| --- |
| language: |
| - en |
| license: mit |
| tags: |
| - physics |
| - pde |
| - pino |
| - fno |
| - neural-operator |
| - burgers-equation |
| - scientific-computing |
| - fluid-dynamics |
| pretty_name: PIFNO-LAW (Learned Adaptive Weighting for Physics-Informed FNO) |
| size_categories: |
| - 1GB<n<10GB |
| --- |
| |
|
|
| ## 📊 Dataset Description |
|
|
| This dataset provides comprehensive one-dimensional inviscid Burgers' equation simulations, explicitly generated for training and evaluating advanced operator learning architectures. |
|
|
| ### 1D Inviscid Burgers' Equation |
| - **Equation**: \\(\partial_t u + u \partial_x u = 0\\) |
| - **Initial Conditions**: Drawn from a Gaussian Random Field (GRF) with a squared exponential kernel ( \\(l=0.1\\) ). |
| - **Solver**: High-fidelity Fifth-order WENO (WENO5) with an HLL Riemann solver and RK3 time integration. |
| - **Goal**: Evaluate accurate resolution of nonlinear wave steepening and shock formation. |
|
|
| ## 📂 Data Structure |
|
|
| ### 1D Benchmark (`burgers.h5`) |
| - **Resolution**: 1,024 spatial points, 51 time steps. |
| - **Fields**: |
| - `x`: Spatial grid |
| - `t`: Temporal grid |
| - `u`: Scalar solution field |
|
|
