End-to-end data-driven prediction of urban airflow and pollutant dispersion

Climate change and the rapid growth of urban populations are intensifying environmental stresses within cities, making the behavior of urban atmospheric flows a critical factor in public health, energy use, and overall livability. This study targets to develop fast and accurate models of urban pollutant dispersion to support decision-makers, enabling them to implement mitigation measures in a timely and cost-effective manner. To reach this goal, an end-to-end data-driven approach is proposed to model and predict the airflow and pollutant dispersion in a street canyon in skimming flow regime. A series of time-resolved snapshots obtained from large eddy simulation (LES) serves as the database. The proposed framework is based on four fundamental steps. Firstly, a reduced basis is obtained by spectral proper orthogonal decomposition (SPOD) of the database. The projection of the time series snapshot data onto the SPOD modes (time-domain approach) provides the temporal coefficients of the dynamics. Secondly, a nonlinear compression of the temporal coefficients is performed by autoencoder to reduce further the dimensionality of the problem. Thirdly, a reduced-order model (ROM) is learned in the latent space using Long Short-Term Memory (LSTM) netowrks. Finally, the pollutant dispersion is estimated from the predicted velocity field through convolutional neural network that maps both fields. The results demonstrate the efficacy of the model in predicting the instantaneous as well as statistically stationary fields over long time horizon.

Dynamical System Identification, Model Selection and Model Uncertainty Quantification by Bayesian Inference

This study presents a Bayesian maximum \textit{a~posteriori} (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized zeroth-order Tikhonov regularization, providing a rational justification for the choice of the residual and regularization terms, respectively, from the negative logarithms of the likelihood and prior distributions. In addition to the estimation of model coefficients, the Bayesian interpretation gives access to the full apparatus for Bayesian inference, including the ranking of models, the quantification of model uncertainties and the estimation of unknown (nuisance) hyperparameters. Two Bayesian algorithms, joint maximum \textit{a~posteriori} (JMAP) and variational Bayesian approximation (VBA), are compared to the popular SINDy algorithm for thresholded least-squares regression, by application to several dynamical systems with added noise. For multivariate Gaussian likelihood and prior distributions, the Bayesian formulation gives Gaussian posterior and evidence distributions, in which the numerator terms can be expressed in terms of the Mahalanobis distance or ``Gaussian norm'' $||\vy-\hat{\vy}||^2_{M^{-1}} = (\vy-\hat{\vy})^\top {M^{-1}} (\vy-\hat{\vy})$, where $\vy$ is a vector variable, $\hat{\vy}$ is its estimator and $M$ is the covariance matrix. The posterior Gaussian norm is shown to provide a robust metric for quantitative model selection.