README.md

metadata

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: ${\mathrm{\partial }}_{t}u+u{\mathrm{\partial }}_{x}u=0\backslash partial\_t\; u\; +\; u\; \backslash partial\_x\; u\; =\; 0$
• Initial Conditions: Drawn from a Gaussian Random Field (GRF) with a squared exponential kernel ( $l=0.1l=0.1$ ).
• 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