Uncertainty Quantification in Computational Modeling

Uncertainty quantification (UQ) encompasses the systematic characterisation and propagation of uncertainties in computational models to assess the credibility of simulation predictions. It addresses both aleatory uncertainty arising from intrinsic variability and epistemic uncertainty due to limited knowledge of model inputs, parameters or structures. Key methodologies include sampling-based approaches such as Monte Carlo and quasi-Monte Carlo methods; spectral techniques typified by polynomial chaos expansions; and surrogate-modelling strategies that construct computationally efficient emulators of expensive numerical codes. Complementary to forward propagation of uncertainty is global sensitivity analysis, which apportions output variance to individual inputs and guides model refinement or experimental design. Recent advances have focused on high-dimensional problems, efficient error estimation and adaptive enrichment of approximation spaces. Applications span climate modelling, aerospace design, materials engineering and systems biology, where reliable quantification of confidence intervals, failure probabilities or risk measures is indispensable for decision-making under uncertainty.

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Non-intrusive polynomial chaos methods have been applied to high-fidelity particle accelerator simulations, demonstrating the construction of surrogate models for beam emittance and energy spread. Global sensitivity indices derived from these surrogates identify dominant uncertainty sources and enable efficient error propagation in cyclotron design tasks. In the field of composite structures, Karhunen–Loève expansions combined with Latin hypercube sampling facilitate stochastic finite-element analyses of quasi-isotropic carbon-fibre-reinforced polymers. This framework yields probability density functions for stress, strain and failure fields, offering probabilistic failure analysis that informs material specification and safety factors. For partial differential equations with lognormal random coefficients, quasi-Monte Carlo sampling integrated with circulant embedding techniques achieves dimension-independent convergence rates. The approach anchors rigorous error bounds for expected values of PDE outputs while accommodating locally refined spatial meshes, thereby enhancing computational efficiency in subsurface flow and heterogeneous media simulations.

Uncertainty Quantification in Computational Modeling publication trend

The graph below shows the total number of articles in uncertainty quantification in computational modeling across all publications each year (not limited to Nature Index journals).

Technical terms

Uncertainty quantification: The process of identifying, modelling and propagating uncertainties through computational simulations.

Surrogate model: A reduced-cost approximation of a high-fidelity simulation used for rapid evaluation of model outputs.

Polynomial chaos expansion: A spectral method representing model outputs as orthogonal polynomial functions of random inputs.

Quasi-Monte Carlo: A deterministic sampling approach using low-discrepancy sequences to improve convergence over standard Monte Carlo.

Sobol’ indices: Variance-based measures that quantify the influence of individual input parameters on output uncertainty.

Karhunen–Loève expansion: A technique for representing a stochastic process by a series of orthogonal functions weighted by uncorrelated random variables.

References

1. On Nonintrusive Uncertainty Quantification and Surrogate Model Construction in Particle Accelerator Modeling. SIAM/ASA Journal on Uncertainty Quantification (2019).
2. Probabilistic failure analysis of quasi-isotropic CFRP structures utilizing the stochastic finite element and the Karhunen–Loève expansion methods. Composites Part B Engineering (2022).
3. Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients. Numerische Mathematik (2018).