Part VII: Calibration & KPZ
Bayesian parameter estimation, stochastic growth interfaces, and high-performance brute-force search.
Part Overview
This part bridges simulation to reality: calibrating urban models with Bayesian inference, connecting stochastic surface growth to the KPZ universality class, and deploying Fortran-level brute-force parameter sweeps for exhaustive exploration of model space.
Key Topics
- • Metropolis-Hastings MCMC
- • Posterior sampling
- • KPZ equation: \(\partial_t h = \nu \nabla^2 h + \tfrac{\lambda}{2}(\nabla h)^2 + \eta\)
- • Roughness exponent measurement
- • Fortran parameter search
3 chapters | Estimation & universality | From posteriors to growth exponents
Chapters
Chapter 1: Bayesian MCMC
Metropolis-Hastings sampling of posterior distributions for urban model parameters. Convergence diagnostics, burn-in, and credible intervals from \(p(\theta \mid \mathcal{D}) \propto \mathcal{L}(\mathcal{D}\mid\theta)\,\pi(\theta)\).
Chapter 2: KPZ Equation
The Kardar-Parisi-Zhang equation \(\partial_t h = \nu \nabla^2 h + \tfrac{\lambda}{2}(\nabla h)^2 + \eta\) as a universal description of stochastic interface growth. Roughness exponents, dynamic scaling, and connections to urban boundary evolution.
Chapter 3: Fortran Parameter Search
High-performance brute-force exploration of parameter space using compiled Fortran. Grid sweeps, parallelization strategies, and identifying optimal parameter regimes for urban simulation models.