fix(thermo): stable kappa_dot/dkd_dloga gradient via n_H_0 rescaling - #20
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fix(thermo): stable kappa_dot/dkd_dloga gradient via n_H_0 rescaling#20MinhMPA wants to merge 1 commit into
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…ling The Friedmann-scan accumulates a spurious d(a_grid[i])/d(omega_b) eigenvalue product (~10^14 at loga=-8). The spline derivative's 1/h factor amplifies this by ~1200x, causing AD to return ~10^17 instead of the physical ~-335. Fix: stop all accumulated gradient in kappa_dot_grid, then restore only the n_H_0 ∝ omega_b path (exact, since kappa_dot ∝ n_H_0 linearly): _kappa_dot_for_deriv = sg(kappa_dot_grid) * n_H_0 / sg(n_H_0) Also adds dkappa_dot_dloga_of_loga to ThermoResult and the regression test test_opacity_logderivative_gradient_matches_fd_for_omega_b (<1% vs FD). Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
This was referenced May 12, 2026
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Summary
Fixes an exploding-gradient bug in the `kappa_dot` spline path. During reverse-mode AD, the Friedmann-scan eigenvalue blows up ~10¹² × for typical `omega_b` perturbations.
Root cause: `kappa_dot ∝ n_H_0 ∝ omega_b / m_H`. The recombination solver builds a spline over a frozen tau grid. During `jax.grad`, JAX differentiates through both the spline evaluation and the frozen-grid construction simultaneously, producing an ill-conditioned Jacobian.
Fix: Rescale at the evaluation site so that traced `n_H_0` enters only as a ratio:
```python
_kd_safe = stop_gradient(kappa_dot) * (n_H_0 / stop_gradient(n_H_0))
```
Value is unchanged (ratio = 1 at evaluation point); gradient routes through the analytic rescaling factor, not the spline Jacobian.
Changes
Merge order (4-PR AD-correctness series)
Test plan