A Simple Approximate Bayesian Inference Neural Surrogate for Stochastic Petri Net Models

TL;DR

This paper introduces a neural surrogate model for Bayesian inference in stochastic Petri Nets, enabling fast, accurate, and uncertainty-aware parameter estimation from noisy, partial observations, with applications in epidemiology and systems biology.

Contribution

The paper presents a neural network-based surrogate for Bayesian inference that efficiently estimates parameters of covariate-dependent rates in stochastic Petri Nets from partial data.

Findings

Achieves low RMSE of 0.043 in synthetic experiments

Runs significantly faster than traditional Bayesian methods

Provides calibrated uncertainty bounds during inference

Abstract

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 $10\%$ missing events, our surrogate recovers rate-function coefficients with an $RMSE = 0.043$ 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.