Title: LINOCS: Lookahead Inference of Networked Operators for Continuous Stability

Abstract: 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.