turing-neural-field-model

Turing Neural Field

Turing Neural Field learns the local dynamics of a Gray–Scott reaction-diffusion system. A compact circular-convolution network receives the two chemical fields plus feed and kill parameters, then predicts one physical update.

Evaluation separates trajectories by ID so test states never appear in training. The project compares one-step error with a no-change baseline and rolls the learned surrogate forward beside the numerical simulator.

Reproduce

uv run python projects/turing-neural-field/generate_data.py
uv run python projects/turing-neural-field/train.py

The generated GIF and Gradio comparison app show actual model rollouts. The simulator is still the source of truth; the neural field is an approximation.

Verified results

• Parameters: 15,090
• Training trajectories: 28
• Validation trajectories: 4
• Test trajectories: 4
• Held-out one-step states: 160
• Neural one-step MSE: 1.115 × 10⁻⁶
• No-change baseline MSE: 1.699 × 10⁻⁶
• One-step improvement: 34.37%
• 120-step final field MSE: 0.00414
• 120-step V-field correlation: 0.606

At step 120, physics had V-field mean 0.0169 and spatial standard deviation 0.0662; the surrogate produced 0.0128 and 0.0458. The learned rollout preserves the central ring topology but underestimates its radius and contrast. The final comparison PNG, animated GIF, and working Space app expose that drift directly.