Metamizer: A Versatile Neural Optimizer for Fast and Accurate Physics Simulations

Nils Wandel, Stefan Schulz, Reinhard Klein

Keywords: Physics-based Deep Learning, Physics Simulations, Meta-Learning

TL;DR: Metamizer is a fast and accurate neural optimizer that iteratively solves a wide range of physical systems, including Poisson, advection-diffusion, wave, Navier-Stokes, and Burgers equations.

Abstract:

Efficient physics simulations are essential for numerous applications, ranging from realistic cloth animations 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 are computationally demanding.
Latest developments in the field of physics-based Deep Learning have led to promising efficiency gains but still suffer from limited generalization capabilities across multiple different PDEs.

Thus, in this work, we introduce **Metamizer**, a novel neural optimizer that iteratively solves a wide range of physical systems without retraining 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 high accuracy 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.

Primary Area: transfer learning, meta learning, and lifelong learning

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Submission Number: 5055