标题： 一种用于随机Petri网模型的简单近似贝叶斯推断神经代理 显示英文标题

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

摘要： 随机Petri网（SPNs）是建模流行病学和系统生物学等领域中离散事件动态的日益流行的工具，但其参数估计通常具有挑战性，尤其是在转换率依赖于外部协变量且显式似然函数不可用的情况下。我们引入了一种神经代理（基于神经网络的后验分布近似）框架，该框架直接从噪声的、部分观测的标记轨迹中预测已知协变量依赖率函数的系数。我们的模型采用了一个轻量级的一维卷积残差网络，在Gillespie模拟的SPN实现上端到端训练，学习在事件丢失的实际条件下反转系统动态。在推理过程中，蒙特卡洛丢弃法提供了校准的不确定性边界以及点估计。在具有20%缺失事件的合成SPNs上，我们的代理以RMSE = 0.108恢复率函数系数，并且比传统的贝叶斯方法运行速度快得多。这些结果表明，数据驱动的、无需似然的代理可以在复杂、部分观测的离散事件系统中实现准确、稳健和实时的参数恢复。 显示英文摘要

摘要： 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.