Modelling and Simulation

Modelling and simulation encompass a suite of methodologies for constructing abstract or mathematical representations of complex systems and executing them on computational platforms to predict behaviour, explore scenarios and guide decision-making. At their core, modelling efforts proceed from a conceptual model—identifying entities, interactions, parameters and assumptions—to a formal specification, whether in the form of differential equations, discrete‐event processes, agent-based rules or hybrid constructs. Simulation then executes these formalisations over a specified observation interval, generating trajectories of system states as functions of time or events. Typical approaches include finite element analysis for continuum mechanics, computational fluid dynamics for flow systems, Monte Carlo methods for stochastic processes, discrete‐event simulation for queuing and logistics, and agent‐based modelling for social, ecological or economic phenomena. Verification and validation ensure that the implemented model reflects its formal specification and is adequately consistent with real-world data or expert judgement. Recent advances have emphasised integration of machine-learning surrogates to accelerate parameter sweeps, real-time ‘digital twins’ for cyber-physical systems, multi-scale coupling across physics, refined uncertainty quantification and exploitation of high-performance computing for ensemble projections. Applications span climate forecasting, structural integrity assessment, autonomous vehicle navigation, manufacturing optimisation, epidemic spread and virtual reality environments for training and design evaluation. As systems grow in complexity and data volumes surge, modelling and simulation remain indispensable for interrogating the possible under alternative design, operational or environmental regimes.

Research from Nature Portfolio

Recent work has dissected the drivers of enhanced summer rainfall in arid basins by employing a hierarchy of climate simulations and statistical diagnostics. These studies demonstrate that internal atmospheric variability—chiefly shifts in the North Atlantic Oscillation—has redirected synoptic storm tracks into major desert regions, accounting for the observed wetting trend independently of direct anthropogenic forcing.

Another contribution has quantified a pronounced historical asymmetry in global ocean uptake of heat and carbon. Coupled-model experiments reveal that, over the twentieth century, the Southern Ocean absorbed the majority of heat uptake while contributing less to carbon uptake, a pattern driven by interhemispheric aerosol forcing. Under moderate future emissions scenarios, this asymmetry is projected to diminish as greenhouse gases increasingly dominate radiative forcing, redistributing uptake more evenly between hemispheres.

Research from all publishers

A comprehensive review of 3D scene reconstruction via unmanned aerial vehicles has compared sampling-based planners (such as Rapidly-Exploring Random Trees) and optimisation-based viewpoint selection frameworks. The study benchmarks metrics for coverage completeness, reconstruction quality and computational overhead, and highlights emerging trends in semantic-aware flight planning, real-time replanning under uncertainty and multi-agent coordination to balance efficiency with model fidelity.

In computational mechanics, enhancements to the smoothed finite element method (S-FEM) have been proposed for hyperelastic and near-incompressible materials. Edge-based and node-based formulations apply strain smoothing on sub-domains to mitigate volumetric locking and mesh distortion sensitivity. A gradient-stable node-based variant further integrates strain gradient terms to eliminate zero-energy modes, yielding robust performance in static and dynamic analyses on highly irregular meshes.

Computational fluid dynamics studies of proton exchange membrane fuel cells have evaluated baffle-enhanced flow fields to intensify reactant mixing and water removal. By inserting cylindrical baffles into channel networks, researchers achieved significant gains in current density, albeit with increased pumping losses due to vortex formation. These findings inform trade-offs in flow field design to optimise mass transfer, minimise entropy production and deliver high power density with manageable parasitic costs.

Modelling and Simulation publication trend

The graph below shows the total number of articles in modelling and simulation across all publications each year (not limited to Nature Index journals).

Technical terms

Digital twin: A real-time, virtual replica of a physical system that synchronises data streams to mirror current operating conditions.

Finite element analysis (FEA): A numerical technique that discretises a continuum domain into elements to solve partial differential equations for stress, deformation and other fields.

Computational fluid dynamics (CFD): The numerical solution of Navier–Stokes and continuity equations to predict fluid flow, heat transfer and species transport in complex geometries.

Discrete-event simulation (DES): A stochastic modelling approach in which system state changes occur at discrete points in time in response to events (e.g. arrivals, departures).

Agent-based model (ABM): A framework in which autonomous agents interact according to defined rules, generating emergent system-level patterns from local behaviours.

Uncertainty quantification (UQ): The process of characterising and reducing uncertainty in model inputs, parameters and predictions through statistical methods and ensemble simulations.

Verification and validation (V&V): Verification checks that a model is implemented correctly relative to its specification; validation assesses its adequacy against real-world data or expert judgement.

Hybrid modelling: An approach that combines continuous dynamics (e.g. differential equations) with discrete events or logical rules to capture systems operating across modes or scales.

References

1. Modelling and Simulation Fundamentals.
2. Recent wetting trend over Taklamakan and Gobi Desert dominated by internal variability. Nature Communications (2024).
3. Asymmetries in the Southern Ocean contribution to global heat and carbon uptake. Nature Climate Change (2024).
4. A Review on Viewpoints and Path Planning for UAV-Based 3-D Reconstruction. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing (2023).
5. Strain smoothing for compressible and nearly-incompressible finite elasticity. Computers & Structures (2017).
6. A Gradient Stable Node‐Based Smoothed Finite Element Method for Solid Mechanics Problems. Shock and Vibration (2019).
7. Numerical investigation of baffle shape effects on performance and mass transfer of proton exchange membrane fuel cell. Energy (2023).