fusion-heat-transport-ai

Fusion Heat Transport PDE Benchmark

Benchmark suite for comparing numerical solvers of the 1D radial heat transport equation in fusion plasmas:

∂T/∂t = (1/r) ∂/∂r (r χ(|∂T/∂r|) ∂T/∂r)

where the nonlinear thermal diffusivity is:

• χ(|T'|) = (|T'| - 0.5)^α + 0.1 if |T'| > 0.5
• χ = 0.1 otherwise

Boundary conditions: Neumann ∂T/∂r = 0 at r=0, Dirichlet T=0 at r=1.

Solvers

Solver	Method	Time (ms)	L2 Error	Notes
cell_centered_fvm	Finite Volume	1.9	0.058	Fastest, conservative form
implicit_fdm	Crank-Nicolson FDM	2.2	0.083	Baseline, banded solver
compact4_fdm	4th-order Compact FDM	2.5	0.115	Higher spatial accuracy
imex_fdm	IMEX FDM	3.4	0.492	Split operator approach
chebyshev_spectral	Chebyshev Spectral	3.6	0.799	Spectral accuracy
p2_fem	P2 Finite Element	39.4	0.108	Quadratic elements, high accuracy
cosine_spectral	Cosine Expansion	2.5	varies	Unstable for α > 0.5
pinn_stub	Physics-Informed NN	-	-	Requires PyTorch (optional)

Performance measured at nr=51, dt=0.001, α=0.5, t_end=0.1

Quick Start

pip install -e ".[dev]"
# Requires: numpy>=1.24, scipy>=1.10, pytest>=7.0

# Run tests
make test

# Run benchmark
make benchmark
# or
python -m app.run_benchmark --alpha 0.0 0.5 1.0

CLI Options

Benchmark mode

--alpha    Nonlinearity parameters (default: 0.0 0.5 1.0)
--nr       Radial grid points (default: 51)
--dt       Time step (default: 0.001)
--t_end    Final time (default: 0.1)

ML solver selector

# Generate training data (~432 parameter combinations)
python -m app.run_benchmark --generate-data

# Train decision tree model
make train
# or: python -m policy.train --generate

# Use ML selector (runs only the predicted best solver)
python -m app.run_benchmark --use-ml-selector --alpha 1.5

# Incremental learning: run benchmark and update model with results
python -m app.run_benchmark --alpha 0.5 1.0 --update

Additional ML options:

--generate-data    Generate training data via parameter sweep
--use-ml-selector  Predict best solver with trained model, run only that one
--update           Append results to training data and retrain model
--model-path       Path to trained model (default: data/solver_model.npz)
--data-path        Path to training CSV (default: data/training_data.csv)

See docs/MANUAL.md for detailed ML selector documentation.

Solver Selection Policy

The best solver is selected by minimizing:

score = L2_error + λ × wall_time

where λ is configurable (default 0.1). The ML selector uses a numpy-only decision tree trained on 12 features (problem parameters + initial condition properties) to predict the best solver before running any computation. See policy/select.py.

Hypothesis-Driven Analysis

An interactive experiment framework for systematic solver analysis:

# Run 3 hypothesis verification cycles
python docs/analysis/experiment_framework.py --cycles 3

# Interactive mode
python docs/analysis/experiment_framework.py --interactive

# Generate final report
python docs/analysis/experiment_framework.py --report

Features:

• Predefined experiments (stability_map, ic_comparison, linear_regime, fine_sweep)
• Hypothesis tracking with verification history
• Automatic report generation in Markdown
• Multi-agent parallel analysis

Project Structure

app/                  CLI entrypoint
features/             PDE feature extraction (gradients, energy, etc.)
solvers/              Solver implementations
  ├── fdm/            FDM solvers (implicit, compact4, imex)
  ├── spectral/       Spectral solvers (cosine, chebyshev)
  ├── fem/            Finite Element (P2)
  ├── fvm/            Finite Volume (cell-centered)
  └── pinn/           Physics-Informed Neural Networks
metrics/              Error metrics (L2, L∞)
policy/               Solver selection policy + ML decision tree
reports/              CSV + markdown report generation
tests/                Unit tests
outputs/              Generated benchmark results (gitignored)
data/                 Training data + trained model (gitignored)
docs/
  ├── analysis/       Hypothesis-driven experiment tools
  │   ├── experiment_framework.py   # Main experiment framework
  │   ├── multi_agent_analysis.py   # Multi-agent analysis system
  │   ├── parallel_multi_agent.py   # Parallel execution
  │   └── verify_hypotheses.py      # Quick hypothesis verification
  ├── figures/        Generated figures for documentation
  └── TUTORIAL.md     Step-by-step guide

Documentation

• Tutorial — Step-by-step guide from first benchmark to ML selector
• Manual — Detailed reference for all features
• Analysis Tutorial — Hypothesis-driven experiment framework guide

Reference Solution

The reference is computed using the implicit FDM solver with 4x grid refinement and 4x smaller time step.

Recent Optimizations

All solvers have been optimized for performance:

Solver	Before	After	Speedup
Compact4 FDM	25.3ms	2.5ms	10.3x
Cell-Centered FVM	14.5ms	1.9ms	7.6x
P2 FEM	285.0ms	39.4ms	7.2x
Chebyshev Spectral	8.1ms	3.6ms	2.3x

Key optimizations:

• Replaced spsolve with solve_banded for tridiagonal systems
• Vectorized matrix assembly (P2 FEM, Chebyshev)
• Precomputed geometric factors outside time loops