arXiv subjects

Andrea Lario

Publications and source records attributed to Andrea Lario.

5 recordsLinked to original sources

arXiv2024

Deep learning-based reduced-order methods for fast transient dynamics

In recent years, large-scale numerical simulations played an essential role in estimating the effects of explosion events in urban environments, for the purpose of ensuring the security and safety of cities. Such simulations are computationally expensive and, often, the time taken for one single computation is large and does not permit parametric studies. The aim of this work is therefore to facilitate real-time and multi-query calculations by employing a non-intrusive Reduced Order Method (ROM). We propose a deep learning-based (DL) ROM scheme able to deal with fast transient dynamics. In the case of blast waves, the parametrised PDEs are time-dependent and non-linear. For such problems, the Proper Orthogonal Decomposition (POD), which relies on a linear superposition of modes, cannot approximate the solutions efficiently. The piecewise POD-DL scheme developed here is a local ROM based on time-domain partitioning and a first dimensionality reduction obtained through the POD. Autoencoders are used as a second and non-linear dimensionality reduction. The latent space obtained is then reconstructed from the time and parameter space through deep forward neural networks. The proposed scheme is applied to an example consisting of a blast wave propagating in air and impacting on the outside of a building. The efficiency of the deep learning-based ROM in approximating the time-dependent pressure field is shown.

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arXiv2023

Kernel-based active subspaces with application to computational fluid dynamics parametric problems using the discontinuous Galerkin method

Nonlinear extensions to the active subspaces method have brought remarkable results for dimension reduction in the parameter space and response surface design. We further develop a kernel-based nonlinear method. In particular we introduce it in a broader mathematical framework that contemplates also the reduction in parameter space of multivariate objective functions. The implementation is thoroughly discussed and tested on more challenging benchmarks than the ones already present in the literature, for which dimension reduction with active subspaces produces already good results. Finally, we show a whole pipeline for the design of response surfaces with the new methodology in the context of a parametric CFD application solved with the Discontinuous Galerkin method.

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arXiv2022

Non-intrusive reduced order models for the accurate prediction of bifurcating phenomena in compressible fluid dynamics

The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations discretised with the Discontinuous Galerkin method. On the other side, from a numerical modelling point of view, two different non-intrusive reduced order modelling techniques are employed to predict the overall behaviour of the bifurcation. Both approaches showed good agreement with full-order simulations even in proximity of the bifurcating points where the solution is particularly non-smooth.

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arXiv2022

Neural-network learning of SPOD latent dynamics

We aim to reconstruct the latent space dynamics of high dimensional, quasi-stationary systems using model order reduction via the spectral proper orthogonal decomposition (SPOD). The proposed method is based on three fundamental steps: in the first, once that the mean flow field has been subtracted from the realizations (also referred to as snapshots), we compress the data from a high-dimensional representation to a lower dimensional one by constructing the SPOD latent space; in the second, we build the time-dependent coefficients by projecting the snapshots containing the fluctuations onto the SPOD basis and we learn their evolution in time with the aid of recurrent neural networks; in the third, we reconstruct the high-dimensional data from the learnt lower-dimensional representation. The proposed method is demonstrated on two different test cases, namely, a compressible jet flow, and a geophysical problem known as the Madden-Julian Oscillation. An extensive comparison between SPOD and the equivalent POD-based counterpart is provided and differences between the two approaches are highlighted. The numerical results suggest that the proposed model is able to provide low rank predictions of complex statistically stationary data and to provide insights into the evolution of phenomena characterized by specific range of frequencies. The comparison between POD and SPOD surrogate strategies highlights the need for further work on the characterization of the interplay of error between data reduction techniques and neural network forecasts.

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arXiv2022

Reduced order modeling for spectral element methods: current developments in Nektar++ and further perspectives

In this paper, we present recent efforts to develop reduced order modeling (ROM) capabilities for spectral element methods (SEM). Namely, we detail the implementation of ROM for both continuous Galerkin and discontinuous Galerkin methods in the spectral/hp element library Nektar++. The ROM approaches adopted are intrusive methods based on the proper orthogonal decomposition (POD). They admit an offline-online decomposition, such that fast evaluations for parameter studies and many-queries are possible. An affine parameter dependency is exploited such that the reduced order model can be evaluated independent of the large-scale discretization size. The implementation in the context of SEM can be found in the open-source model reduction software ITHACA-SEM.

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