Journal: Royal Society of London. Proceedings A

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Royal Society

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1364-5021
1471-2946

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2015 - 201912020 - 20256
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Publications 1 - 7 of 7
  • Interpretable learning of effective dynamics for multiscale systems
    Item type: Journal Article
    Menier, Emmanuel; Kaltenbach, Sebastian; Yagoubi, Mouadh; et al. (2025)
    Royal Society of London. Proceedings A
    The modelling and simulation of high-dimensional multiscale systems is a critical challenge across all areas of science and engineering. It is broadly believed that even with today's computer advances resolving all spatio-temporal scales described by the governing equations remains a remote target. This realization has prompted intense efforts to develop model-order reduction techniques. In recent years, techniques based on deep recurrent neural networks (RNNs) have produced promising results for the modelling and simulation of complex spatiotemporal systems and offer large flexibility in model development as they can incorporate experimental and computational data. However, neural networks lack interpretability, which limits their utility and generalizability across complex systems. Here, we propose a novel framework of interpretable learning effective dynamics (iLED) that offers comparable accuracy to state-of-the-art RNN-based approaches while providing the added benefit of interpretability. The iLED framework is motivated by Mori-Zwanzig and Koopman operator (KO) theory, which justifies the choice of the specific architecture. We demonstrate the effectiveness of the proposed framework in simulations of three benchmark multiscale systems. Our results show that the iLED framework can generate accurate predictions and obtain interpretable dynamics, making it a promising approach for solving high-dimensional multiscale systems.
  • Significance of the actual nonlinear slope geometry for catastrophic failure in submarine landslides
    Item type: Journal Article
    Puzrin, Alexander M.; Gray, Thomas E.; Hill, Andrew J. (2015)
    Royal Society of London. Proceedings A
  • Generalized Brillouin zone for non-reciprocal systems
    Item type: Journal Article
    Ammari, Habib; Barandun, Silvio; Liu, Ping; et al. (2025)
    Royal Society of London. Proceedings A
    Non-reciprocal physical systems, such as waveguides with imaginary gauge potentials or mass-spring chains with active elements, present new mathematical challenges beyond those of ordinary Hermitian structures. In a phenomenon known as the non-Hermitian skin effect, eigenmodes condensate at one edge of the structure and decay exponentially in space. Traditional Floquet-Bloch theory, relying on real-valued quasi-periodicities, fails to capture this decay and thus gives incomplete predictions of spectral behaviour. In this paper, we develop a rigorous theory to address this shortcoming. By extending the Brillouin zone into the complex plane, we introduce the notion of generalized Brillouin zone. We show that this complex formulation reflects the unidirectional decay inherent in non-reciprocal systems and provides an accurate framework for spectral analysis. Our main results are proven in the general context of k-Toeplitz matrices and operators, which model a wide variety of both finite and semi-infinite or infinite non-Hermitian periodic structures. We demonstrate that our generalized Floquet-Bloch formalism correctly identifies spectra and restores spectral convergences for large finite lattices.
  • Nonlinear acoustics of an aperture under grazing flow
    Item type: Journal Article
    Stoychev, Alexander K.; Pedergnana, Tiemo; Noiray, Nicolas (2024)
    Royal Society of London. Proceedings A
    This work presents a mathematical model of a dynamically forced, acoustically compact aperture subject to one-sided mean grazing flow in two or three dimensions. By contrast to other simplified theoretical representations of a grazed aperture, the one proposed in this contribution considers some of the nonlinear effects a reduced order model should naturally inherit from the conservation equations governing the primary system's dynamics. Furthermore, unlike other nonlinear developments, this one is able to reproduce the acoustic forcing amplitude dependence of the fundamental-frequency-based impedance, measured in recent experiments, without relying on empirical parameters. This nonlinear model offers further insight into the dominant physical mechanisms determining the aforementioned behaviour and allows reasonable a priori estimates of the aeroacoustic dynamics of the aperture. This could be used as a building block of more sophisticated systems or for the derivation of even simpler representations suitable for acoustic network modelling.
  • Approximate Lie symmetries and singular perturbation theory
    Item type: Journal Article
    Dear, Alexander J.; Mahadevan, Lakshminarayana (2025)
    Royal Society of London. Proceedings A
    Perturbation theory plays a central role in the approximate solution of nonlinear differential equations. However, its na & iuml;ve application often yields divergent series solutions. While these can be made convergent using singular perturbation methods of various types, the procedures used can be subtle owing to the lack of globally applicable algorithms. Inspired by the fact that all exact solutions of differential equations are consequences of their (Lie) symmetries, we reformulate perturbation theory for differential equations as a series expansion of their solutions' symmetries. This is a change in perspective from the usual method of obtaining series expansions of the solutions themselves. We show that these approximate symmetries are straightforward to calculate and are never singular; their integration is therefore an easier way of constructing uniformly convergent solutions. This geometric viewpoint naturally subsumes the renormalization group-inspired approach of Chen, Goldenfeld and Oono, the method of multiple scales and the Poincare-Lindstedt method, by exploiting a fundamental class of symmetries that we term 'hidden scale symmetries'. It also clarifies when and why these singular perturbation methods succeed and just as importantly, when they fail. More broadly, direct, algorithmic identification and integration of these hidden scale symmetries permits solution of problems where other methods are impractical.
  • Space-time wave localization in systems of subwavelength resonators
    Item type: Journal Article
    Ammari, Habib; Hiltunen, Erik Orvehed; Rueff, Liora (2025)
    Royal Society of London. Proceedings A
    In this article, we study the dynamics of metamaterials composed of high-contrast subwavelength resonators and show the existence of localized modes in such a setting. A crucial assumption in this article is time-modulated material parameters. We prove a so-called capacitance matrix approximation of the wave equation in the form of an ordinary differential equation. These formulas set the ground for the derivation of a first-principle characterization of localized modes in terms of the generalized capacitance matrix. Furthermore, we provide numerical results supporting our analytical results showing for the first time the phenomenon of space-time localized waves in a perturbed time-modulated metamaterial. Such spatio-temporal localization is only possible in the presence of subwavelength resonances in the unperturbed structure. We introduce the time-dependent degree of localization to quantitatively determine the localized modes and provide a variety of numerical experiments to illustrate our formulations and results.
  • Using spatial extreme-value theory with machine learning to model and understand spatially compounding weather extremes
    Item type: Journal Article
    Koh, Jonathan; Steinfeld, Daniel; Martius, Olivia (2025)
    Royal Society of London. Proceedings A
    When extreme weather events affect large areas, their regional to sub-continental spatial scale is important for their impacts. We propose a novel machine learning (ML) framework that integrates spatial extreme-value theory to model weather extremes and to quantify probabilities associated with the occurrence, intensity and spatial extent of these events. Our approach employs new loss functions adapted to extreme values, enabling our model to prioritize the tail rather than the bulk of the data distribution. Applied to a case study of Western European summertime heat extremes, we use daily 500-hPa geopotential height fields and local soil moisture as predictors to capture the complex interplay between local and remote physical processes. Our generative model reveals that different facets of heat extremes are influenced by individual circulation features, such as the relative position of upper-level ridges and troughs that are part of a large-scale wave pattern. This enriches our process understanding from a data-driven perspective. Our approach can extrapolate beyond the range of the data to make risk-related probabilistic statements. It applies more generally to other weather extremes and offers an alternative to traditional physical and ML-based techniques that focus less on the extremal aspects of weather data.
Publications 1 - 7 of 7