Deep neural network based surrogates for partial differential equations have recently gained increased interest. However, akin to their numerical counterparts, different techniques are used across applications, even if the underlying dynamics of the systems are similar. A prominent example is the Lagrangian and Eulerian specification in computational fluid dynamics, posing a challenge for neural networks to effectively model particle- as opposed to grid-based dynamics. We introduce Universal Physics Transformers (UPTs), a novel learning paradigm which models a wide range of spatio-temporal problems - both for Lagrangian and Eulerian discretization schemes. UPTs operate without grid- or particle-based latent structures, enabling flexibility across meshes and particles. UPTs efficiently propagate dynamics in the latent space, emphasized by inverse encoding and decoding techniques. Finally, UPTs allow for queries of the latent space representation at any point in space-time. We demonstrate the efficacy of UPTs in mesh-based fluid simulations, steady-state Reynolds averaged Navier-Stokes simulations, and Lagrangian-based dynamics. Project page: https://ml-jku.github.io/UPT

翻译：基于深度神经网络的偏微分方程替代模型近年来受到越来越多的关注。然而，类似于其数值对应方法，即使系统的基本动力学相似，不同应用中也使用了不同的技术。计算流体动力学中的拉格朗日与欧拉规范便是一个典型例子，这对神经网络有效建模基于粒子而非网格的动力学提出了挑战。我们引入了通用物理变换器（UPTs），这是一种新颖的学习范式，能够建模广泛的时空问题——既适用于拉格朗日离散化方案，也适用于欧拉离散化方案。UPTs无需基于网格或粒子的潜在结构，从而在网格和粒子上展现出灵活性。UPTs通过逆编码与逆解码技术，在潜在空间中高效传播动力学特性。最后，UPTs允许在时空任意点上对潜在空间表示进行查询。我们在基于网格的流体模拟、稳态雷诺平均纳维-斯托克斯模拟以及基于拉格朗日动力学的实验中展示了UPTs的有效性。项目页面：https://ml-jku.github.io/UPT