Neural Inference of Dynamic Systems

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.