A Simple Approximate Bayesian Inference Neural Surrogate for Stochastic Petri Net Models
This work addresses parameter estimation for researchers in epidemiology and systems biology using SPNs, offering a practical, incremental improvement for partially observed systems.
The authors tackled the challenge of parameter estimation in Stochastic Petri Net models with covariate-dependent rates and missing data by introducing a neural-surrogate framework, achieving an RMSE of 0.108 for coefficient recovery and faster inference than traditional Bayesian methods.
Stochastic Petri Nets (SPNs) are an increasingly popular tool of choice for modeling discrete-event dynamics in areas such as epidemiology and systems biology, yet their parameter estimation remains challenging in general and in particular when transition rates depend on external covariates and explicit likelihoods are unavailable. We introduce a neural-surrogate (neural-network--based approximation of the posterior distribution) framework that predicts the coefficients of known covariate-dependent rate functions directly from noisy, partially observed token trajectories. Our model employs a lightweight 1D Convolutional Residual Network trained end-to-end on Gillespie-simulated SPN realizations, learning to invert system dynamics under realistic conditions of event dropout. During inference, Monte Carlo dropout provides calibrated uncertainty bounds together with point estimates. On synthetic SPNs with 20% missing events, our surrogate recovers rate-function coefficients with an RMSE = 0.108 and substantially runs faster than traditional Bayesian approaches. These results demonstrate that data-driven, likelihood-free surrogates can enable accurate, robust, and real-time parameter recovery in complex, partially observed discrete-event systems.