conference Online attended
Presented at the 2026 CAA Doctoral Academic Exchange — East China Regional Forum
Presented the talk 随机动态系统的概率预测：一个上界，一个下界，和中间的空间 (Probabilistic Prediction of Stochastic Dynamical Systems: A Ceiling, a Floor, and the Space in Between) at the 2026 CAA Doctoral Academic Exchange (中国自动化学会博士学术交流会) East China Regional Forum, held online — nominated by the School of Automation and Intelligent Sensing. The forum allowed 10 minutes for the talk plus 5 minutes of discussion with the expert panel; the session was recorded and is available on Bilibili.
Following the forum's selection, based on the report and the discussion, I was invited to present at the annual main forum (2026-10-30, Beijing).
Talk
随机动态系统的概率预测：一个上界，一个下界，和中间的空间 (Probabilistic Prediction of Stochastic Dynamical Systems: A Ceiling, a Floor, and the Space in Between)
Probabilistic prediction asks not for a point estimate of the future state, but for its conditional probability distribution. This talk brackets the limits of that task from two complementary sides. From above, an ε-logarithm score is proposed, and the probabilistic predictability of a stochastic dynamical system is shown to be determined quantitatively by the tolerance radius, the differential entropies of the process noises, and the system dimension — a ceiling that no predictor can exceed. From below, for the case where the nominal model is inevitably biased, a distributionally robust probabilistic prediction (DRPP) framework certifies worst-case performance over an ambiguity set of dynamics and makes the price of robustness explicit. Together the two delimit the room actually available to a predictor. The results are published in Automatica and IEEE Transactions on Automatic Control.
Related publications
Probabilistic Predictability of Stochastic Dynamical Systems
Automatica
TL;DR Quantifies how predictably a stochastic system behaves via an -logarithm score, tied to differential entropy and system dimension.
Abstract & PDF
To assess the quality of a probabilistic prediction for stochastic dynamical systems (SDSs), scoring rules assign a numerical score based on the predictive distribution and the measured state. We propose an -logarithm score that generalizes the logarithm score by considering a neighborhood of radius . We characterize the probabilistic predictability of an SDS by optimizing the expected score over the space of probability measures, and show how predictability is quantitatively determined by the neighborhood radius, the differential entropies of process noises, and the system dimension. For any predictor, we provide approximations of the expected score with error . We also analyze the asymptotic behaviors of the score on individual trajectories, proving convergence to the expected score for i.i.d. process noises with speed in probability. Numerical examples elaborate the results.
Distributionally Robust Probabilistic Prediction for Stochastic Dynamical Systems
IEEE Transactions on Automatic Control
TL;DR A distributionally robust probabilistic prediction framework that certifies worst-case predictive performance over an ambiguity set of dynamics.
Abstract & PDF
Probabilistic prediction of stochastic dynamical systems (SDSs) aims to accurately predict the conditional probability distributions of future states. However, accurate probabilistic predictions hinge on accurate distributional information from a nominal model, which is rarely available in practice. We propose a novel functional-maximin-based distributionally robust probabilistic prediction (DRPP) framework, in which one can design probabilistic predictors with worst-case performance guarantees over a pre-defined ambiguity set of SDSs. Although DRPP requires optimizing over the space of probability measures — generally intractable — we develop a methodology that equivalently transforms the maximin problem from function spaces to Euclidean spaces. Two suboptimal solutions are derived: Noise-DRPP (relaxing constraints on the ambiguity set) and Eig-DRPP (relaxing constraints on the predictor), together with their optimality gaps against the global optimum. Numerical simulations compare the performance of the predictors under different SDSs.