Exact Discrete Stochastic Simulation with Deep-Learning-Scale Gradient Optimization

Fuente: arXiv
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Main Authors: Vilar, Jose M. G., Saiz, Leonor
Format: Preprint
Published: 2026
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author Vilar, Jose M. G.
Saiz, Leonor
author_facet Vilar, Jose M. G.
Saiz, Leonor
contents 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% MNIST accuracy (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.
format Preprint
id arxiv_https___arxiv_org_abs_2602_19775
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Exact Discrete Stochastic Simulation with Deep-Learning-Scale Gradient Optimization
Vilar, Jose M. G.
Saiz, Leonor
Quantitative Methods
Statistical Mechanics
Machine Learning
Computational Physics
Molecular Networks
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% MNIST accuracy (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.
title Exact Discrete Stochastic Simulation with Deep-Learning-Scale Gradient Optimization
topic Quantitative Methods
Statistical Mechanics
Machine Learning
Computational Physics
Molecular Networks
url https://arxiv.org/abs/2602.19775