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@h-livv h-livv released this 04 Jul 19:48
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Tempest v1.0.0

The first stable release of Tempest, a modular framework for simulating, validating, and learning PDE evolution operators.

This release establishes the numerical and architectural foundations of the project, including a validated PDE framework, automated verification pipeline, and an initial scientific machine learning workflow.


Major Features

Numerical Simulation

Implemented support for:

  • Linear advection
  • Diffusion
  • Wave equation
  • Burgers' equation
  • Shallow water equations

along with a modular framework for structured grids, boundary conditions, initial conditions, and configurable numerical methods.

Numerical Methods

Time integration:

  • Explicit Euler
  • Runge–Kutta 4
  • Leapfrog
  • Lax–Friedrichs
  • Lax–Wendroff

Spatial discretization:

  • Upwind gradients
  • Central gradients
  • Laplacian

Validation & Verification

Introduced a comprehensive validation pipeline including:

  • Analytical solution comparison
  • Error analysis
  • Grid convergence studies
  • Stability diagnostics
  • Energy conservation monitoring

The framework reproduces several classical numerical behaviors, including numerical diffusion, dispersion, Hamiltonian conservation, and the limitations of linear schemes near discontinuities.


Scientific Machine Learning

Added the first experimental machine learning pipeline for learning PDE evolution operators.

Current capabilities include:

  • Lightweight CNN surrogate
  • Stable autoregressive rollout
  • Translation-consistent transport
  • Generalization to unseen initial conditions
  • Long-horizon prediction
  • Significant inference speedup over numerical integration
  • Architecture

The framework is organized into independent modules for:

  • Simulation
  • Physics
  • Numerical methods
  • Validation
  • Diagnostics
  • Visualization
  • Machine learning

allowing numerical solvers and learned operators to share a common computational pipeline.


Looking Ahead

Development beyond v1.0.0 will focus on:

  • Simulation of increasingly complex two-dimensional physical phenomena
  • Atmospheric and geophysical flows
  • Multi-dimensional surrogate models
  • Neural operators
  • Additional PDE families beyond fluid dynamics

The long-term objective is to develop Tempest into a unified computational framework for numerical simulation, scientific machine learning, and the study of physical systems governed by partial differential equations.