TortillaChip/burgers1d-periodic

这是一个用于训练和基准测试神经算子的1D粘性Burgers方程在周期性域上的输入-输出对数据集。每个样本将一个初始条件u_0(x) = u(x, 0)映射到解u(x, t_end)。初始条件是从高斯随机场中抽取的，并使用伪谱方法数值求解PDE。1D粘性Burgers方程在周期性域x ∈ [0, 1)上定义为∂u/∂t = -u∂u/∂x + ν∂²u/∂x²，其中ν > 0是运动粘度。初始条件根据u_0 ∼ N(0, 625(-Δ + 25I)⁻²)采样，其中Δ是拉普拉斯算子。时间积分采用四阶Runge-Kutta方法处理对流项，后向欧拉方法处理扩散项，并在谱空间中通过点乘精确求解线性系统。数据集包含1280个样本，空间分辨率为8192，运动粘度为0.02，时间步长为1e-5，结束时间为1.0。

Input–output pairs for the 1D viscous Burgers equation on a periodic domain, intended for training and benchmarking neural operators. Each sample maps an initial condition u_0(x) = u(x, 0) to the solution u(x, t_end). Initial conditions are drawn from a Gaussian random field and the PDE is solved numerically with a pseudo-spectral method. The 1D viscous Burgers equation on a periodic domain x ∈ [0, 1) is defined as ∂u/∂t = -u∂u/∂x + ν∂²u/∂x², where ν > 0 is the kinematic viscosity. Initial conditions are sampled according to u_0 ∼ N(0, 625(-Δ + 25I)⁻²), where Δ is the Laplacian. The equation is integrated forward in time with a fourth-order Runge-Kutta method for the convective term and a backward Euler method for the diffusive term, with the resulting linear system solved exactly by a point-wise multiplication in spectral space. The dataset contains 1280 samples with a spatial resolution of 8192, kinematic viscosity of 0.02, time-step size of 1e-5, and end time of 1.0.