用于学习拉格朗日流体力学的对称基卷积
Symmetric Basis Convolutions for Learning Lagrangian Fluid Mechanics
AI总结：
提出基于可分离基函数的连续卷积通用公式，证明奇偶对称性对稳定性和准确性至关重要，且基于Fourier的卷积在准确性和泛化性上表现最优，使窗口函数等先验偏置不再必要。
摘要：
学习物理模拟一直是近期机器学习研究的核心，特别是针对基于Navier-Stokes的流体力学。传统数值求解器计算成本高昂且难以用于逆问题，而神经求解器旨在通过机器学习解决这两个问题。我们提出了一种使用可分离基函数的连续卷积通用公式，作为现有方法的超集，并在以下场景中评估了大量基函数：(a) 可压缩1D SPH模拟，(b) 弱可压缩2D SPH模拟，(c) 不可压缩2D SPH模拟。我们证明基函数中包含的奇偶对称性是稳定性和准确性的关键。广泛评估表明，基于Fourier的连续卷积在准确性和泛化性上优于所有其他架构。最后，使用这些基于Fourier的网络，我们证明先前的归纳偏置（如窗口函数）不再必要。我们的方法实现、完整数据集和求解器实现可在 https://github.com/tum-pbs/SFBC 获取。
英文摘要：
Learning physical simulations has been an essential and central aspect of many recent research efforts in machine learning, particularly for Navier-Stokes-based fluid mechanics. Classic numerical solvers have traditionally been computationally expensive and challenging to use in inverse problems, whereas Neural solvers aim to address both concerns through machine learning. We propose a general formulation for continuous convolutions using separable basis functions as a superset of existing methods and evaluate a large set of basis functions in the context of (a) a compressible 1D SPH simulation, (b) a weakly compressible 2D SPH simulation, and (c) an incompressible 2D SPH Simulation. We demonstrate that even and odd symmetries included in the basis functions are key aspects of stability and accuracy. Our broad evaluation shows that Fourier-based continuous convolutions outperform all other architectures regarding accuracy and generalization. Finally, using these Fourier-based networks, we show that prior inductive biases, such as window functions, are no longer necessary. An implementation of our approach, as well as complete datasets and solver implementations, is available at https://github.com/tum-pbs/SFBC.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
