop Meta-Learning](https://mlsanity.com/paper/1910.01727/) (2019)
- [SNUG: Self-Supervised Neural Dynamic Garments](https://mlsanity.com/paper/2204.02219/) (2022)
- [learn2learn: A Library for Meta-Learning Research](https://mlsanity.com/paper/2008.12284/) (2020)
- [Physics-based Deep Learning](https://mlsanity.com/paper/2109.05237/) (2021)
- [Training Stronger Baselines for Learning to Optimize](https://mlsanity.com/paper/2010.09089/) (2020)
- [Teaching the Incompressible Navier-Stokes Equations to Fast Neural Surrogate Models in 3D](https://mlsanity.com/paper/2012.11893/) (2020)
- [Physics-informed Neural Networks to Model and Control Robots: a Theoretical and Experimental Investigation](https://mlsanity.com/paper/2305.05375/) (2023)
- [A Deep Conjugate Direction Method for Iteratively Solving Linear Systems](https://mlsanity.com/paper/2205.10763/) (2022)
- [RAMP-Net: A Robust Adaptive MPC for Quadrotors via Physics-informed Neural Network](https://mlsanity.com/paper/2209.09025/) (2022)
- [PCE-PINNs: Physics-Informed Neural Networks for Uncertainty Propagation in Ocean Modeling](https://mlsanity.com/paper/2105.02939/) (2021)
- [Physics-guided Shape-from-Template: Monocular Video Perception through Neural Surrogate Models](https://mlsanity.com/paper/2311.12796/) (2023)
- [Scale-invariant Learning by Physics Inversion](https://mlsanity.com/paper/2109.15048/) (2021)
- [RANS-PINN based Simulation Surrogates for Predicting Turbulent Flows](https://mlsanity.com/paper/2306.06034/) (2023)

## Built on by (most cited first, 7 of 7)

- [Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operators](https://mlsanity.com/paper/2601.14517/) (2026)
- [Physics-based machine learning for mantle convection simulations](https://mlsanity.com/paper/2505.16041/) (2025)
- [SAFT: Shape and Appearance of Fabrics from Template via Differentiable Physical Simulations from Monocular Video](https://mlsanity.com/paper/2509.08828/) (2025)
- [FNOPT: Resolution-Agnostic, Self-Supervised Cloth Simulation using Meta-Optimization with Fourier Neural Operators](https://mlsanity.com/paper/2512.05762/) (2025)
- [CloDS: Visual-Only Unsupervised Cloth Dynamics Learning in Unknown Conditions](https://mlsanity.com/paper/2602.01844/) (2026)
- [Alpha-RF: Automated RF-Filter-Circuit Design with Neural Simulator and Reinforcement Learning](https://mlsanity.com/paper/2603.00104/) (2026)
- [MetaColloc: Optimization-Free PDE Solving via Meta-Learned Basis Functions](https://mlsanity.com/paper/2605.12368/) (2026)

## Abstract (arXiv)

Efficient physics simulations are essential for numerous applications, ranging from realistic cloth animations or smoke effects in video games, to analyzing pollutant dispersion in environmental sciences, to calculating vehicle drag coefficients in engineering applications. Unfortunately, analytical solutions to the underlying physical equations are rarely available, and numerical solutions require high computational resources. Latest developments in the field of physics-based Deep Learning have led to promising efficiency improvements but still suffer from limited generalization capabilities and low accuracy compared to numerical solvers. In this work, we introduce Metamizer, a novel neural optimizer that iteratively solves a wide range of physical systems with high accuracy by minimizing a physics-based loss function. To this end, our approach leverages a scale-invariant architecture that enhances gradient descent updates to accelerate convergence. Since the neural network itself acts as an optimizer, training this neural optimizer falls into the category of meta-optimization approaches. We demonstrate that Metamizer achieves unprecedented accuracy for deep learning based approaches - sometimes approaching machine precision - across multiple PDEs after training on the Laplace, advection-diffusion and incompressible Navier-Stokes equation as well as on cloth simulations. Remarkably, the model also generalizes to PDEs that were not covered during training such as the Poisson, wave and Burgers equation. Our results suggest that Metamizer could have a profound impact on future numerical solvers, paving the way for fast and accurate neural physics simulations without the need for retraining.