---
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