Dynamical system prediction from sparse observations using deep neural networks with Voronoi tessellation and physics constraint

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.

Spatially-Aware Diffusion Models with Cross-Attention for Global Field Reconstruction with Sparse Observations

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.

TorchDA: A Python package for performing data assimilation with deep learning forward and transformation functions

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.

Deep learning surrogate models of JULES-INFERNO for wildfire prediction on a global scale

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).

Deep learning-based sequential data assimilation for chaotic dynamics identifies local instabilities from single state forecasts

We investigate the ability to discover data assimilation (DA) schemes meant for chaotic dynamics with deep learning (DL). 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 (EnKF), 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.

Explainable Global Wildfire Prediction Models using Graph Neural Networks

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.

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.

Freeze the backbones: A Parameter-Efficient Contrastive Approach to Robust Medical Vision-Language Pre-training

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.

G2D: From Global to Dense Radiography Representation Learning via Vision-Language Pre-training

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 will be released upon acceptance.

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.