35 lines
815 B
Markdown
35 lines
815 B
Markdown
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# Mean Field Games
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Solve 1D Mean Field Games and Mean Field-Type Control problems using the Rust backend.
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## Key Concepts
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- Coupled HJB–Fokker-Planck PDE system
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- Density evolution over time/space
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- Congestion and noise parameters control stability
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## Usage
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```python
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from optimizr import MFGConfig, solve_mfg_1d_rust
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config = MFGConfig(
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nx=64,
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nt=40,
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x_min=-3.0,
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x_max=3.0,
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T=1.0,
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epsilon=0.1,
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kappa=1.0,
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)
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solution = solve_mfg_1d_rust(config)
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print("Converged:", solution.converged)
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print("Value function grid:", solution.value_function.shape)
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print("Density grid:", solution.density.shape)
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```
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## Tips
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- Increase `nx`/`nt` for smoother solutions; expect higher compute.
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- Reduce `epsilon` for sharper dynamics; increase if unstable.
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- Use `kappa` to control congestion cost.
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