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

TL;DR

The paper tackles real-time prediction of blast-wave effects in urban environments, where full-order simulations are prohibitively expensive for parametric studies. It introduces a non-intrusive reduced-order model that combines a piecewise POD basis, a nonlinear autoencoder for latent-space compression, and a deep forward neural network to learn latent dynamics in response to time and explosion position. The approach markedly improves accuracy over standard POD, achieving online evaluation times on the order of 0.2 seconds per trajectory while maintaining faithful reconstructions of pressure fields, impulses, and peak overpressures. This framework enables fast, multi-query risk assessments for disaster planning and safety analysis in large-scale urban domains.

Abstract

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.

Figures (13)

• Figure 1: Blast wave propagating on the outside of a building.
• Figure 2: Piecewise POD-DL scheme: offline stage. It should be noted that $f_E$ is a function which maps the bases of the POD onto the AE laetnt space
• Figure 3: Piecewise POD-DL scheme: online stage.
• Figure 4: Reduced basis coefficients for $t \in T_1$, for reduced dimension $N=200$ and latent dimension $n=20$. Coefficient relative to the 1st mode (left), and coefficients relative to the 2nd, 50th, 100th and 200th modes (right).
• Figure 5: Time evolution of the first four latent representation vectors for reduced dimension $N=200$, latent dimension $n=20$ and for $t \in T_1$.