用神经网络快速估算复杂事件系统的参数，支持不完整数据。
A Simple Approximate Bayesian Inference Neural Surrogate for Stochastic Petri Net Models
- 用1D卷积残差网络直接从噪声轨迹预测速率函数系数
- 在10%事件缺失下，系数估计均方误差仅0.043，速度远超传统方法
- 适合需要实时参数推断的生物、流行病等复杂系统建模
随机佩特里网（SPNs）在流行病学和系统生物学等领域广泛用于建模离散事件动态，但其参数估计仍具挑战性，尤其当转移速率依赖外部协变量且无显式似然时。本文提出一种基于神经网络的后验近似框架，可直接从含噪、部分观测的令牌轨迹预测已知协变量依赖速率函数的系数。模型采用轻量级1D卷积残差网络，在吉布斯模拟的SPN实现上端到端训练，学习在真实事件丢失条件下反演系统动态。推理时，蒙特卡洛丢弃提供校准的不确定性边界与点估计。在10%事件缺失的合成SPN上，该代理模型系数估计均方误差为0.043，显著快于传统贝叶斯方法。结果表明，数据驱动的似然自由代理能实现复杂、部分观测离散事件系统的准确、鲁棒与实时参数恢复。
原文摘要 · Abstract (English)
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.
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