Identifying latent interactions within complex systems is key to unlocking
deeper insights into their operational dynamics, including how their elements
affect each other and contribute to the overall system behavior. For instance,
in neuroscience, discovering neuron-to-neuron interactions is essential for
understanding brain function; in ecology, recognizing the interactions among
populations is key for understanding complex ecosystems. Such systems, often
modeled as dynamical systems, typically exhibit noisy high-dimensional and
non-stationary temporal behavior that renders their identification challenging.
Existing dynamical system identification methods often yield operators that
accurately capture short-term behavior but fail to predict long-term trends,
suggesting an incomplete capture of the underlying process. Methods that
consider extended forecasts (e.g., recurrent neural networks) lack explicit
representations of element-wise interactions and require substantial training
data, thereby failing to capture interpretable network operators. Here we
introduce Lookahead-driven Inference of Networked Operators for Continuous
Stability (LINOCS), a robust learning procedure for identifying hidden
dynamical interactions in noisy time-series data. LINOCS integrates several
multi-step predictions with adaptive weights during training to recover
dynamical operators that can yield accurate long-term predictions. We
demonstrate LINOCS' ability to recover the ground truth dynamical operators
underlying synthetic time-series data for multiple dynamical systems models
(including linear, piece-wise linear, time-changing linear systems'
decomposition, and regularized linear time-varying systems) as well as its
capability to produce meaningful operators with robust reconstructions through
various real-world examples.

识别复杂系统中的潜在相互作用对于深入了解其操作动态至关重要，其中包括了探究元素之间的相互影响及其对整体系统行为的贡献。我们引入了 LINOCS，这是一种用于识别噪声时间序列数据中隐藏动态相互作用的鲁棒学习过程，能够恢复动态算子并产生有意义的重建。

LINOCS: 基于网络操作的连续稳定性的前瞻推理

LINOCS: Lookahead Inference of Networked Operators for Continuous  Stability

Large quantifies of online user activity data, such as weekly web search
volumes, which co-evolve with the mutual influence of several queries and
locations, serve as an important social sensor. It is an important task to
accurately forecast the future activity by discovering latent interactions from
such data, i.e., the ecosystems between each query and the flow of influences
between each area. However, this is a difficult problem in terms of data
quantity and complex patterns covering the dynamics. To tackle the problem, we
propose FluxCube, which is an effective mining method that forecasts large
collections of co-evolving online user activity and provides good
interpretability. Our model is the expansion of a combination of two
mathematical models: a reaction-diffusion system provides a framework for
modeling the flow of influences between local area groups and an ecological
system models the latent interactions between each query. Also, by leveraging
the concept of physics-informed neural networks, FluxCube achieves high
interpretability obtained from the parameters and high forecasting performance,
together. Extensive experiments on real datasets showed that FluxCube
outperforms comparable models in terms of the forecasting accuracy, and each
component in FluxCube contributes to the enhanced performance. We then show
some case studies that FluxCube can extract useful latent interactions between
queries and area groups.

提出了一种名为 FluxCube 的方法，通过挖掘在线用户活动数据中的潜在交互关系，包括查询之间的生态系统和区域之间的影响流。该模型基于两种数学模型的组合，即反应 - 扩散系统和生态系统，并利用物理信息神经网络的概念实现了高可解释性和高预测性能。实验结果表明，FluxCube 在预测准确性方面优于其他模型，并且每个组件都有助于提高性能。