Discover network dynamics with neural symbolic regression

Yu et al., 2025

Discovering network dynamics—automatically

Complex systems are everywhere: from ecosystems and gene networks to epidemics and social behavior. Each consists of many interacting components whose collective dynamics are notoriously difficult to model. Traditionally, scientists have relied on intuition and simplified equations—but for most real systems, the governing laws remain unknown.

Zihan Yu, Jingtao Ding & Yong Li  introduce ND2, a neural symbolic regression framework that discovers network dynamics directly from data. The key insight is to reduce the overwhelming search space of possible equations—normally exploding with the number of nodes—to an equivalent one-dimensional symbolic problem. ND2 combines graph neural networks and transformers (via a pretrained model called NDformer) with Monte Carlo tree search to automatically uncover concise, interpretable formulas that explain how networks evolve.

Applied to ten benchmark systems, ND2 correctly recovered the governing equations of classics such as Kuramoto oscillators, FitzHugh–Nagumo neurons, and Lotka–Volterra populations. More impressively, when tested on real data, it corrected existing biological models—reducing prediction errors by 60% in gene regulation and 56% in microbial communities—by revealing hidden higher-order interactions. In epidemic networks, ND2 uncovered transmission laws that explain cross-country differences in intervention effects and even captured the same power-law patterns across scales.

This study demonstrates how machine-driven discovery can bridge observational data and theoretical understanding, advancing complexity science from describing what we observe to deriving why it happens—directly from the data itself.

Abstract:

Network dynamics are fundamental to analyzing the properties of high-dimensional complex systems and understanding their behavior. Despite the accumulation of observational data across many domains, mathematical models exist in only a few areas with clear underlying principles. Here we show that a neural symbolic regression approach can bridge this gap by automatically deriving formulas from data. Our method reduces searches on high-dimensional networks to equivalent one-dimensional systems and uses pretrained neural networks to guide accurate formula discovery. Applied to ten benchmark systems, it recovers the correct forms and parameters of underlying dynamics. In two empirical natural systems, it corrects existing models of gene regulation and microbial communities, reducing prediction error by 59.98% and 55.94%, respectively. In epidemic transmission across human mobility networks of various scales, it discovers dynamics that exhibit the same power-law distribution of node correlations across scales and reveal country-level differences in intervention effects. These results demonstrate that machine-driven discovery of network dynamics can enhance understandings of complex systems and advance the development of complexity science.

https://www.nature.com/articles/s43588-025-00893-8

Rafael Araujo

GEOMETRY/Flight

http://rafael-araujo.com

AI is helping to decode animals’ speech. Will it also let us talk with them?

Rachel Fieldhouse

Deep in the rainforests of the Democratic Republic of the Congo, Mélissa Berthet found bonobos doing something thought to be uniquely human.

During the six months that Berthet observed the primates, they combined calls in several ways to make complex phrases1. In one example, bonobos (Pan paniscus) that were building nests together added a yelp, meaning ‘let’s do this’, to a grunt that says ‘look at me’. “It’s really a way to say: ‘Look at what I’m doing, and let’s do this all together’,” says Berthet, who studies primates and linguistics at the University of Rennes, France.

In another case, a peep that means ‘I would like to do this’ was followed by a whistle signalling ‘let’s stay together’. The bonobos combine the two calls in sensitive social contexts, says Berthet. “I think it’s to bring peace.”

The study, reported in April, is one of several examples from the past few years that highlight just how sophisticated vocal communication in non-human animals can be. In some species of primate, whale and bird, researchers have identified features and patterns of vocalization that have long been considered defining characteristics of human language. These results challenge ideas about what makes human language special — and even how ‘language’ should be defined.

Perhaps unsurprisingly, many scientists turn to artificial intelligence (AI) tools to speed up the detection and interpretation of animal sounds, and to probe aspects of communication that human listeners might miss. “It’s doing something that just wasn’t possible through traditional means,” says David Robinson, an AI researcher at the Earth Species Project, a non-profit organization based in Berkeley, California, that is developing AI systems to decode communication across the animal kingdom.

As the research advances, there is increasing interest in using AI tools not only to listen in on animal speech, but also to potentially talk back.

Continue reading:

https://www.nature.com/articles/d41586-025-02917-9

Common mycorrhizal networks facilitate plant disease resistance by altering rhizosphere microbiome assemblyAuthor links open overlay panel

Zhang et al., 2025

Arbuscular mycorrhizal fungi can interconnect the roots of individual plants by forming common mycorrhizal networks (CMNs). These symbiotic structures can act as conduits for interplant communication. Despite their importance, the mechanisms of signal transfer via CMNs and their implications for plant community performance remain unknown. Here, we demonstrate that CMNs act as a pathway to elicit defense responses in healthy receiver plants connected to pathogen-infected donors. Specifically, we show that donor plants infected by the phytopathogen Botrytis cinerea transfer jasmonic acid via CMNs, which then act as a chemical signal in receiver plants. This signal transfer to receiver plants induces shifts in root exudates, promoting the recruitment of specific microbial taxa (Streptomyces and Actinoplanes) that are directly linked to the suppression of B. cinerea infection. Collectively, our study reveals that CMNs act as interplant chemical communication conduits, transferring signals that contribute to plant disease resistance via modulation of the rhizosphere microbiota.

https://www.sciencedirect.com/science/article/pii/S1931312825003427

Meta-analysis shows that planting nitrogen-fixing species increases soil organic carbon stock

Sun et al., 2025

Nitrogen (N)-fixing species are widely used in forestation and agriculture. The effects of planting N-fixing species on soil organic carbon (SOC) stock, however, remain uncertain, limiting policy development and their application towards a possible climate change mitigation strategy. Here we conduct a global meta-analysis of 385 datapoints from 136 studies comparing SOC stock with planting N-fixing versus non-N-fixing species. Planting N-fixing species increases SOC stock by 16% compared with non-N-fixing species. This SOC increase is closely accompanied by soil N increases, with an average accumulation of 7.8 g of SOC per gram of soil N increase. Climate mediates SOC responses, with greater SOC sequestration observed in drier and warmer regions, particularly in the tropics. We estimate that an additional increase of 0.29–0.75 PgC yr−1 in global SOC stock could be achieved by adopting N-fixing species for forestation, agriculture and regeneration of marginal lands, highlighting their potential for climate change mitigation.

Global distribution of the selected studies testing the effects of planting N-fixing species on SOC stock in this meta-analysis. Green and orange dots represent the geographic locations of studies on tree and crop planting, respectively. The green and orange shaded areas show the distribution ranges of planted forests and croplands, respectively. Inset: the distribution of the sites in the global biomes based on climatic conditions: MAT and MAP. Black dots indicate study sites in this meta-analysis.

https://www.nature.com/articles/s41559-025-02861-x.epdf