Age-structured population equations avoid simulating every neuron, but convex spike hazards make first-moment closures systematically biased. We develop a predictive joint-Gaussian closure for adaptive stochastic escape-rate neurons. It evolves age-conditioned voltage and adaptation means, variances, and covariance, while Gaussian exponential tilting supplies spike-selected moment loss and conservative reinjection at age zero. Against matched microscopic Monte Carlo (MC) ground truth, mean-only, prescribed-voltage-variance, and dynamic-joint closures have baseline $50\text{−}\mathrm{ms}$-smoothed root-mean-square errors (RMSEs) of 1.017, 0.274, and 0.090 Hz. The dynamic closure predicts the empirical conditional hazard with log-RMSE 0.002 03 without using MC moments as inputs. Its RMSE remains 0.091–0.108 Hz across nine voltage-gain/noise combinations and 0.095–0.103 Hz over a fourfold adaptation-strength sweep. Its total finite-size error scales as $N^{-0.492}$ with a fitted bias floor statistically consistent with zero, and closed-loop normalized RMSE remains below one for normalized feedback $g\le 0.321$. For a 2-s benchmark at $1\mathrm{ms}$ age resolution, the joint partial differential equation  reaches 0.0131 Hz error in $6.16\mathrm{s}$, whereas $N=5\times {10}^4$ MC reaches 0.0334 Hz in $25.9\mathrm{s}$. The less expensive prescribed correction remains useful at moderate accuracy. The joint closure does not remove step-response latency error and loses finite-moment stability at stronger feedback, providing explicit boundaries on its validity.

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• Dynamics of networks
• Neuronal dynamics