麻豆淫院

A research team has developed a novel method for estimating the predictability of complex dynamical systems. Their work, "Time-lagged recurrence: A data-driven method to estimate the predictability of dynamical systems," published on 16 May 2025, in the , introduces a technique called Time-Lagged Recurrence (TLR) that addresses a fundamental question in science and engineering: given a system's current state, how far into the future can we reliably predict its behavior?

Predictability refers to how well future states of a system can be forecasted if we know its present state. In the mid-20th century, scientists discovered that even deterministic systems (systems governed by fixed physical laws) can exhibit extreme sensitivity to initial conditions.

This phenomenon, often known as the "butterfly effect," means that even tiny uncertainties at the beginning can grow quickly, making it impossible to predict what will happen after a certain amount of time. In the 1960s, scientist Edward Lorenz discovered that this is why we cannot trust weather forecasts too far into the future.

Scientists have since learned that this limit is not always the same鈥攊t changes depending on the state of the system. That means some situations are more predictable than others. Knowing where these limits are, and when a system becomes especially unpredictable, is essential in many fields, not just weather and climate, but also in finance, economics, and biology.

A new approach to determining predictability

To tackle this challenge, Asst Prof Mengaldo and his team developed Time-Lagged Recurrence (TLR), a new metric for quantifying predictability in a purely data-driven way. Unlike traditional approaches that rely on knowing the system's equations or making simplifying assumptions, TLR needs only data as input.

The method builds on the concept of recurrences鈥攎oments when a system's state recurs (i.e. returns close) to a previous state. By tracking these recurrences, TLR evaluates how an ensemble of similar initial states evolves over a specified time lag (a chosen forecast horizon) and gauges how much those trajectories diverge.

In simple terms, TLR asks: if the system is in a certain state now, and we find other times it was in a similar state, do those similar histories stay similar in the future? The degree of similarity, assessed statistically given all available observations, determines the local predictability at that state.

To validate TLR and showcase its versatility, the researchers tested it on a wide array of dynamical systems, ranging from idealized models of chaos to real-world datasets, including Lorenz and Rossler chaotic attractors, ECG and EEG biological signals, simulated slow earthquake data, and atmospheric data.

The various tests showed how TLR was able to identify known predictability features when available. For instance, in the context of atmospheric data, they applied TLR to the large-scale circulation patterns over the Euro-Atlantic sector and obtained conclusions consistent with those based on reforecast studies, further confirming the variability of the intrinsic predictability of circulation patterns in this region.

Asst Prof Mengaldo stated, "Its generality and ease of use make TLR a useful diagnostic tool capable of enhancing the understanding of local dynamics and their predictability across diverse scientific domains, including physics, geophysics, finance, and engineering. It may also be applied in the realm of artificial intelligence (AI) as a diagnostic tool. Indeed, in my group, we are currently working on bridging AI and dynamical systems theory."

Future application

TLR can be applied to any complex dynamical system and can serve as a diagnostic tool to understand when a dynamical system is less predictable; this in turn can help adjust or better understand forecasting expectations, thereby refining, e.g., communications to stakeholders.

In addition, in the realm of AI and complex data-driven systems, TLR could serve as a diagnostic add-on: for example, AI models that predict time-series data might use TLR to self-evaluate the uncertainty of their predictions based on the current input state.

The research team was led by Assistant Professor Gianmarco Mengaldo from the Department of Mechanical Engineering in the College of Design and Engineering at the National University of Singapore (NUS), together with his doctoral student Chenyu Dong and collaborators Dr. Davide Faranda (LSCE, France), Assistant Professor Adriano Gualandi (University of Cambridge, UK), and Professor Valerio Lucarini (University of Leicester, UK).