Spatiotemporal processes are a fundamental tool for modeling dynamics across
various domains, from heat propagation in materials to oceanic and atmospheric
flows. However, currently available neural network-based modeling approaches
fall short when faced with data collected randomly over time and space, as is
often the case with sensor networks in real-world applications like
crowdsourced earthquake detection or pollution monitoring. In response, we
developed a new spatiotemporal method that effectively handles such randomly
sampled data. Our model integrates techniques from amortized variational
inference, neural differential equations, neural point processes, and implicit
neural representations to predict both the dynamics of the system and the
probabilistic locations and timings of future observations. It outperforms
existing methods on challenging spatiotemporal datasets by offering substantial
improvements in predictive accuracy and computational efficiency, making it a
useful tool for modeling and understanding complex dynamical systems observed
under realistic, unconstrained conditions.

我们开发了一种新的时空方法，通过集成从摊销变分推断、神经微分方程、神经点过程和隐式神经表示等技术，有效处理随机采样的数据，并对未来观测的概率位置和时间进行预测，从而在预测准确性和计算效率上显著超越现有方法，成为研究和理解在真实无约束条件下观察到的复杂动力系统的有用工具。

建模随机观测的时空动力系统

Modeling Randomly Observed Spatiotemporal Dynamical Systems

Continuously-observed event occurrences, often exhibit self- and
mutually-exciting effects, which can be well modeled using temporal point
processes. Beyond that, these event dynamics may also change over time, with
certain periodic trends. We propose a novel variational auto-encoder to capture
such a mixture of temporal dynamics. More specifically, the whole time interval
of the input sequence is partitioned into a set of sub-intervals. The event
dynamics are assumed to be stationary within each sub-interval, but could be
changing across those sub-intervals. In particular, we use a sequential latent
variable model to learn a dependency graph between the observed dimensions, for
each sub-interval. The model predicts the future event times, by using the
learned dependency graph to remove the noncontributing influences of past
events. By doing so, the proposed model demonstrates its higher accuracy in
predicting inter-event times and event types for several real-world event
sequences, compared with existing state of the art neural point processes.

提出了一种新颖的变分自编码器来捕捉时间动态的混合，通过使用学习到的依赖图来预测未来事件时间和事件类型，在预测真实世界事件序列中表现出更高的准确性，相较于现有先进的神经点过程。