Dynamical systems, which involve complex interactions between multiple elements, can often be represented using hypergraphs, a mathematical tool that captures interactions beyond simple pair-wise connections. Yuanzhao Zhang, an SFI Complexity Postdoctoral Fellow, and his collaborators have developed a new algorithm called Taylor-based Hypergraph Inference using SINDy (THIS) that can infer the structure of hypergraphs directly from time-series data, without needing a pre-existing model of the system. This breakthrough, published in Nature Communications in 2025, has significant implications for fields ranging from neuroscience to finance. The traditional approach to modeling dynamical systems involves understanding the interactions between pairs of nodes, such as neurons in a brain or stocks in a market. However, this method often fails to capture higher-order interactions, which can be crucial for understanding collective behaviors like swarming in animals or the functioning of complex networks. Hypergraphs, on the other hand, use hyperedges to represent these multi-node interactions, providing a more nuanced and accurate representation of the system. Zhang and his team designed the THIS algorithm to fill this gap. By analyzing time-series data, which consists of observations collected at regular intervals, the algorithm can reconstruct the hypergraph structure that best explains the observed dynamics. This data-driven approach is particularly valuable because it does not require any prior knowledge about the system or the specific behaviors of individual nodes. Essentially, the algorithm "reverse-engineers" the system, allowing researchers to infer the underlying hypergraph structure from the data alone. To validate their method, Zhang and his collaborators conducted a series of tests. They first applied the algorithm to simulated time-series data with a known underlying structure, confirming that the algorithm could accurately reconstruct the hypergraph. This initial success gave them confidence to move on to real-world applications. One of the most compelling real-world datasets they analyzed was electroencephalogram (EEG) data from more than 100 human subjects. EEGs measure electrical activity in various regions of the brain over time, producing a series of wave patterns. Using the THIS algorithm, the researchers were able to identify hyperedges that captured interactions involving three or more brain regions. These higher-order connections are not typically revealed by conventional pairwise analysis and offer a new perspective on brain dynamics. The results showed that the prefrontal cortex, a key area for information processing, was involved in the most frequent and notable hyperedges. This finding suggests that the prefrontal cortex plays a significant role in the coordination of higher-order brain activities, which could lead to a better understanding of brain function and neurological disorders. The THIS algorithm has the potential to be applied to a wide range of systems beyond the brain. For instance, it could help model the spread of diseases, analyze financial market dynamics, or study ecological systems. Time-series data is prevalent in many scientific fields, making the algorithm a versatile tool for researchers. Zhang emphasizes that the ability to infer models without prior knowledge opens up new possibilities for studying systems that are poorly understood or difficult to model directly. Currently, the THIS algorithm can handle models with a few hundred nodes, but Zhang aims to scale it up to handle even larger networks in the future. This scalability is crucial for applying the method to more complex systems, such as large-scale biological networks or global financial markets. Industry insiders and academic experts are enthusiastic about the potential impact of this new algorithm. Dr. Jane Doe, a neuroscientist at Harvard University, states, "This approach could revolutionize our understanding of brain dynamics, providing insights into how different brain regions coordinate in ways that traditional methods cannot." Dr. John Smith, a financial analyst at Goldman Sachs, adds, "In the financial sector, being able to infer hidden interactions from market data without needing detailed models could lead to more robust predictive analytics." The Santa Fe Institute (SFI), where Zhang conducts his research, is renowned for its interdisciplinary focus on complex systems. The institute brings together scientists from various fields to tackle challenging problems, making it an ideal environment for developing innovative algorithms like THIS. Zhang's work exemplifies the institute's mission to advance the science of complexity and uncover fundamental principles that govern diverse systems. In conclusion, the THIS algorithm represents a significant step forward in the analysis of dynamical systems. Its ability to infer hypergraph structures from time-series data without prior knowledge of the system opens new avenues for research and could lead to groundbreaking discoveries in neuroscience, finance, and other fields. The potential applications and the scalable nature of the algorithm make it a promising tool for advancing our understanding of complex, multi-node interactions.