Exact Discrete Stochastic Simulation With Deep‐Learning‐Scale Gradient Optimization

ABSTRACT Exact stochastic simulation of continuous‐time Markov chains (CTMCs) is essential when discreteness and noise drive system behavior, but the hard categorical event selection in Gillespie‐type algorithms blocks gradient‐based learning. We eliminate this constraint by decoupling forward simulation from backward differentiation, with hard categorical sampling generating exact trajectories and gradients propagating through a continuous massively‐parallel Gumbel‐Softmax straight‐through surrogate. Our approach enables accurate optimization at parameter scales over four orders of magnitude beyond existing simulators. We validate for accuracy, scalability, and reliability on a reversible dimerization model (0.09% error), a genetic oscillator (1.2% error), a 203,796‐parameter gene regulatory network achieving 98.4% accuracy on the MNIST handwritten‐digit dataset (a prototypical deep‐learning multilayer perceptron benchmark), and experimental patch‐clamp recordings of ion channel gating (R ² = 0.987) in the single‐channel regime. Our GPU implementation delivers 1.9 billion steps per second, matching the scale of non‐differentiable simulators. By making exact stochastic simulation massively parallel and autodiff‐compatible, our results enable high‐dimensional parameter inference and inverse design across systems biology, chemical kinetics, physics, and related CTMC‐governed domains.