Applied mathematics articles from across Nature Portfolio

Higher-order interactions, such as those found in hypernetworks, are increasingly recognized for their significance in complex systems like the brain and ecosystems, where traditional pairwise interaction models may fall short. This study reveals a synchronization phenomenon termed “hyperlocking," which occurs in hypernetworks, demonstrating the emergence of a stable phase locking with higher-order relations between the frequencies.

Dismantling directed networks is critical for controlling complex systems. Here, authors introduce TAD, a trophic analysis-based method that efficiently fragments networks by targeting nodes with high network incoherence centrality.

Non-Markovian theory models epidemic spread on contact graphs with varied infection and curing times. Generation times measured from many real diseases are shown to follow a Weibull distribution with shape parameter α>1, implying that the simpler Markovian theory (α=1) suffices to provide reliable bounds for epidemic predictions.

Alternating Neural Integrators (ANI) offer a non-intrusive “reuse-and-correct” framework to upgrade legacy simulators by alternating prior model evolution with learned neural corrections, improving fidelity in complex systems and enabling interpretable, data-driven refinement.

This Resource presents the Quantum Optimization Benchmarking Library, which enables fair, reproducible benchmarks of quantum heuristics for ten difficult combinatorial optimization classes with baseline results to track progress towards quantum advantage.

The International System of Units is defined in terms of seven physical constants. Ensuring that computers can understand their values exactly as we do is not as trivial as it might seem, say Cristhian Paredes and Juris Meija.

Free boundary problems, such as modelling glacier melt, are difficult to capture with neural operators. A new framework addresses this challenge by leveraging the mathematical principle of topological conjugacy.

Engineering simulations traditionally rely on finite element methods, which are accurate but computationally expensive, while scientific machine learning offers faster, data-driven alternatives. The recently developed neural-operator element method combines both approaches, making simulations more efficient and scalable.

From protein folding to fluid mechanics and galaxy formation, particle-based simulation shapes modern science. Here, the author argues that this computational tradition begins with the code Mary Tsingou wrote at Los Alamos in 1953, a contribution that still is not fully recognised.

Neural networks may be overconfident before they see real data. By briefly training on random noise, models can learn to be uncertain, leading to better calibration, improved identification of out-of-distribution inputs and thus more reliable predictions.

A recent study demonstrates the applicability of quantum computers for multi-objective optimization, bringing quantum computing a step closer towards practical applications.