Neural Inference of Dynamic Systems

该研究项目将推进动态系统的统计推断。动态系统是一种多用途的方法，用于在广泛的领域（包括社会、行为和经济科学）中对现象的随时间发展进行建模。通过利用深度学习和统计建模，本研究将提高统计分析在不同领域的时间依赖性现象的效率、准确性和可解释性。该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。新框架不同于传统的基于似然的方法或贝叶斯方法。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遍性。该项目将通过提供校准良好的动态系统来促进社会、行为和经济科学，这些系统可以增强创新能力，做出明智的决策，并推动积极的变革。这项研究的结果将通过学术出版物、会议和开源软件传播，从而确保广泛利用，并使该领域的研究人员和实践者受益。研究者将在研究过程中涉及研究生和一小群高中生。本研究计划将探讨动态系统中有关估计、预测和不确定性量化的关键问题。动态系统的统计推断可能是困难的，因为数值求解常微分方程的计算量很大，或者随机微分方程的转移密度固有的复杂性。该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的方法或贝叶斯方法。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，并使学习-验证过程成为可能。将发展渐近理论，从贝叶斯的角度衡量学习算法的近似误差和后验一致性。新框架将与保形推理相结合，提供无假设有限样本边际覆盖保证的预测置信区间，以及特定条件下额外的局部覆盖保证。该项目还将通过采用神经过程先验来解决动态系统在获得其样本路径具有挑战性时的推断问题。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.