Assessing uncertainty and heterogeneity in machine learning-based spatiotemporal ozone prediction in Beijing-Tianjin- Hebei region in China

Accurate prediction of spatiotemporal ozone concentration is of great significance to effectively establish advanced early warning systems and regulate air pollution control. However, the comprehensive assessment of uncertainty and heterogeneity in spatiotemporal ozone prediction remains unknown. Here, we systematically analyze the hourly and daily spatiotemporal predictive performances using convolutional long short term memory (ConvLSTM) and deep convolutional generative adversarial network (DCGAN) models over the Beijing-Tianjin-Hebei region in China from 2013 to 2018. In extensive scenarios, our results show that the machine learning-based (ML-based) models achieve better spatiotemporal ozone concentration prediction performance with multiple meteorological conditions. A further comparison to the air pollution model-Nested Air Quality Prediction Modelling System (NAQPMS) and monitoring observations, the ConvLSTM model demonstrates the practical feasibility of identifying high ozone concentration distribution and capturing spatiotemporal ozone variation patterns at a high spatial resolution (here 15 km × 15 km)

Ensemble Kalman filter for GAN-ConvLSTM based long lead-time forecasting

Data-driven machine learning techniques have been increasingly utilized for accelerating nonlinear dynamic system prediction. However, machine learning-based models for long lead-time forecasts remain a significant challenge due to the accumulation of uncertainty along the time dimension in online deployment. To tackle this issue, the ensemble Kalman filter (EnKF) has been introduced to machine learning-based long-term forecast models to reduce the uncertainty of long lead-time forecasts of chaotic dynamic systems. Both the deep convolutional generative adversarial network (DCGAN) and convolutional long short term memory (ConvLSTM) are used for learning the complex nonlinear relationships between the past and future states of dynamic systems. Using an iterative Multi-Input Multi-Output (MIMO) algorithm, the two-hybrid forecast models (DCGAN-EnKF and ConvLSTM-EnKF) are able to yield long lead-time forecasts of dynamic states. The performance of the hybrid models has been demonstrated by one-level and two-level Lorenz 96 models. Our results show that the use of EnKF in ConvLSTM and DCGAN models successfully corrects online model errors and significantly improves the real-time forecasting of dynamic systems for a long lead-time

A real-time flow forecasting with deep convolutional generative adversarial network: Application to flooding event in Denmark

Real-time flood forecasting is crucial for supporting emergency responses to inundation-prone regions. Due to uncertainties in the future (e.g., meteorological conditions and model parameter inputs), it is challenging to make accurate forecasts of spatiotemporal floods. In this paper, a real-time predictive deep convolutional generative adversarial network (DCGAN) is developed for flooding forecasting. The proposed methodology consists of a two-stage process: (1) dynamic flow learning and (2) real-time forecasting. In dynamic flow learning, the deep convolutional neural networks are trained to capture the underlying flow patterns of spatiotemporal flow fields. In real-time forecasting, the DCGAN adopts a cascade predictive procedure. The last one-time step-ahead forecast from the DCGAN can act as a new input for the next time step-ahead forecast, which forms a long lead-time forecast in a recursive way. The model capability is assessed using a 100-year return period extreme flood event occurred in Greve, Denmark. The results indicate that the predictive fluid flows from the DCGAN and the high fidelity model are in a good agreement (the correlation coefficien

A domain decomposition non-intrusive reduced order model for turbulent flows

In this paper, a new Domain Decomposition Non-Intrusive Reduced Order Model (DDNIROM) is developed for turbulent flows. The method works by partitioning the computational domain into a number of subdomains in such a way that the summation of weights associated with the finite element nodes within each subdomain is approximately equal, and the communication between subdomains is minimised. With suitably chosen weights, it is expected that there will be approximately equal accuracy associated with each subdomain. This accuracy is maximised by allowing the partitioning to occur through areas of the domain that have relatively little flow activity, which, in this case, is characterised by the pointwise maximum Reynolds stresses.A Gaussian Process Regression (GPR) machine learning method is used to construct a set of local approximation functions (hypersurfaces) for each subdomain. Each local hypersurface represents not only the fluid dynamics over the subdomain it belongs to, but also the interactions of the flow dynamics with the surrounding subdomains. Thus, in this way, the surrounding subdomains may be viewed as providing boundary conditions for the current subdomain.We consider a specific example of turbulent air flow within an urban neighbourhood at a test site in London and demonstrate the effectiveness of the proposed DDNIROM

Machine learning-based rapid response tools for regional air pollution modelling

A parameterised non-intrusive reduced order model (P-NIROM) based on proper orthogonal decomposition (POD) and machine learning methods has been firstly developed for model reduction of pollutant transport equations. Our motivation is to provide rapid response urban air pollution predictions and controls. The varying parameters in the P-NIROM are pollutant sources. The training data sets are obtained from the high fidelity modelling solutions (called snapshots) for selected parameters (pollutant sources, here) over the parameter space . From these training data sets, the machine learning method is used to generate the relationship between the reduced solutions and inputs (pollutant sources) over . Furthermore a set of hyper-surface functions associated with each POD basis function is constructed for representing the fluid dynamics over the reduced space. The accuracy of the P-NIROM is highly dependent on the quality of the training set, here obtained from the high fidelity model. Over existing machine learning methods, the P-NIROM algorithm proposed here has the advantages that (1) it is combined with NIROM, thus providing rapid and reasonably accurate solutions; and (2) it is a robust and efficient approach for representation of any parametrised partial differential equations as the model parameters/inputs vary. In this study, we demonstrate the way how to implement the P-NIROM for the pollutant transport equation (but not limited to due to its robustness). Its predictive capability is illustrated in a three-dimensional (3-D) simulation of power plant plumes over a large region in China, where the varying parameters are the emission intensity at three locations. Results indicate that in comparison to the high fidelity model, the CPU cost is reduced by factor up to five orders of magnitude while reasonable accuracy remains

Non-intrusive model reduction for a 3D unstructured mesh control volume finite element reservoir model and its application to fluvial channels

A non-intrusive model reduction computational method using hypersurfaces representation has been developed for reservoir simulation and further applied to 3D fluvial channel problems in this work. This is achieved by a combination of a radial basis function (RBF) interpolation and proper orthogonal decomposition (POD) method. The advantage of the method is that it is generic and non-intrusive, that is, it does not require modifications to the original complex source code, for example, a 3D unstructured mesh control volume finite element (CVFEM) reservoir model used here. The capability of this non-intrusive reduced order model (NIROM) based on hypersurfaces representation has been numerically illustrated in a horizontally layered porous media case, and then further applied to a 3D complex fluvial channel case. By comparing the results of the NIROM against the solutions obtained from the high fidelity full model, it is shown that this NIROM results in a large reduction in the CPU computation cost while much of the details are captured

Non-intrusive reduced order modelling of the Navier–Stokes equations

This article presents two new non-intrusive reduced order models based upon proper orthogonal decomposition (POD) for solving the Navier–Stokes equations. The novelty of these methods resides in how the reduced order models are formed, that is, how the coefficients of the POD expansions are calculated. Rather than taking a standard approach of projecting the underlying equations onto the reduced space through a Galerkin projection, here two different techniques are employed. The first method applies a second order Taylor series to calculate the POD coefficients at each time step from the POD coefficients at earlier time steps. The second method uses a Smolyak sparse grid collocation method to calculate the POD coefficients, where again the coefficients at earlier time steps are used as the inputs. The advantage of both approaches are that they are non-intrusive and so do not require modifications to a system code; they are therefore very easy to implement. They also provide accurate solutions for modelling flow problems, and this has been demonstrated by the simulation of flows past a cylinder and within a gyre. It is demonstrated that accuracy relative to the high fidelity model is maintained whilst CPU times are reduced by several orders of magnitude in comparison to high fidelity models

Spatio-temporal hourly and daily ozone forecasting in china using a hybrid machine learning model: autoencoder and generative adversarial networks

Efficient and accurate real-time forecasting of national spatial ozone distribution is critical to the provision of effective early warning. Traditional numerical air quality models require a high computational cost associated with running large-scale numerical simulations. In this work, we introduce a hybrid model (VAE-GAN) combining a generative adversarial network (GAN) with a variational autoencoder (VAE) to learn the dynamic ozone distributions in spatial and temporal spaces. The VAE-GAN model can not only decipher the complex nonlinear relationship between the inputs (the past states/ozone and meteorological factors) and outputs (ozone), but also provide ozone forecasts for a long lead-time beyond the training period. The performance of VAE-GAN is demonstrated in hourly and daily spatio-temporal ozone forecasts over China. The training datasets from 2013 to 2017 and validation datasets from 2018 to 2019 are the collection of data from the air quality reanalysis datasets. With the use of VAE, large dataset sizes are decreased by three orders of magnitude, enabling hourly and daily forecasts to be computed in seconds. Results show that the VAE-GAN achieves a reasonable accuracy in the prediction of both the spatial and temporal evolution patterns of hourly and daily ozone fields, as compared to the Nested Air Quality Prediction Modeling System (commonly used in China), the reanalysis data and observations during the validation period. Thus, the VAE-GAN is a cost-effective tool for large data-driven predictions, which can potentially reinforce air pollution prediction efforts in providing risk assessment and management in a timely manner

A reduced order model for turbulent flows in the urban environment using machine learning

To help create a comfortable and healthy indoor and outdoor environment in which to live, there is a need to understand turbulent air flows within the urban environment. To this end, building on a previously reported method [1], we develop a fast-running Non-Intrusive Reduced Order Model (NIROM) for predicting the turbulent air flows found within an urban environment. To resolve larger scale turbulent fluctuations, we employ a Large Eddy Simulation (LES) model and solve the resulting computational model on unstructured meshes. The objective is to construct a rapid-running NIROM from these results that will have ‘similar’ dynamics to the original LES model. Based on Proper Orthogonal Decomposition (POD) and machine learning techniques, this Reduced Order Model (ROM) is six orders of magnitude faster than the high-fidelity LES model and we demonstrate how ‘similar’ it can be to the high-fidelity model by comparing statistical quantities such as the mean flows, Reynolds stresses and probability densities of the velocities. We also include validation of the high-fidelity model against data from wind tunnel experiments.This paper represents a key step towards the use of reduced order modelling for operational purposes with the tantalising possibility of it being used in place of Gaussian plume models, and the potential for greatly improved model fidelity and confidence