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

TL;DR

Metamizer is a neural optimizer that significantly improves the accuracy and generalization of physics simulations across various PDEs and applications, potentially transforming numerical solver methods.

Contribution

Introduces Metamizer, a neural optimizer with a scale-invariant architecture that achieves high accuracy and generalizes to unseen PDEs, advancing physics-based deep learning methods.

Findings

Achieves near machine precision accuracy on multiple PDEs.

Generalizes to PDEs not seen during training.

Outperforms existing neural physics simulation approaches.

Abstract

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.