Preconditioning of the background error covariance matrix in data assimilation for the Caspian Sea

Data Assimilation (DA) is an uncertainty quantification technique used for improving numerical forecasted results by incorporating observed data into prediction models. As a crucial point into DA models is the ill conditioning of the covariance matrices involved, it is mandatory to introduce, in a DA software, preconditioning methods. Here we present first studies concerning the introduction of two different preconditioning methods in a DA software we are developing (we named S3DVAR) which implements a Scalable Three Dimensional Variational Data Assimilation model for assimilating sea surface temperature (SST) values collected into the Caspian Sea by using the Regional Ocean Modeling System (ROMS) with observations provided by the Group of High resolution sea surface temperature (GHRSST). We also present the algorithmic strategies we employ

Multi-fidelity physics constrained neural networks for dynamical systems

Physics-constrained neural networks are commonly employed to enhance prediction robustness compared to purely data-driven models, achieved through the inclusion of physical constraint losses during the model training process. However, one of the major challenges of physics-constrained neural networks consists of the training complexity especially for high-dimensional systems. In fact, conventional physics-constrained models rely on singular-fidelity data necessitating the assessment of physical constraints within high-dimensional fields, which introduces computational difficulties. Furthermore, due to the fixed input size of the neural networks, employing multi-fidelity training data can also be cumbersome. In this paper, we propose the Multi-Scale Physics-Constrained Neural Network (MSPCNN), which offers a novel methodology for incorporating data with different levels of fidelity into a unified latent space through a customised multi-fidelity autoencoder. Additionally, multiple decoders are concurrently trained to map latent representations of inputs into various fidelity physical spaces. As a result, during the training of predictive models, physical constraints can be evaluated within low-fidelity spaces, yielding a trade-off between training efficiency and accuracy. In addition, unlike conventional methods, MSPCNN also manages to employ multi-fidelity data to train the predictive model. We assess the performance of MSPCNN in two fluid dynamics problems, namely a two-dimensional Burgers' system and a shallow water system. Numerical results clearly demonstrate the enhancement of prediction accuracy and noise robustness when introducing physical constraints in low-fidelity fields. On the other hand, as expected, the training complexity can be significantly reduced by computing physical constraint loss in the low-fidelity field rather than the high-fidelity one

A scalable approach for Variational Data Assimilation

Data assimilation (DA) is a methodology for combining mathematical models simulating complex systems (the background knowledge) and measurements (the reality or observational data) in order to improve the estimate of the system state (the forecast). The DA is an inverse and ill posed problem usually used to handle a huge amount of data, so, it is a large and computationally expensive problem. Here we focus on scalable methods that makes DA applications feasible for a huge number of background data and observations. We present a scalable algorithm for solving variational DA which is highly parallel. We provide a mathematical formalization of this approach and we also study the performance of the resulted algorith

Reduced order digital twin and latent data assimilation for global wildfire prediction

The occurrence of forest fires can impact vegetation in the ecosystem, property, and human health, but also indirectly affect the climate. JULES-INFERNO is a global land surface model, which simulates vegetation, soils, and fire occurrence driven by environmental factors. However, this model incurs substantial computational costs due to the high data dimensionality and the complexity of differential equations. Deep learning-based digital twins have an advantage in handling large amounts of data. They can reduce the computational cost of subsequent predictive models by extracting data features through Reduced Order Modelling (ROM) and then compressing the data to a low-dimensional latent space. This study proposes a JULES-INFERNO-based digital twin fire model using ROM techniques and deep learning prediction networks to improve the efficiency of global wildfire predictions. The iterative prediction implemented in the proposed model can use current-year data to predict fires in subsequent years. To avoid the accumulation of errors from the iterative prediction, Latent data Assimilation (LA) is applied to the prediction process. LA manages to efficiently adjust the prediction results to ensure the stability and sustainability of the prediction. Numerical results show that the proposed model can effectively encode the original data and achieve accurate surrogate predictions. Furthermore, the application of LA can also effectively adjust the bias of the prediction results. The proposed digital twin also runs 500 times faster for online predictions than the original JULES-INFERNO model without requiring High-Performance Computing (HPC) clusters. The implementation code of this study and the developed models are available at https://github.com/DL-WG/Digital-twin-LA-global-wildfire.</p

parallel parity games a multicore attractor for the zielonka recursive algorithm

Abstract Parity games are abstract infinite-duration two-player games, widely studied in computer science. Several solution algorithms have been proposed and also implemented in the community tool of choice called PGSolver, which has declared the Zielonka Recursive (ZR) algorithm the best performing on randomly generated games. With the aim of scaling and solving wider classes of parity games, several improvements and optimizations have been proposed over the existing algorithms. However, no one has yet explored the benefit of using the full computational power of which even common modern multicore processors are capable of. This is even more surprisingly by considering that most of the advanced algorithms in PGSolver are sequential. In this paper we introduce and implement, on a multicore architecture, a parallel version of the Attractor algorithm, that is the main kernel of the ZR algorithm. This choice follows our investigation that more of the 99% of the execution time of the ZR algorithm is spent in this module. We provide testing on graphs up to 20K nodes generated through PGSolver and we discuss performance analysis in terms of strong and weak scaling

Efficient deep data assimilation with sparse observations and time-varying sensors

Variational Data Assimilation (DA) has been broadly used in engineering problems for field reconstruction and prediction by performing a weighted combination of multiple sources of noisy data. In recent years, the integration of deep learning (DL) techniques in DA has shown promise in improving the efficiency and accuracy in high-dimensional dynamical systems. Nevertheless, existing deep DA approaches face difficulties in dealing with unstructured observation data, especially when the placement and number of sensors are dynamic over time. We introduce a novel variational DA scheme, named Voronoi-tessellation Inverse operator for VariatIonal Data assimilation (VIVID), that incorporates a DL inverse operator into the assimilation objective function. By leveraging the capabilities of the Voronoi-tessellation and convolutional neural networks, VIVID is adept at handling sparse, unstructured, and time-varying sensor data. Furthermore, the incorporation of the DL inverse operator establishes a direct link between observation and state space, leading to a reduction in the number of minimization steps required for DA. Additionally, VIVID can be seamlessly integrated with Proper Orthogonal Decomposition (POD) to develop an end-to-end reduced-order DA scheme, which can further expedite field reconstruction. Numerical experiments in a fluid dynamics system demonstrate that VIVID can significantly outperform existing DA and DL algorithms. The robustness of VIVID is also accessed through the application of various levels of prior error, the utilization of varying numbers of sensors, and the misspecification of error covariance in DA

Fluvial and eolian ichnofaunas from the Lower Permian of South America (Patquía Formation, Paganzo Basin)

The Lower Permian Patquía Formation is the youngest unit of the Paganzo Basin, western Argentina. The lower section consists of red mudstones, and fine- and coarse grained sandstones deposited in fluvial systems with extensive and thick floodplain deposits. These rocks contain a low-diversity and relatively abundant association of trace fossils suggesting the activity of a sub-superficial to superficial fauna. The association is characterized by Rusophycus carbonarius (Cubichnia), Cruziana problematica (Repichnia), and Palaeophycus tubularis (Domichnia) of the Scoyenia ichnofacies. Disarticulated fish remains are also present. The upper section is dominated by red, cross-bedded, medium- to fine-grained sandstones deposited in eolian systems that host a lowdiversity and low-abundance association of trace fossils that indicates the activity of a mainly superficial fauna. Tetrapod footprints (Chelichnus duncani, oval digit imprints, short parallel grooves, and sinusoidal grooves), horizontal to vertical burrows (Palaeophycus tubularis and Skolithos isp. respectively), and arthropod trackways are the typical components of these deposits. The association shows elements of the three presently proposed eolian ichnofacies (Chelichnus, Octopodichnus and Entradichnus ichnofacies) suggesting the necessity of revision and the possible integration of these separate ichnofacies into a single model. The record of fossil vertebrate tracks is uncommon in Lower Permian strata of South America. Therefore, the ichnologic record of the Patquía Formation is a significant contribution to the understanding of Lower Permian South American ichnofaunas

Toward the S3DVAR data assimilation software for the Caspian Sea

Data Assimilation (DA) is an uncertainty quantification technique used to incorporate observed data into a prediction model in order to improve numerical forecasted results. The forecasting model used for producing oceanographic prediction into the Caspian Sea is the Regional Ocean Modeling System (ROMS). Here we propose the computational issues we are facing in a DA software we are developing (we named S3DVAR) which implements a Scalable Three Dimensional Variational Data Assimilation model for assimilating sea surface temperature (SST) values collected into the Caspian Sea with observations provided by the Group of High resolution sea surface temperature (GHRSST). We present the algorithmic strategies we employ and the numerical issues on data collected in two of the months which present the most significant variability in water temperature: August and March