Neural Inference of Dynamic Systems

这一研究项目将推进动态系统的统计推断。动态系统是一种通用的方法，可以用来模拟包括社会、行为和经济科学在内的广泛领域中现象的随时间变化的过程。通过利用深度学习和统计建模，本研究将提高统计分析的效率、准确性和可解释性，以应对不同领域的时间依赖现象。该项目将引入一种新的神经推理框架，用于估计和推断动态系统。新的框架不同于传统的基于似然方法或贝叶斯方法。新的框架将允许更有效的估计和预测，同时也提高了方法的普适性。该项目将通过提供经过良好校准的动态系统来为社会、行为和经济科学做出贡献，这些动态系统可以增强创新、做出明智决策和推动积极变革的能力。这项研究的结果将通过学术出版物、会议和开放源码软件传播，从而确保广泛使用，并使该领域的研究人员和从业人员受益。研究人员将让研究生和一小部分高中生参与研究过程。这项研究项目将解决与动态系统中的估计、预测和不确定性量化相关的关键问题。由于常微分方程数值求解的计算要求很高，或者随机微分方程跃迁密度的内在复杂性，动力系统的统计推断可能是困难的。这个项目将引入一种新的神经推理框架来估计和推断动态系统，它不同于传统的基于似然方法或贝叶斯方法。通过利用深度神经网络的能力，该框架将使用与不同参数相关联的合成数据集在数据空间和参数空间之间创建直接映射。新算法将同时提供未知参数的异常估计，并实现学习-验证过程。渐近理论将被用来从贝叶斯的角度来衡量学习算法的逼近误差和后验一致性。新的框架将与保角推理相结合，在一定条件下提供无假设的有限样本边际覆盖保证和额外的局部覆盖保证的预测可信区间。该项目还将通过采用神经过程优先级来解决在获得动态系统的样本路径具有挑战性时对动态系统进行推断的问题。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This research project will advance statistical inference on dynamic systems. Dynamic systems are a versatile method to model the time-dependent progression of phenomena in a wide range of fields, including the social, behavioral, and economic sciences. By leveraging deep learning and statistical modeling, this research will enhance the efficiency, accuracy, and interpretability of statistical analysis in time-dependent phenomena across various domains. The project will introduce a new neural inference framework for estimating and inferring dynamic systems. The new framework differs from the conventional likelihood-based method or Bayesian approach. The new framework will allow for more efficient estimation and prediction, while also improving the generalizability of the methods. The project will contribute to the social, behavioral, and economic sciences by providing well-calibrated dynamic systems that can enhance the ability to innovate, make informed decisions, and drive positive change. The results of this research will be disseminated through academic publications, conferences, and open-source software, thus ensuring widespread utilization, and benefiting researchers and practitioners in the field. The investigator will involve both graduate students and a small group of high school students in the research process.This research project will address key questions related to estimation, prediction, and uncertainty quantification in dynamic systems. Statistical inference for dynamic systems can be difficult, due to the high computational demands of solving ordinary differential equations numerically or the inherent complexity of the transition density of stochastic differential equations. This project will introduce a new neural inference framework for estimating and inferring dynamic systems, which differs from the conventional likelihood-based method or Bayesian approach. By leveraging the capacity of deep neural networks, the framework will create a direct mapping between the data space and the parameter space using synthetic datasets associated with different parameters. The new algorithm will offer simultaneously an exceptional estimate of the unknown parameter and enable a learning-verification process. Asymptotic theory will be developed to measure the approximation error of the learning algorithm and the posterior consistency from a Bayesian perspective. The new framework will be combined with conformal inference to provide predictive confidence intervals with the assumption-free finite-sample marginal coverage guarantees, and additional local coverage guarantees under certain conditions. The project also will tackle the issue of inferring on dynamic systems when obtaining its sample path is challenging by adopting the neural process prior.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.