用拉普拉斯采样实现神经网络演化模型的不确定性量化，兼顾精度与效率。
Uncertainty quantification of neural network models of evolving processes via Langevin sampling
- 构建基于神经微分方程的动态过程模型，通过超网络实现参数后验近似采样。
- 在化学反应与材料物理数据上，采样结果优于标准变分推断，且计算成本可控。
- 适合需要高置信度预测的科学建模场景，如复杂系统演化分析。
我们提出一种可扩展的近似推断超网络框架，用于建模依赖历史的过程。该灵活的数据模型基于神经微分方程（NODE）描述内部状态演化，并包含可训练的观测子模块。模型参数的后验分布遵循一个与后验梯度相关的随机微分方程，其漂移项由数据模型参数联合学习。该拉普拉斯采样方法可在数据模型评估成本与参数后验密度近似之间灵活权衡。我们在化学反应和材料物理数据上验证了该集成采样超网络的性能，并与标准变分推断进行对比。
原文摘要 · Abstract (English)
We propose a scalable, approximate inference hypernetwork framework for a general model of history-dependent processes. The flexible data model is based on a neural ordinary differential equation (NODE) representing the evolution of internal states together with a trainable observation model subcomponent. The posterior distribution corresponding to the data model parameters (weights and biases) follows a stochastic differential equation with a drift term related to the score of the posterior that is learned jointly with the data model parameters. This Langevin sampling approach offers flexibility in balancing the computational budget between the evaluation cost of the data model and the approximation of the posterior density of its parameters. We demonstrate performance of the ensemble sampling hypernetwork on chemical reaction and material physics data and compare it to standard variational inference.
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