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。