Vinicius L. S. Silva

Vinicius L. S. Silva, Gabriel S. Seabra, Alexandre A. Emerick

We propose two new methods based/inspired by machine learning for tabular data and distance-free localization to enhance the covariance estimations in an ensemble data assimilation. The main goal is to enhance the data assimilation results by mitigating loss of variance due to sampling errors. We also analyze the suitability of several machine learning models and the balance between accuracy and computational cost of the covariance estimations. We introduce two distance-free localization techniques leveraging machine learning methods specifically tailored for tabular data. The methods are integrated into the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) framework. The results show that the proposed localizations improve covariance accuracy and enhance data assimilation and uncertainty quantification results. We observe reduced variance loss for the input variables using the proposed methods. Furthermore, we compare several machine learning models, assessing their suitability for the problem in terms of computational cost, and quality of the covariance estimation and data match. The influence of ensemble size is also investigated, providing insights into balancing accuracy and computational efficiency. Our findings demonstrate that certain machine learning models are more suitable for this problem. This study introduces two novel methods that mitigate variance loss for model parameters in ensemble-based data assimilation, offering practical solutions that are easy to implement and do not require any additional numerical simulation or hyperparameter tuning.

Vinicius L. S. Silva, Claire E. Heaney, Nenko Nenov et al.

We propose a new method in which a generative network (GN) integrate into a reduced-order model (ROM) framework is used to solve inverse problems for partial differential equations (PDE). The aim is to match available measurements and estimate the corresponding uncertainties associated with the states and parameters of a numerical physical simulation. The GN is trained using only unconditional simulations of the discretized PDE model. We compare the proposed method with the golden standard Markov chain Monte Carlo. We apply the proposed approaches to a spatio-temporal compartmental model in epidemiology. The results show that the proposed GN-based ROM can efficiently quantify uncertainty and accurately match the measurements and the golden standard, using only a few unconditional simulations of the full-order numerical PDE model.

Vinicius L. S. Silva, Claire E. Heaney, Yaqi Li et al.

We propose the novel use of a generative adversarial network (GAN) (i) to make predictions in time (PredGAN) and (ii) to assimilate measurements (DA-PredGAN). In the latter case, we take advantage of the natural adjoint-like properties of generative models and the ability to simulate forwards and backwards in time. GANs have received much attention recently, after achieving excellent results for their generation of realistic-looking images. We wish to explore how this property translates to new applications in computational modelling and to exploit the adjoint-like properties for efficient data assimilation. To predict the spread of COVID-19 in an idealised town, we apply these methods to a compartmental model in epidemiology that is able to model space and time variations. To do this, the GAN is set within a reduced-order model (ROM), which uses a low-dimensional space for the spatial distribution of the simulation states. Then the GAN learns the evolution of the low-dimensional states over time. The results show that the proposed methods can accurately predict the evolution of the high-fidelity numerical simulation, and can efficiently assimilate observed data and determine the corresponding model parameters.