Fast and stable fluid simulations are an essential prerequisite for applications ranging from computer-generated imagery to computer-aided design in research and development. However, solving the partial differential equations of incompressible fluids is a challenging task and traditional numerical approximation schemes come at high computational costs. Recent deep learning based approaches promise vast speed-ups but do not generalize to new fluid domains, require fluid simulation data for training, or rely on complex pipelines that outsource major parts of the fluid simulation to traditional methods.
In this work, we propose a novel physics-constrained training approach that generalizes to new fluid domains, requires no fluid simulation data, and allows convolutional neural networks to map a fluid state from time-point t to a subsequent state at time t + dt in a single forward pass. This simplifies the pipeline to train and evaluate neural fluid models. After training, the framework yields models that are capable of fast fluid simulations and can handle various fluid phenomena including the Magnus effect and Karman vortex streets. We present an interactive real-time demo to show the speed and generalization capabilities of our trained models. Moreover, the trained neural networks are efficient differentiable fluid solvers as they offer a differentiable update step to advance the fluid simulation in time. We exploit this fact in a proof-of-concept optimal control experiment. Our models significantly outperform a recent differentiable fluid solver in terms of computational speed and accuracy.
Project and Generate: Divergence-Free Neural Operators for Incompressible Flows
Incubation Institute, Fudan University, Shanghai, China（复旦大学上海孵化院）；Shanghai Academy of Artificial Intelligence for Science, Shanghai, China（上海人工智能科学研究院）
Deep Random Vortex Method for Simulation and Inference of Navier-Stokes Equations
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）；Microsoft Research（微软研究院）；Bielefeld University（比勒费尔德大学）
纳维-斯托克斯方程是描述诸如液体和空气的流体运动的重要偏微分方程。由于纳维-斯托克斯方程的重要性，发展高效的数值格式对科学和工程都具有重要意义。近年来，随着人工智能技术的发展，人们设计了多种方法将深度神经网络集成到不可压纳维-斯托克斯方程的流体动力学模拟和推断中，这些方法可以以无网格和可微的方式加速模拟或推断过程。本文指出现有的深度Navier-Stokes方法在处理非光滑或分数阶方程时能力有限，而这两种情况在现实中是非常关键的。为此，我们提出了\emph{Deep Random Vortex Method}（DRVM），它结合了神经网络与随机涡动力学系统相当于纳维-斯托克斯方程。具体而言，随机涡流动力学激励基于蒙特卡罗的损失函数用于训练神经网络，这避免了通过自微分计算导数。因此，DRVM不仅可以高效地求解包含粗糙路径、不可微初始条件和分数阶算子的纳维-斯托克斯方程，而且继承了基于深度学习的求解器的无网格和可微的优点。我们进行实验的柯西问题，参数求解器学习，以及2-D和3-D不可压缩的纳维-斯托克斯方程的反问题。该方法对纳维-斯托克斯方程的数值模拟和推导都取得了较好的结果。特别是在初始条件奇异的情况下，DRVM的性能明显优于现有的PINN方法。
Physics-integrated neural differentiable modeling for immersed boundary systems
State Key Lab of Ocean Engineering, School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China（海洋工程国家重点实验室，海洋与civil工程学院，上海交通大学，上海200240，中国）；State Key Laboratory of Maritime Technology and Safety, Shanghai Ship and Shipping Research Institute Co., Ltd, Shanghai 200135, China（海洋技术与安全国家重点实验室，上海船舶研究所有限公司，上海200135，中国）
Efficient Symbolic Policy Learning with Differentiable Symbolic Expression
SKL of Processors, Institute of Computing Technology, CAS（中国科学院计算技术研究所处理器芯片全国重点实验室）；Intelligent Software Research Center, Institute of Software, CAS（中国科学院软件研究所智能软件研究中心）；University of Science and Technology of China, USTC（中国科学技术大学）；Cambricon Technologies（寒武纪科技）；Shanghai Innovation Center for Processor Technologies, SHIC（上海处理器技术创新中心）；University of Chinese Academy of Sciences, UCAS（中国科学院大学）
Generalizable data-driven turbulence closure modeling on unstructured grids with differentiable physics
School of Mechanical Engineering, Purdue University, West Lafayette, 47907, IN, USA（机械工程学院，普渡大学）；Mechanical Engineering Department, Carnegie Mellon University, Pittsburgh, 15213, PA, USA（机械工程系，卡内基梅隆大学）；Department of Aerospace Engineering, University of Michigan, Ann Arbor, 48109, MI, USA（航空航天工程系，密歇根大学）；College of Information Sciences and Technology, Pennsylvania State University, University Park, 16802, PA, USA（信息科学与技术学院，宾夕法尼亚州立大学）；Computer Science Division, Argonne National Laboratory, Lemont, 60439, IL, USA（计算机科学 division，阿贡国家实验室）
Neural Physics: Using AI Libraries to Develop Physics-Based Solvers for Incompressible Computational Fluid Dynamics
Applied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College London（地球科学与工程系应用建模与计算组，帝国理工学院伦敦分校）；Centre for AI-Physics Modelling, Imperial-X, Imperial College London（人工智能-物理建模中心，帝国-X，帝国理工学院伦敦分校）；Data Assimilation Laboratory, Data Science Institute, Imperial College London（数据同化实验室，数据科学研究所，帝国理工学院伦敦分校）
Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics
U.S. Army Engineer Research and Development Center（美国陆军工程研究与发展中心）
用于流体流动模拟的模型降阶在许多科学和工程领域中仍然具有极大的兴趣。在这里，我们探索了神经常微分方程的使用，这是一种最近引入的连续深度可微网络家族（Chen et al 2018），作为在降阶模型中传播潜在空间动力学的一种方式。我们比较他们的行为与两个经典的非侵入性方法的基础上适当的正交分解和径向基函数插值以及动态模式分解。我们考虑的测试问题包括不可压缩的圆柱绕流，以及在河流和河口系统的浅水流体动力学的实际应用。我们的研究结果表明，神经常微分方程提供了一个优雅的框架，潜在的空间动力学的稳定和准确的演变与外推预测的一个有前途的潜力。然而，为了促进它们在大规模系统中的广泛采用，需要做出重大努力来加快它们的培训时间。这将使超参数空间的更全面的探索，以建立广义的神经ODE近似在广泛的系统动力学。
