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Despite the success of various methods in addressing the issue of spatial reconstruction of dynamical systems with sparse observations, spatio-temporal prediction for sparse fields remains a challenge. Existing Kriging-based frameworks for spatio-temporal sparse field prediction fail to meet the accuracy and inference time required for nonlinear dynamic prediction problems. In this paper, we introduce the Dynamical System Prediction from Sparse Observations using Voronoi Tessellation (DSOVT) framework, an innovative methodology based on Voronoi tessellation which combines convolutional encoder-decoder (CED) and long short-term memory (LSTM) and utilizing Convolutional Long Short-Term Memory (ConvLSTM). By integrating Voronoi tessellations with spatio-temporal deep learning models, DSOVT is adept at predicting dynamical systems with unstructured, sparse, and time-varying observations. CED-LSTM maps Voronoi tessellations into a low-dimensional representation for time series prediction, while ConvLSTM directly uses these tessellations in an end-to-end predictive model. Furthermore, we incorporate physics constraints during the training process for dynamical systems with explicit formulas. Compared to purely data-driven models, our physics-based approach enables the model to learn physical laws within explicitly formulated dynamics, thereby enhancing the robustness and accuracy of rolling forecasts. Numerical experiments on real sea surface data and shallow water systems clearly demonstrate our framework's accuracy and computational efficiency with sparse and time-varying observations.

Data assimilation techniques are often confronted with challenges handling complex high dimensional physical systems, because high precision simulation in complex high dimensional physical systems is computationally expensive and the exact observation functions that can be applied in these systems are difficult to obtain. It prompts growing interest in integrating deep learning models within data assimilation workflows, but current software packages for data assimilation cannot handle deep learning models inside. This study presents a novel Python package seamlessly combining data assimilation with deep neural networks to serve as models for state transition and observation functions. The package, named TorchDA, implements Kalman Filter, Ensemble Kalman Filter (EnKF), 3D Variational (3DVar), and 4D Variational (4DVar) algorithms, allowing flexible algorithm selection based on application requirements. Comprehensive experiments conducted on the Lorenz 63 and a two-dimensional shallow water system demonstrate significantly enhanced performance over standalone model predictions without assimilation. The shallow water analysis validates data assimilation capabilities mapping between different physical quantity spaces in either full space or reduced order space. Overall, this innovative software package enables flexible integration of deep learning representations within data assimilation, conferring a versatile tool to tackle complex high dimensional dynamical systems across scientific domains.

Global wildfire models play a crucial role in anticipating and responding to changing wildfire regimes. JULES-INFERNO is a global vegetation and fire model simulating wildfire emissions and area burnt on a global scale. However, because of the high data dimensionality and system complexity, JULES-INFERNO's computational costs make it challenging to apply to fire risk forecasting with unseen initial conditions. Typically, running JULES-INFERNO for 30 years of prediction will take several hours on High Performance Computing (HPC) clusters. To tackle this bottleneck, two data-driven models are built in this work based on Deep Learning techniques to surrogate the JULES-INFERNO model and speed up global wildfire forecasting. More precisely, these machine learning models take global temperature, vegetation density, soil moisture and previous forecasts as inputs to predict the subsequent global area burnt on an iterative basis. Average Error per Pixel (AEP) and Structural Similarity Index Measure (SSIM) are used as metrics to evaluate the performance of the proposed surrogate models. A fine tuning strategy is also proposed in this work to improve the algorithm performance for unseen scenarios. Numerical results show a strong performance of the proposed models, in terms of both computational efficiency (less than 20 seconds for 30 years of prediction on a laptop CPU) and prediction accuracy (with AEP under 0.3\% and SSIM over 98\% compared to the outputs of JULES-INFERNO).

Diffusion models have gained attention for their ability to represent complex distributions and incorporate uncertainty, making them ideal for robust predictions in the presence of noisy or incomplete data. In this study, we develop and enhance score-based diffusion models in field reconstruction tasks, where the goal is to estimate complete spatial fields from partial observations. We introduce a condition encoding approach to construct a tractable mapping mapping between observed and unobserved regions using a learnable integration of sparse observations and interpolated fields as an inductive bias. With refined sensing representations and an unraveled temporal dimension, our method can handle arbitrary moving sensors and effectively reconstruct fields. Furthermore, we conduct a comprehensive benchmark of our approach against a deterministic interpolation-based method across various static and time-dependent PDEs. Our study attempts to addresses the gap in strong baselines for evaluating performance across varying sampling hyperparameters, noise levels, and conditioning methods. Our results show that diffusion models with cross-attention and the proposed conditional encoding generally outperform other methods under noisy conditions, although the deterministic method excels with noiseless data. Additionally, both the diffusion models and the deterministic method surpass the numerical approach in accuracy and computational cost for the steady problem. We also demonstrate the ability of the model to capture possible reconstructions and improve the accuracy of fused results in covariance-based correction tasks using ensemble sampling.

We investigate the ability to discover data assimilation (DA) schemes meant for chaotic dynamics with deep learning. The focus is on learning the analysis step of sequential DA, from state trajectories and their observations, using a simple residual convolutional neural network, while assuming the dynamics to be known. Experiments are performed with the Lorenz 96 dynamics, which display spatiotemporal chaos and for which solid benchmarks for DA performance exist. The accuracy of the states obtained from the learned analysis approaches that of the best possibly tuned ensemble Kalman filter, and is far better than that of variational DA alternatives. Critically, this can be achieved while propagating even just a single state in the forecast step. We investigate the reason for achieving ensemble filtering accuracy without an ensemble. We diagnose that the analysis scheme actually identifies key dynamical perturbations, mildly aligned with the unstable subspace, from the forecast state alone, without any ensemble-based covariances representation. This reveals that the analysis scheme has learned some multiplicative ergodic theorem associated to the DA process seen as a non-autonomous random dynamical system.

Wildfires have significant impacts on global vegetation, wildlife, and humans. They destroy plant communities and wildlife habitats and contribute to increased emissions of carbon dioxide, nitrogen oxides, methane, and other pollutants. The prediction of wildfires relies on various independent variables combined with regression or machine learning methods. In this technical review, we describe the options for independent variables, data processing techniques, models, independent variables collinearity and importance estimation methods, and model performance evaluation metrics. First, we divide the independent variables into 4 aspects, including climate and meteorology conditions, socio-economical factors, terrain and hydrological features, and wildfire historical records. Second, preprocessing methods are described for different magnitudes, different spatial-temporal resolutions, and different formats of data. Third, the collinearity and importance evaluation methods of independent variables are also considered. Fourth, we discuss the application of statistical models, traditional machine learning models, and deep learning models in wildfire risk prediction. In this subsection, compared with other reviews, this manuscript particularly discusses the evaluation metrics and recent advancements in deep learning methods. Lastly, addressing the limitations of current research, this paper emphasizes the need for more effective deep learning time series forecasting algorithms, the utilization of three-dimensional data including ground and trunk fuel, extraction of more accurate historical fire point data, and improved model evaluation metrics.

Wildfire prediction has become increasingly crucial due to the escalating impacts of climate change. Traditional CNN-based wildfire prediction models struggle with handling missing oceanic data and addressing the long-range dependencies across distant regions in meteorological data. In this paper, we introduce an innovative Graph Neural Network (GNN)-based model for global wildfire prediction. We propose a hybrid model that combines the spatial prowess of Graph Convolutional Networks (GCNs) with the temporal depth of Long Short-Term Memory (LSTM) networks. Our approach uniquely transforms global climate and wildfire data into a graph representation, addressing challenges such as null oceanic data locations and long-range dependencies inherent in traditional models. Benchmarking against established architectures using an unseen ensemble of JULES-INFERNO simulations, our model demonstrates superior predictive accuracy. Furthermore, we emphasise the model's explainability, unveiling potential wildfire correlation clusters through community detection and elucidating feature importance via Integrated Gradient analysis. Our findings not only advance the methodological domain of wildfire prediction but also underscore the importance of model transparency, offering valuable insights for stakeholders in wildfire management.

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.

Modern healthcare often utilises radiographic images alongside textual reports for diagnostics, encouraging the use of Vision-Language Self-Supervised Learning (VL-SSL) with large pre-trained models to learn versatile medical vision representations. However, most existing VL-SSL frameworks are trained end-to-end, which is computation-heavy and can lose vital prior information embedded in pre-trained encoders. To address both issues, we introduce the backbone-agnostic Adaptor framework, which preserves medical knowledge in pre-trained image and text encoders by keeping them frozen, and employs a lightweight Adaptor module for cross-modal learning. Experiments on medical image classification and segmentation tasks across three datasets reveal that our framework delivers competitive performance while cutting trainable parameters by over 90% compared to current pre-training approaches. Notably, when fine-tuned with just 1% of data, Adaptor outperforms several Transformer-based methods trained on full datasets in medical image segmentation., Comment: Accepted by ICASSP 2024

Recently, medical vision-language pre-training (VLP) has reached substantial progress to learn global visual representation from medical images and their paired radiology reports. However, medical imaging tasks in real world usually require finer granularity in visual features. These tasks include visual localization tasks (e.g., semantic segmentation, object detection) and visual grounding task. Yet, current medical VLP methods face challenges in learning these fine-grained features, as they primarily focus on brute-force alignment between image patches and individual text tokens for local visual feature learning, which is suboptimal for downstream dense prediction tasks. In this work, we propose a new VLP framework, named \textbf{G}lobal to \textbf{D}ense level representation learning (G2D) that achieves significantly improved granularity and more accurate grounding for the learned features, compared to existing medical VLP approaches. In particular, G2D learns dense and semantically-grounded image representations via a pseudo segmentation task parallel with the global vision-language alignment. Notably, generating pseudo segmentation targets does not incur extra trainable parameters: they are obtained on the fly during VLP with a parameter-free processor. G2D achieves superior performance across 6 medical imaging tasks and 25 diseases, particularly in semantic segmentation, which necessitates fine-grained, semantically-grounded image features. In this task, G2D surpasses peer models even when fine-tuned with just 1\% of the training data, compared to the 100\% used by these models. The code can be found in https://github.com/cheliu-computation/G2D-NeurIPS24/tree/main., Comment: Accepted by NeurIPS2024

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.

In the field of medical Vision-Language Pre-training (VLP), significant efforts have been devoted to deriving text and image features from both clinical reports and associated medical images. However, most existing methods may have overlooked the opportunity in leveraging the inherent hierarchical structure of clinical reports, which are generally split into `findings' for descriptive content and `impressions' for conclusive observation. Instead of utilizing this rich, structured format, current medical VLP approaches often simplify the report into either a unified entity or fragmented tokens. In this work, we propose a novel clinical prior guided VLP framework named IMITATE to learn the structure information from medical reports with hierarchical vision-language alignment. The framework derives multi-level visual features from the chest X-ray (CXR) images and separately aligns these features with the descriptive and the conclusive text encoded in the hierarchical medical report. Furthermore, a new clinical-informed contrastive loss is introduced for cross-modal learning, which accounts for clinical prior knowledge in formulating sample correlations in contrastive learning. The proposed model, IMITATE, outperforms baseline VLP methods across six different datasets, spanning five medical imaging downstream tasks. Comprehensive experimental results highlight the advantages of integrating the hierarchical structure of medical reports for vision-language alignment. The code related to this paper is available at https://github.com/cheliu-computation/IMITATE-TMI2024., Comment: Accepted by TMI2024

In the domain of cardiovascular healthcare, the Electrocardiogram (ECG) serves as a critical, non-invasive diagnostic tool. Although recent strides in self-supervised learning (SSL) have been promising for ECG representation learning, these techniques often require annotated samples and struggle with classes not present in the fine-tuning stages. To address these limitations, we introduce ECG-Text Pre-training (ETP), an innovative framework designed to learn cross-modal representations that link ECG signals with textual reports. For the first time, this framework leverages the zero-shot classification task in the ECG domain. ETP employs an ECG encoder along with a pre-trained language model to align ECG signals with their corresponding textual reports. The proposed framework excels in both linear evaluation and zero-shot classification tasks, as demonstrated on the PTB-XL and CPSC2018 datasets, showcasing its ability for robust and generalizable cross-modal ECG feature learning., Comment: under review

Recent increase in wildfires worldwide has led to the need for real-time fire nowcasting. Physics-driven models, such as cellular automata and computational fluid dynamics can provide high-fidelity fire spread simulations but they are computationally expensive and time-consuming. Much effort has been put into developing machine learning models for fire prediction. However, these models are often region-specific and require a substantial quantity of simulation data for training purpose. This results in a significant amount of computational effort for different ecoregions. In this work, a generative model is proposed using a three-dimensional Vector-Quantized Variational Autoencoders to generate spatial-temporal sequences of unseen wildfire burned areas in a given ecoregion. The model is tested in the ecoregion of a recent massive wildfire event in California, known as the Chimney fire. Numerical results show that the model succeed in generating coherent and structured fire scenarios, taking into account the impact from geophysical variables, such as vegetation and slope. Generated data are also used to train a surrogate model for predicting wildfire dissemination, which has been tested on both simulation data and the real Chimney fire event.

Medical vision-language models enable co-learning and integrating features from medical imaging and clinical text. However, these models are not easy to train and the latent representation space can be complex. Here we propose a novel way for pre-training and regularising medical vision-language models. The proposed method, named Medical vision-language pre-training with Frozen language models and Latent spAce Geometry optimization (M-FLAG), leverages a frozen language model for training stability and efficiency and introduces a novel orthogonality loss to harmonize the latent space geometry. We demonstrate the potential of the pre-trained model on three downstream tasks: medical image classification, segmentation, and object detection. Extensive experiments across five public datasets demonstrate that M-FLAG significantly outperforms existing medical vision-language pre-training approaches and reduces the number of parameters by 78\%. Notably, M-FLAG achieves outstanding performance on the segmentation task while using only 1\% of the RSNA dataset, even outperforming ImageNet pre-trained models that have been fine-tuned using 100\% of the data., Comment: Accepted by MICCAI 2023

Vision-Language Pretraining (VLP) has demonstrated remarkable capabilities in learning visual representations from textual descriptions of images without annotations. Yet, effective VLP demands large-scale image-text pairs, a resource that suffers scarcity in the medical domain. Moreover, conventional VLP is limited to 2D images while medical images encompass diverse modalities, often in 3D, making the learning process more challenging. To address these challenges, we present Generative Text-Guided 3D Vision-Language Pretraining for Unified Medical Image Segmentation (GTGM), a framework that extends of VLP to 3D medical images without relying on paired textual descriptions. Specifically, GTGM utilizes large language models (LLM) to generate medical-style text from 3D medical images. This synthetic text is then used to supervise 3D visual representation learning. Furthermore, a negative-free contrastive learning objective strategy is introduced to cultivate consistent visual representations between augmented 3D medical image patches, which effectively mitigates the biases associated with strict positive-negative sample pairings. We evaluate GTGM on three imaging modalities - Computed Tomography (CT), Magnetic Resonance Imaging (MRI), and electron microscopy (EM) over 13 datasets. GTGM's superior performance across various medical image segmentation tasks underscores its effectiveness and versatility, by enabling VLP extension into 3D medical imagery while bypassing the need for paired text.

The scarcity of data presents a critical obstacle to the efficacy of medical visionlanguage pre-training (VLP). A potential solution lies in the combination of datasets from various language communities. Nevertheless, the main challenge stems from the complexity of integrating diverse syntax and semantics, language-specific medical terminology, and culture-specific implicit knowledge. Therefore, one crucial aspect to consider is the presence of community bias caused by different languages. This paper presents a novel framework named Unifying Cross-Lingual Medical Vision-Language Pre-Training (Med-UniC), designed to integrate multimodal medical data from the two most prevalent languages, English and Spanish. Specifically, we propose Cross-lingual Text Alignment Regularization (CTR) to explicitly unify cross-lingual semantic representations of medical reports originating from diverse language communities. CTR is optimized through latent language disentanglement, rendering our optimization objective to not depend on negative samples, thereby significantly mitigating the bias from determining positive-negative sample pairs within analogous medical reports. Furthermore, it ensures that the cross-lingual representation is not biased toward any specific language community. Med-UniC reaches superior performance across 5 medical image tasks and 10 datasets encompassing over 30 diseases, offering a versatile framework for unifying multi-modal medical data within diverse linguistic communities. The experimental outcomes highlight the presence of community bias in cross-lingual VLP. Reducing this bias enhances the performance not only in vision-language tasks but also in uni-modal visual tasks., Comment: NeurIPS 2023 Main track

Predicting drop coalescence based on process parameters is crucial for experiment design in chemical engineering. However, predictive models can suffer from the lack of training data and more importantly, the label imbalance problem. In this study, we propose the use of deep learning generative models to tackle this bottleneck by training the predictive models using generated synthetic data. A novel generative model, named double space conditional variational autoencoder (DSCVAE) is developed for labelled tabular data. By introducing label constraints in both the latent and the original space, DSCVAE is capable of generating consistent and realistic samples compared to standard conditional variational autoencoder (CVAE). Two predictive models, namely random forest and gradient boosting classifiers, are enhanced on synthetic data and their performances are evaluated on real experimental data. Numerical results show that considerable improvement in prediction accuracy can be achieved by using synthetic data and the proposed DSCVAE clearly outperforms the standard CVAE. This research clearly brings more insight into handling imbalanced data for classification problems, especially in chemical engineering, Comment: 12 pages, 9 figures, journal articles

The electrocardiogram (ECG) is one of the most commonly used non-invasive, convenient medical monitoring tools that assist in the clinical diagnosis of heart diseases. Recently, deep learning (DL) techniques, particularly self-supervised learning (SSL), have demonstrated great potential in the classification of ECG. SSL pre-training has achieved competitive performance with only a small amount of annotated data after fine-tuning. However, current SSL methods rely on the availability of annotated data and are unable to predict labels not existing in fine-tuning datasets. To address this challenge, we propose Multimodal ECG-Text Self-supervised pre-training (METS), the first work to utilize the auto-generated clinical reports to guide ECG SSL pre-training. We use a trainable ECG encoder and a frozen language model to embed paired ECG and automatically machine-generated clinical reports separately. The SSL aims to maximize the similarity between paired ECG and auto-generated report while minimize the similarity between ECG and other reports. In downstream classification tasks, METS achieves around 10% improvement in performance without using any annotated data via zero-shot classification, compared to other supervised and SSL baselines that rely on annotated data. Furthermore, METS achieves the highest recall and F1 scores on the MIT-BIH dataset, despite MIT-BIH containing different classes of ECG compared to the pre-trained dataset. The extensive experiments have demonstrated the advantages of using ECG-Text multimodal self-supervised learning in terms of generalizability, effectiveness, and efficiency.

The properties of silver nanoparticles (AgNPs) are affected by various parameters, making optimisation of their synthesis a laborious task. This optimisation is facilitated in this work by concurrent use of a T-junction microfluidic system and machine learning approach. The AgNPs are synthesized by reducing silver nitrate with tannic acid in the presence of trisodium citrate, which has a dual role in the reaction as reducing and stabilizing agent. The study uses a decision tree-guided design of experiment method for the size of AgNPs. The developed approach uses kinetic nucleation and growth constants derived from an independent set of experiments to account for chemistry of synthesis, the Reynolds number and the ratio of Dean number to Reynolds number to reveal effect of hydrodynamics and mixing within device and storage temperature to account for particle stability after collection. The obtained model was used to define a parameter space for additional experiments carried out to improve the model further. The numerical results illustrate that well-designed experiments can contribute more effectively to the development of different machine learning models (decision tree, random forest and XGBoost) as opposed to randomly added experiments.

Data Assimilation (DA) and Uncertainty quantification (UQ) are extensively used in analysing and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical applications span from computational fluid dynamics (CFD) to geoscience and climate systems. Recently, much effort has been given in combining DA, UQ and machine learning (ML) techniques. These research efforts seek to address some critical challenges in high-dimensional dynamical systems, including but not limited to dynamical system identification, reduced order surrogate modelling, error covariance specification and model error correction. A large number of developed techniques and methodologies exhibit a broad applicability across numerous domains, resulting in the necessity for a comprehensive guide. This paper provides the first overview of the state-of-the-art researches in this interdisciplinary field, covering a wide range of applications. This review aims at ML scientists who attempt to apply DA and UQ techniques to improve the accuracy and the interpretability of their models, but also at DA and UQ experts who intend to integrate cutting-edge ML approaches to their systems. Therefore, this article has a special focus on how ML methods can overcome the existing limits of DA and UQ, and vice versa. Some exciting perspectives of this rapidly developing research field are also discussed.

Electrocardiography (ECG) signals can be considered as multi-variable time-series. The state-of-the-art ECG data classification approaches, based on either feature engineering or deep learning techniques, treat separately spectral and time domains in machine learning systems. No spectral-time domain communication mechanism inside the classifier model can be found in current approaches, leading to difficulties in identifying complex ECG forms. In this paper, we proposed a novel deep learning model named Spectral Cross-domain neural network (SCDNN) with a new block called Soft-adaptive threshold spectral enhancement (SATSE), to simultaneously reveal the key information embedded in spectral and time domains inside the neural network. More precisely, the domain-cross information is captured by a general Convolutional neural network (CNN) backbone, and different information sources are merged by a self-adaptive mechanism to mine the connection between time and spectral domains. In SATSE, the knowledge from time and spectral domains is extracted via the Fast Fourier Transformation (FFT) with soft trainable thresholds in modified Sigmoid functions. The proposed SCDNN is tested with several classification tasks implemented on the public ECG databases \textit{PTB-XL} and \textit{MIT-BIH}. SCDNN outperforms the state-of-the-art approaches with a low computational cost regarding a variety of metrics in all classification tasks on both databases, by finding appropriate domains from the infinite spectral mapping. The convergence of the trainable thresholds in the spectral domain is also numerically investigated in this paper. The robust performance of SCDNN provides a new perspective to exploit knowledge across deep learning models from time and spectral domains. The repository can be found: https://github.com/DL-WG/SCDNN-TS

Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a system which combines reduced-order surrogate models with a novel data assimilation (DA) technique used to incorporate real-time observations from different physical spaces. We make use of local smooth surrogate functions which link the space of encoded system variables and the one of current observations to perform variational DA with a low computational cost. The new system, named Generalised Latent Assimilation can benefit both the efficiency provided by the reduced-order modelling and the accuracy of data assimilation. A theoretical analysis of the difference between surrogate and original assimilation cost function is also provided in this paper where an upper bound, depending on the size of the local training set, is given. The new approach is tested on a high-dimensional CFD application of a two-phase liquid flow with non-linear observation operators that current Latent Assimilation methods can not handle. Numerical results demonstrate that the proposed assimilation approach can significantly improve the reconstruction and prediction accuracy of the deep learning surrogate model which is nearly 1000 times faster than the CFD simulation.

Data assimilation techniques are widely used to predict complex dynamical systems with uncertainties, based on time-series observation data. Error covariance matrices modelling is an important element in data assimilation algorithms which can considerably impact the forecasting accuracy. The estimation of these covariances, which usually relies on empirical assumptions and physical constraints, is often imprecise and computationally expensive especially for systems of large dimension. In this work, we propose a data-driven approach based on long short term memory (LSTM) recurrent neural networks (RNN) to improve both the accuracy and the efficiency of observation covariance specification in data assimilation for dynamical systems. Learning the covariance matrix from observed/simulated time-series data, the proposed approach does not require any knowledge or assumption about prior error distribution, unlike classical posterior tuning methods. We have compared the novel approach with two state-of-the-art covariance tuning algorithms, namely DI01 and D05, first in a Lorenz dynamical system and then in a 2D shallow water twin experiments framework with different covariance parameterization using ensemble assimilation. This novel method shows significant advantages in observation covariance specification, assimilation accuracy and computational efficiency., Comment: The manuscript is accepted for publication in Neural computing and applications

Accurate estimation of error covariances (both background and observation) is crucial for efficient observation compression approaches in data assimilation of large-scale dynamical problems. We propose a new combination of a covariance tuning algorithm with existing PCA-type data compression approaches, either observation- or information-based, with the aim of reducing the computational cost of real-time updating at each assimilation step. Relying on a local assumption of flow-independent error covariances, dynamical assimilation residuals are used to adjust the covariance in each assimilation window. The estimated covariances then contribute to better specify the principal components of either the observation dynamics or the state-observation sensitivity. The proposed approaches are first validated on a shallow water twin experiment with correlated and non-homogeneous observation error. Proper selection of flow-independent assimilation windows, together with sampling density for background error estimation, and sensitivity of the approaches to the observations error covariance knowledge, are also discussed and illustrated with various numerical tests and results. The method is then applied to a more challenging industrial hydrological model with real-world data and a non-linear transformation operator provided by an operational precipitation-flow simulation software.

Vaccination strategy is crucial in fighting against the COVID-19 pandemic. Since the supply is limited, contact network-based interventions can be most powerful to set an optimal strategy by identifying high-risk individuals or communities. However, due to the high dimension, only partial and noisy network information can be available in practice, especially for dynamical systems where the contact networks are highly time-variant. Furthermore, numerous mutations of SARS-CoV-2 impact considerably the current infectious probability, requiring real-time network updating algorithms. In this study, we propose a sequential network updating approach based on data assimilation techniques to combine different sources of temporal information. We then prioritise the individuals with high-degree or high-centrality, obtained from the assimilated networks, for vaccination. The assimilation-based approach is compared with the standard method (based on partially observed networks) and a random selection strategy in terms of vaccination effectiveness in a SIR model. The numerical comparison is first carried out using real-world face-to-face dynamical networks collected in a high school, following by sequential multi-layer networks, generated relying on the Barabasi-Albert model emulating the department of Computing at Imperial College London in the UK as an example.

An original graph clustering approach to efficient localization of error covariances is proposed within an ensemble-variational data assimilation framework. Here the localization term is very generic and refers to the idea of breaking up a global assimilation into subproblems. This unsupervised localization technique based on a linearizedstate-observation measure is general and does not rely on any prior information such as relevant spatial scales, empirical cut-off radius or homogeneity assumptions. It automatically segregates the state and observation variables in an optimal number of clusters (otherwise named as subspaces or communities), more amenable to scalable data assimilation.The application of this method does not require underlying block-diagonal structures of prior covariance matrices. In order to deal with inter-cluster connectivity, two alternative data adaptations are proposed. Once the localization is completed, an adaptive covariance diagnosis and tuning is performed within each cluster. Numerical tests show that this approach is less costly and more flexible than a global covariance tuning, and most often results in more accurate background and observations error covariances.

In order to leverage the information embedded in the background state and observations, covariance matrices modelling is a pivotal point in data assimilation algorithms. These matrices are often estimated from an ensemble of observations or forecast differences. Nevertheless, for many industrial applications the modelling still remains empirical based on some form of expertise and physical constraints enforcement in the absence of historical observations or predictions. We have developed two novel robust adaptive assimilation methods named CUTE (Covariance Updating iTerativE) and PUB (Partially Updating BLUE). These two non-parametric methods are based on different optimization objectives, both capable of sequentially adapting background error covariance matrices in order to improve assimilation results under the assumption of a good knowledge of the observation error covariances. We have compared these two methods with the standard approach using a misspecified background matrix in a shallow water twin experiments framework with a linear observation operator. Numerical experiments have shown that the proposed methods bear a real advantage both in terms of posterior error correlation identification and assimilation accuracy.

We study diffusion on a multilayer network where the contact dynamics between the nodes is governed by a random process and where the waiting time distribution differs for edges from different layers. We study the impact on a random walk of the competition that naturally emerges between the edges of the different layers. In opposition to previous studies which have imposed a priori inter-layer competition, the competition is here induced by the heterogeneity of the activity on the different layers. We first study the precedence relation between different edges and by extension between different layers, and show that it determines biased paths for the walker. We also discuss the emergence of cyclic, rock-paper-scissors random walks, when the precedence between layers is non-transitive. Finally, we numerically show the slowing-down effect due to the competition on a heterogeneous multilayer as the walker is likely to be trapped for a longer time either on a single layer, or on an oriented cycle . Keywords: random walks; multilayer networks; dynamical systems on networks; models of networks; simulations of networks; competition between layers., Comment: 8 pages, 5 figures