Issues Encountered

1. Numerical instability / NaNs

• ODE solver can produce NaNs for extreme parameter values.
• Fixes: check parameter bounds, improve initialization, catch exceptions and return large loss.

2. Stiff dynamics

• Some parameter regimes are stiff (very small or large rates).
• Fixes: use a stiff solver (e.g., scipy.integrate.solve_ivp with method='BDF'), tighten tolerances.

3. Overfitting to noise

• Deterministic optimizers can pick parameters that explain a particular noise realization.
• Fixes: regularize loss, fit across multiple noise realizations, or use Bayesian inference.

4. MCMC walker initialization problems

• Walkers outside priors cause immediate failure.
• Fixes: sample initial walker positions from a distribution strictly inside priors.