Gustau Camps-Valls

Ioannis Prapas, Nikolaos Ioannis Bountos, Spyros Kondylatos et al.

Wildfires are increasingly exacerbated as a result of climate change, necessitating advanced proactive measures for effective mitigation. It is important to forecast wildfires weeks and months in advance to plan forest fuel management, resource procurement and allocation. To achieve such accurate long-term forecasts at a global scale, it is crucial to employ models that account for the Earth system's inherent spatio-temporal interactions, such as memory effects and teleconnections. We propose a teleconnection-driven vision transformer (TeleViT), capable of treating the Earth as one interconnected system, integrating fine-grained local-scale inputs with global-scale inputs, such as climate indices and coarse-grained global variables. Through comprehensive experimentation, we demonstrate the superiority of TeleViT in accurately predicting global burned area patterns for various forecasting windows, up to four months in advance. The gain is especially pronounced in larger forecasting windows, demonstrating the improved ability of deep learning models that exploit teleconnections to capture Earth system dynamics. Code available at https://github.com/Orion-Ai-Lab/TeleViT.

Spyros Kondylatos, Ioannis Prapas, Gustau Camps-Valls et al.

We introduce Mesogeos, a large-scale multi-purpose dataset for wildfire modeling in the Mediterranean. Mesogeos integrates variables representing wildfire drivers (meteorology, vegetation, human activity) and historical records of wildfire ignitions and burned areas for 17 years (2006-2022). It is designed as a cloud-friendly spatio-temporal dataset, namely a datacube, harmonizing all variables in a grid of 1km x 1km x 1-day resolution. The datacube structure offers opportunities to assess machine learning (ML) usage in various wildfire modeling tasks. We extract two ML-ready datasets that establish distinct tracks to demonstrate this potential: (1) short-term wildfire danger forecasting and (2) final burned area estimation given the point of ignition. We define appropriate metrics and baselines to evaluate the performance of models in each track. By publishing the datacube, along with the code to create the ML datasets and models, we encourage the community to foster the implementation of additional tracks for mitigating the increasing threat of wildfires in the Mediterranean.

José A. Padrón-Hidalgo, Valero Laparra, Gustau Camps-Valls

Anomaly detection is a field of intense research. Identifying low probability events in data/images is a challenging problem given the high-dimensionality of the data, especially when no (or little) information about the anomaly is available a priori. While plenty of methods are available, the vast majority of them do not scale well to large datasets and require the choice of some (very often critical) hyperparameters. Therefore, unsupervised and computationally efficient detection methods become strictly necessary. We propose an unsupervised method for detecting anomalies and changes in remote sensing images by means of a multivariate Gaussianization methodology that allows to estimate multivariate densities accurately, a long-standing problem in statistics and machine learning. The methodology transforms arbitrarily complex multivariate data into a multivariate Gaussian distribution. Since the transformation is differentiable, by applying the change of variables formula one can estimate the probability at any point of the original domain. The assumption is straightforward: pixels with low estimated probability are considered anomalies. Our method can describe any multivariate distribution, makes an efficient use of memory and computational resources, and is parameter-free. We show the efficiency of the method in experiments involving both anomaly detection and change detection in different remote sensing image sets. Results show that our approach outperforms other linear and nonlinear methods in terms of detection power in both anomaly and change detection scenarios, showing robustness and scalability to dimensionality and sample sizes.

Daniel Heestermans Svendsen, Daniel Hernández-Lobato, Luca Martino et al.

Earth observation from satellites offers the possibility to monitor our planet with unprecedented accuracy. Radiative transfer models (RTMs) encode the energy transfer through the atmosphere, and are used to model and understand the Earth system, as well as to estimate the parameters that describe the status of the Earth from satellite observations by inverse modeling. However, performing inference over such simulators is a challenging problem. RTMs are nonlinear, non-differentiable and computationally costly codes, which adds a high level of difficulty in inference. In this paper, we introduce two computational techniques to infer not only point estimates of biophysical parameters but also their joint distribution. One of them is based on a variational autoencoder approach and the second one is based on a Monte Carlo Expectation Maximization (MCEM) scheme. We compare and discuss benefits and drawbacks of each approach. We also provide numerical comparisons in synthetic simulations and the real PROSAIL model, a popular RTM that combines land vegetation leaf and canopy modeling. We analyze the performance of the two approaches for modeling and inferring the distribution of three key biophysical parameters for quantifying the terrestrial biosphere.

Kristoffer Wickstrøm, J. Emmanuel Johnson, Sigurd Løkse et al.

This paper presents the kernelized Taylor diagram, a graphical framework for visualizing similarities between data populations. The kernelized Taylor diagram builds on the widely used Taylor diagram, which is used to visualize similarities between populations. However, the Taylor diagram has several limitations such as not capturing non-linear relationships and sensitivity to outliers. To address such limitations, we propose the kernelized Taylor diagram. Our proposed kernelized Taylor diagram is capable of visualizing similarities between populations with minimal assumptions of the data distributions. The kernelized Taylor diagram relates the maximum mean discrepancy and the kernel mean embedding in a single diagram, a construction that, to the best of our knowledge, have not been devised prior to this work. We believe that the kernelized Taylor diagram can be a valuable tool in data visualization.

David Montero, Guido Kraemer, Anca Anghelea et al.

Recent advancements in Earth system science have been marked by the exponential increase in the availability of diverse, multivariate datasets characterised by moderate to high spatio-temporal resolutions. Earth System Data Cubes (ESDCs) have emerged as one suitable solution for transforming this flood of data into a simple yet robust data structure. ESDCs achieve this by organising data into an analysis-ready format aligned with a spatio-temporal grid, facilitating user-friendly analysis and diminishing the need for extensive technical data processing knowledge. Despite these significant benefits, the completion of the entire ESDC life cycle remains a challenging task. Obstacles are not only of a technical nature but also relate to domain-specific problems in Earth system research. There exist barriers to realising the full potential of data collections in light of novel cloud-based technologies, particularly in curating data tailored for specific application domains. These include transforming data to conform to a spatio-temporal grid with minimum distortions and managing complexities such as spatio-temporal autocorrelation issues. Addressing these challenges is pivotal for the effective application of Artificial Intelligence (AI) approaches. Furthermore, adhering to open science principles for data dissemination, reproducibility, visualisation, and reuse is crucial for fostering sustainable research. Overcoming these challenges offers a substantial opportunity to advance data-driven Earth system research, unlocking the full potential of an integrated, multidimensional view of Earth system processes. This is particularly true when such research is coupled with innovative research paradigms and technological progress.

Víctor Elvira, Émilie Chouzenoux, Jordi Cerdà et al.

Granger causality (GC) is often considered not an actual form of causality. Still, it is arguably the most widely used method to assess the predictability of a time series from another one. Granger causality has been widely used in many applied disciplines, from neuroscience and econometrics to Earth sciences. We revisit GC under a graphical perspective of state-space models. For that, we use GraphEM, a recently presented expectation-maximisation algorithm for estimating the linear matrix operator in the state equation of a linear-Gaussian state-space model. Lasso regularisation is included in the M-step, which is solved using a proximal splitting Douglas-Rachford algorithm. Experiments in toy examples and challenging climate problems illustrate the benefits of the proposed model and inference technique over standard Granger causality methods.

Vasileios Sitokonstantinou, Emiliano Díaz Salas Porras, Jordi Cerdà Bautista et al.

In a changing climate, sustainable agriculture is essential for food security and environmental health. However, it is challenging to understand the complex interactions among its biophysical, social, and economic components. Predictive machine learning (ML), with its capacity to learn from data, is leveraged in sustainable agriculture for applications like yield prediction and weather forecasting. Nevertheless, it cannot explain causal mechanisms and remains descriptive rather than prescriptive. To address this gap, we propose causal ML, which merges ML's data processing with causality's ability to reason about change. This facilitates quantifying intervention impacts for evidence-based decision-making and enhances predictive model robustness. We showcase causal ML through eight diverse applications that benefit stakeholders across the agri-food chain, including farmers, policymakers, and researchers.

Danfeng Hong, Chenyu Li, Xuyang Li et al.

Remote sensing (RS) techniques are increasingly crucial for deepening our understanding of the planet. As the volume and diversity of RS data continue to grow exponentially, there is an urgent need for advanced data modeling and understanding capabilities to manage and interpret these vast datasets effectively. Foundation models present significant new growth opportunities and immense potential to revolutionize the RS field. In this paper, we conduct a comprehensive technical survey on foundation models in RS, offering a brand-new perspective by exploring their evolution from unimodality to multimodality. We hope this work serves as a valuable entry point for researchers interested in both foundation models and RS and helps them launch new projects or explore new research topics in this rapidly evolving area. This survey addresses the following three key questions: What are foundation models in RS? Why are foundation models needed in RS? How can we effectively guide junior researchers in gaining a comprehensive and practical understanding of foundation models in RS applications? More specifically, we begin by outlining the background and motivation, emphasizing the importance of foundation models in RS. We then review existing foundation models in RS, systematically categorizing them into unimodal and multimodal approaches. Additionally, we provide a tutorial-like section to guide researchers, especially beginners, on how to train foundation models in RS and apply them to real-world tasks. The survey aims to equip researchers in RS with a deeper and more efficient understanding of foundation models, enabling them to get started easily and effectively apply these models across various RS applications.

Jordi Cerdà-Bautista, José María Tárraga, Vasileios Sitokonstantinou et al.

In the face of climate change-induced droughts, vulnerable regions encounter severe threats to food security, demanding urgent humanitarian assistance. This paper introduces a causal inference framework for the Horn of Africa, aiming to assess the impact of cash-based interventions on food crises. Our contributions include identifying causal relationships within the food security system, harmonizing a comprehensive database including socio-economic, weather and remote sensing data, and estimating the causal effect of humanitarian interventions on malnutrition. On a country level, our results revealed no significant effects, likely due to limited sample size, suboptimal data quality, and an imperfect causal graph resulting from our limited understanding of multidisciplinary systems like food security. Instead, on a district level, results revealed significant effects, further implying the context-specific nature of the system. This underscores the need to enhance data collection and refine causal models with domain experts for more effective future interventions and policies, improving transparency and accountability in humanitarian aid.

Zhitong Xiong, Yi Wang, Fahong Zhang et al.

Earth observation (EO) in open-world settings presents a unique challenge: different applications rely on diverse sensor modalities, each with varying ground sampling distances, spectral ranges, and numbers of spectral bands. However, existing EO foundation models are typically tailored to specific sensor types, making them inflexible when generalizing across the heterogeneous landscape of EO data. To address this, we propose the Dynamic One-For-All (DOFA) model, a unified, multimodal foundation framework designed for diverse vision tasks in EO. Inspired by neural plasticity, DOFA utilizes a wavelength-conditioned dynamic hypernetwork to process inputs from five distinct satellite sensors flexibly. By continually pretraining on five EO modalities, DOFA achieves state-of-the-art performance across multiple downstream tasks and generalizes well to unseen modalities. Enhanced with hybrid continual pretraining, DOFA+ requires significantly fewer computational resources while outperforming counterparts trained with extensive GPU budgets. Experiments on diverse datasets highlight DOFA's potential as a foundation for general-purpose vision models in the sensor-diverse EO domain. The code and pre-trained weights are publicly available at https://github.com/zhu-xlab/DOFA.

Nathan Mankovich, Homer Durand, Emiliano Diaz et al.

Detecting latent confounders from proxy variables is an essential problem in causal effect estimation. Previous approaches are limited to low-dimensional proxies, sorted proxies, and binary treatments. We remove these assumptions and present a novel Proxy Confounder Factorization (PCF) framework for continuous treatment effect estimation when latent confounders manifest through high-dimensional, mixed proxy variables. For specific sample sizes, our two-step PCF implementation, using Independent Component Analysis (ICA-PCF), and the end-to-end implementation, using Gradient Descent (GD-PCF), achieve high correlation with the latent confounder and low absolute error in causal effect estimation with synthetic datasets in the high sample size regime. Even when faced with climate data, ICA-PCF recovers four components that explain $75.9\%$ of the variance in the North Atlantic Oscillation, a known confounder of precipitation patterns in Europe. Code for our PCF implementations and experiments can be found here: https://github.com/IPL-UV/confound_it. The proposed methodology constitutes a stepping stone towards discovering latent confounders and can be applied to many problems in disciplines dealing with high-dimensional observed proxies, e.g., spatiotemporal fields.

Spyros Kondylatos, Nikolaos Ioannis Bountos, Dimitrios Michail et al.

Recent advances in Computer Vision have introduced the concept of pretrained representation uncertainty, enabling zero-shot uncertainty estimation. This holds significant potential for Earth Observation (EO), where trustworthiness is critical, yet the complexity of EO data poses challenges to uncertainty-aware methods. In this work, we investigate the generalization of representation uncertainty in EO, considering the domain's unique semantic characteristics. We pretrain uncertainties on large EO datasets and propose an evaluation framework to assess their zero-shot performance in multi-label classification and segmentation EO tasks. Our findings reveal that, unlike uncertainties pretrained on natural images, EO-pretraining exhibits strong generalization across unseen EO domains, geographic locations, and target granularities, while maintaining sensitivity to variations in ground sampling distance. We demonstrate the practical utility of pretrained uncertainties showcasing their alignment with task-specific uncertainties in downstream tasks, their sensitivity to real-world EO image noise, and their ability to generate spatial uncertainty estimates out-of-the-box. Initiating the discussion on representation uncertainty in EO, our study provides insights into its strengths and limitations, paving the way for future research in the field. Code and weights are available at: https://github.com/Orion-AI-Lab/EOUncertaintyGeneralization.

Chenyu Li, Danfeng Hong, Bing Zhang et al.

Object extraction and segmentation from remote sensing (RS) images is a critical yet challenging task in urban environment monitoring. Urban morphology is inherently complex, with irregular objects of diverse shapes and varying scales. These challenges are amplified by heterogeneity and scale disparities across RS data sources, including sensors, platforms, and modalities, making accurate object segmentation particularly demanding. While the Segment Anything Model (SAM) has shown significant potential in segmenting complex scenes, its performance in handling form-varying objects remains limited due to manual-interactive prompting. To this end, we propose UrbanSAM, a customized version of SAM specifically designed to analyze complex urban environments while tackling scaling effects from remotely sensed observations. Inspired by multi-resolution analysis (MRA) theory, UrbanSAM incorporates a novel learnable prompter equipped with a Uscaling-Adapter that adheres to the invariance criterion, enabling the model to capture multiscale contextual information of objects and adapt to arbitrary scale variations with theoretical guarantees. Furthermore, features from the Uscaling-Adapter and the trunk encoder are aligned through a masked cross-attention operation, allowing the trunk encoder to inherit the adapter's multiscale aggregation capability. This synergy enhances the segmentation performance, resulting in more powerful and accurate outputs, supported by the learned adapter. Extensive experimental results demonstrate the flexibility and superior segmentation performance of the proposed UrbanSAM on a global-scale dataset, encompassing scale-varying urban objects such as buildings, roads, and water.

Claudio Persello, Jan Dirk Wegner, Ronny Hänsch et al. · mila

The synergistic combination of deep learning models and Earth observation promises significant advances to support the sustainable development goals (SDGs). New developments and a plethora of applications are already changing the way humanity will face the living planet challenges. This paper reviews current deep learning approaches for Earth observation data, along with their application towards monitoring and achieving the SDGs most impacted by the rapid development of deep learning in Earth observation. We systematically review case studies to 1) achieve zero hunger, 2) sustainable cities, 3) deliver tenure security, 4) mitigate and adapt to climate change, and 5) preserve biodiversity. Important societal, economic and environmental implications are concerned. Exciting times ahead are coming where algorithms and Earth data can help in our endeavor to address the climate crisis and support more sustainable development.

Kai-Hendrik Cohrs, Gherardo Varando, Nuno Carvalhais et al.

Hybrid modeling integrates machine learning with scientific knowledge to enhance interpretability, generalization, and adherence to natural laws. Nevertheless, equifinality and regularization biases pose challenges in hybrid modeling to achieve these purposes. This paper introduces a novel approach to estimating hybrid models via a causal inference framework, specifically employing Double Machine Learning (DML) to estimate causal effects. We showcase its use for the Earth sciences on two problems related to carbon dioxide fluxes. In the $Q_{10}$ model, we demonstrate that DML-based hybrid modeling is superior in estimating causal parameters over end-to-end deep neural network (DNN) approaches, proving efficiency, robustness to bias from regularization methods, and circumventing equifinality. Our approach, applied to carbon flux partitioning, exhibits flexibility in accommodating heterogeneous causal effects. The study emphasizes the necessity of explicitly defining causal graphs and relationships, advocating for this as a general best practice. We encourage the continued exploration of causality in hybrid models for more interpretable and trustworthy results in knowledge-guided machine learning.

Shan Zhao, Ioannis Prapas, Ilektra Karasante et al.

Wildfire forecasting is notoriously hard due to the complex interplay of different factors such as weather conditions, vegetation types and human activities. Deep learning models show promise in dealing with this complexity by learning directly from data. However, to inform critical decision making, we argue that we need models that are right for the right reasons; that is, the implicit rules learned should be grounded by the underlying processes driving wildfires. In that direction, we propose integrating causality with Graph Neural Networks (GNNs) that explicitly model the causal mechanism among complex variables via graph learning. The causal adjacency matrix considers the synergistic effect among variables and removes the spurious links from highly correlated impacts. Our methodology's effectiveness is demonstrated through superior performance forecasting wildfire patterns in the European boreal and mediterranean biome. The gain is especially prominent in a highly imbalanced dataset, showcasing an enhanced robustness of the model to adapt to regime shifts in functional relationships. Furthermore, SHAP values from our trained model further enhance our understanding of the model's inner workings.

Nathan Mankovich, Gustau Camps-Valls, Tolga Birdal

Principal component analysis (PCA), along with its extensions to manifolds and outlier contaminated data, have been indispensable in computer vision and machine learning. In this work, we present a unifying formalism for PCA and its variants, and introduce a framework based on the flags of linear subspaces, ie a hierarchy of nested linear subspaces of increasing dimension, which not only allows for a common implementation but also yields novel variants, not explored previously. We begin by generalizing traditional PCA methods that either maximize variance or minimize reconstruction error. We expand these interpretations to develop a wide array of new dimensionality reduction algorithms by accounting for outliers and the data manifold. To devise a common computational approach, we recast robust and dual forms of PCA as optimization problems on flag manifolds. We then integrate tangent space approximations of principal geodesic analysis (tangent-PCA) into this flag-based framework, creating novel robust and dual geodesic PCA variations. The remarkable flexibility offered by the 'flagification' introduced here enables even more algorithmic variants identified by specific flag types. Last but not least, we propose an effective convergent solver for these flag-formulations employing the Stiefel manifold. Our empirical results on both real-world and synthetic scenarios, demonstrate the superiority of our novel algorithms, especially in terms of robustness to outliers on manifolds.

Pedram Ghamisi, Weikang Yu, Xiaokang Zhang et al.

Foundation Models (FMs) are large-scale, pre-trained artificial intelligence (AI) systems that have revolutionized natural language processing and computer vision, and are now advancing geospatial analysis and Earth Observation (EO). They promise improved generalization across tasks, scalability, and efficient adaptation with minimal labeled data. However, despite the rapid proliferation of geospatial FMs, their real-world utility and alignment with global sustainability goals remain underexplored. We introduce SustainFM, a comprehensive benchmarking framework grounded in the 17 Sustainable Development Goals with extremely diverse tasks ranging from asset wealth prediction to environmental hazard detection. This study provides a rigorous, interdisciplinary assessment of geospatial FMs and offers critical insights into their role in attaining sustainability goals. Our findings show: (1) While not universally superior, FMs often outperform traditional approaches across diverse tasks and datasets. (2) Evaluating FMs should go beyond accuracy to include transferability, generalization, and energy efficiency as key criteria for their responsible use. (3) FMs enable scalable, SDG-grounded solutions, offering broad utility for tackling complex sustainability challenges. Critically, we advocate for a paradigm shift from model-centric development to impact-driven deployment, and emphasize metrics such as energy efficiency, robustness to domain shifts, and ethical considerations.

Ilias Tsoumas, Vasileios Sitokonstantinou, Georgios Giannarakis et al.

Pesticides serve as a common tool in agricultural pest control but significantly contribute to the climate crisis. To combat this, Integrated Pest Management (IPM) stands as a climate-smart alternative. Despite its potential, IPM faces low adoption rates due to farmers' skepticism about its effectiveness. To address this challenge, we introduce an advanced data analysis framework tailored to enhance IPM adoption. Our framework provides i) robust pest population predictions across diverse environments with invariant and causal learning, ii) interpretable pest presence predictions using transparent models, iii) actionable advice through counterfactual explanations for in-season IPM interventions, iv) field-specific treatment effect estimations, and v) assessments of the effectiveness of our advice using causal inference. By incorporating these features, our framework aims to alleviate skepticism and encourage wider adoption of IPM practices among farmers.

Nathan Mankovich, Ignacio Santamaria, Gustau Camps-Valls et al.

Flag manifolds encode nested sequences of subspaces and serve as powerful structures for various computer vision and machine learning applications. Despite their utility in tasks such as dimensionality reduction, motion averaging, and subspace clustering, current applications are often restricted to extracting flags using common matrix decomposition methods like the singular value decomposition. Here, we address the need for a general algorithm to factorize and work with hierarchical datasets. In particular, we propose a novel, flag-based method that decomposes arbitrary hierarchical real-valued data into a hierarchy-preserving flag representation in Stiefel coordinates. Our work harnesses the potential of flag manifolds in applications including denoising, clustering, and few-shot learning.

Spyros Kondylatos, Nikolaos Ioannis Bountos, Ioannis Prapas et al.

Label noise poses a significant challenge in Earth Observation (EO), often degrading the performance and reliability of supervised Machine Learning (ML) models. Yet, given the critical nature of several EO applications, developing robust and trustworthy ML solutions is essential. In this study, we take a step in this direction by leveraging probabilistic ML to model input-dependent label noise and quantify data uncertainty in EO tasks, accounting for the unique noise sources inherent in the domain. We train uncertainty-aware probabilistic models across a broad range of high-impact EO applications-spanning diverse noise sources, input modalities, and ML configurations-and introduce a dedicated pipeline to assess their accuracy and reliability. Our experimental results show that the uncertainty-aware models consistently outperform the standard deterministic approaches across most datasets and evaluation metrics. Moreover, through rigorous uncertainty evaluation, we validate the reliability of the predicted uncertainty estimates, enhancing the interpretability of model predictions. Our findings emphasize the importance of modeling label noise and incorporating uncertainty quantification in EO, paving the way for more accurate, reliable, and trustworthy ML solutions in the field.

Jose Manuel Aroca-Fernandez, Jose Francisco Diez-Pastor, Pedro Latorre-Carmona et al.

Soil organic carbon (SOC) is a key indicator of soil health, fertility, and carbon sequestration, making it essential for sustainable land management and climate change mitigation. However, large-scale SOC monitoring remains challenging due to spatial variability, temporal dynamics, and multiple influencing factors. We present WALGREEN, a platform that enhances SOC inference by overcoming limitations of current applications. Leveraging machine learning and diverse soil samples, WALGREEN generates predictive models using historical public and private data. Built on cloud-based technologies, it offers a user-friendly interface for researchers, policymakers, and land managers to access carbon data, analyze trends, and support evidence-based decision-making. Implemented in Python, Java, and JavaScript, WALGREEN integrates Google Earth Engine and Sentinel Copernicus via scripting, OpenLayers, and Thymeleaf in a Model-View-Controller framework. This paper aims to advance soil science, promote sustainable agriculture, and drive critical ecosystem responses to climate change.

Ioannis Prapas, Nikolaos Papadopoulos, Nikolaos-Ioannis Bountos et al.

Forecasting wildfires weeks to months in advance is difficult, yet crucial for planning fuel treatments and allocating resources. While short-term predictions typically rely on local weather conditions, long-term forecasting requires accounting for the Earth's interconnectedness, including global patterns and teleconnections. We introduce TeleViT, a Teleconnection-aware Vision Transformer that integrates (i) fine-scale local fire drivers, (ii) coarsened global fields, and (iii) teleconnection indices. This multi-scale fusion is achieved through an asymmetric tokenization strategy that produces heterogeneous tokens processed jointly by a transformer encoder, followed by a decoder that preserves spatial structure by mapping local tokens to their corresponding prediction patches. Using the global SeasFire dataset (2001-2021, 8-day resolution), TeleViT improves AUPRC performance over U-Net++, ViT, and climatology across all lead times, including horizons up to four months. At zero lead, TeleViT with indices and global inputs reaches AUPRC 0.630 (ViT 0.617, U-Net 0.620), at 16x8day lead (around 4 months), TeleViT variants using global input maintain 0.601-0.603 (ViT 0.582, U-Net 0.578), while surpassing the climatology (0.572) at all lead times. Regional results show the highest skill in seasonally consistent fire regimes, such as African savannas, and lower skill in boreal and arid regions. Attention and attribution analyses indicate that predictions rely mainly on local tokens, with global fields and indices contributing coarse contextual information. These findings suggest that architectures explicitly encoding large-scale Earth-system context can extend wildfire predictability on subseasonal-to-seasonal timescales.

Qingsong Xu, Jonathan L Bamber, Nils Thuerey et al.

Accurate long-term forecasting of spatiotemporal dynamics remains a fundamental challenge across scientific and engineering domains. Existing machine learning methods often neglect governing physical laws and fail to quantify inherent uncertainties in spatiotemporal predictions. To address these challenges, we introduce a physics-consistent neural operator (PCNO) that enforces physical constraints by projecting surrogate model outputs onto function spaces satisfying predefined laws. A physics-consistent projection layer within PCNO efficiently computes mass and momentum conservation in Fourier space. Building upon deterministic predictions, we further propose a diffusion model-enhanced PCNO (DiffPCNO), which leverages a consistency model to quantify and mitigate uncertainties, thereby improving the accuracy and reliability of forecasts. PCNO and DiffPCNO achieve high-fidelity spatiotemporal predictions while preserving physical consistency and uncertainty across diverse systems and spatial resolutions, ranging from turbulent flow modeling to real-world flood/atmospheric forecasting. Our two-stage framework provides a robust and versatile approach for accurate, physically grounded, and uncertainty-aware spatiotemporal forecasting.

Nathan Mankovich, Kai-Hendrik Cohrs, Homer Durand et al.

Earth observation involves collecting, analyzing, and processing an ever-growing mass of data. Automatically harvesting information is crucial for addressing significant societal, economic, and environmental challenges, ranging from environmental monitoring to urban planning and disaster management. However, the high dimensionality of these data poses challenges in terms of sparsity, inefficiency, and the curse of dimensionality, which limits the effectiveness of machine learning models. Dimensionality reduction (DR) techniques, specifically feature extraction, address these challenges by preserving essential data properties while reducing complexity and enhancing tasks such as data compression, cleaning, fusion, visualization, anomaly detection, and prediction. This review provides a handbook for leveraging DR across the RS data value chain and identifies opportunities for under-explored DR algorithms and their application in future research.

Spyros Kondylatos, Gustau Camps-Valls, Ioannis Papoutsis

Wildfires are among the most severe natural hazards, posing a significant threat to both humans and natural ecosystems. The growing risk of wildfires increases the demand for forecasting models that are not only accurate but also reliable. Deep Learning (DL) has shown promise in predicting wildfire danger; however, its adoption is hindered by concerns over the reliability of its predictions, some of which stem from the lack of uncertainty quantification. To address this challenge, we present an uncertainty-aware DL framework that jointly captures epistemic (model) and aleatoric (data) uncertainty to enhance short-term wildfire danger forecasting. In the next-day forecasting, our best-performing model improves the F1 Score by 2.3% and reduces the Expected Calibration Error by 2.1% compared to a deterministic baseline, enhancing both predictive skill and calibration. Our experiments confirm the reliability of the uncertainty estimates and illustrate their practical utility for decision support, including the identification of uncertainty thresholds for rejecting low-confidence predictions and the generation of well-calibrated wildfire danger maps with accompanying uncertainty layers. Extending the forecast horizon up to ten days, we observe that aleatoric uncertainty increases with time, showing greater variability in environmental conditions, while epistemic uncertainty remains stable. Finally, we show that although the two uncertainty types may be redundant in low-uncertainty cases, they provide complementary insights under more challenging conditions, underscoring the value of their joint modeling for robust wildfire danger prediction. In summary, our approach significantly improves the accuracy and reliability of wildfire danger forecasting, advancing the development of trustworthy wildfire DL systems.

Homer Durand, Gherardo Varando, Gustau Camps-Valls

We propose a novel approach for learning causal response representations. Our method aims to extract directions in which a multidimensional outcome is most directly caused by a treatment variable. By bridging conditional independence testing with causal representation learning, we formulate an optimisation problem that maximises the evidence against conditional independence between the treatment and outcome, given a conditioning set. This formulation employs flexible regression models tailored to specific applications, creating a versatile framework. The problem is addressed through a generalised eigenvalue decomposition. We show that, under mild assumptions, the distribution of the largest eigenvalue can be bounded by a known $F$-distribution, enabling testable conditional independence. We also provide theoretical guarantees for the optimality of the learned representation in terms of signal-to-noise ratio and Fisher information maximisation. Finally, we demonstrate the empirical effectiveness of our approach in simulation and real-world experiments. Our results underscore the utility of this framework in uncovering direct causal effects within complex, multivariate settings.

Gustau Camps-Valls, Miguel-Ángel Fernández-Torres, Kai-Hendrik Cohrs et al.

In recent years, artificial intelligence (AI) has deeply impacted various fields, including Earth system sciences. Here, AI improved weather forecasting, model emulation, parameter estimation, and the prediction of extreme events. However, the latter comes with specific challenges, such as developing accurate predictors from noisy, heterogeneous and limited annotated data. This paper reviews how AI is being used to analyze extreme events (like floods, droughts, wildfires and heatwaves), highlighting the importance of creating accurate, transparent, and reliable AI models. We discuss the hurdles of dealing with limited data, integrating information in real-time, deploying models, and making them understandable, all crucial for gaining the trust of stakeholders and meeting regulatory needs. We provide an overview of how AI can help identify and explain extreme events more effectively, improving disaster response and communication. We emphasize the need for collaboration across different fields to create AI solutions that are practical, understandable, and trustworthy for analyzing and predicting extreme events. Such collaborative efforts aim to enhance disaster readiness and disaster risk reduction.

Chaonan Ji, Tonio Fincke, Vitus Benson et al.

With climate extremes' rising frequency and intensity, robust analytical tools are crucial to predict their impacts on terrestrial ecosystems. Machine learning techniques show promise but require well-structured, high-quality, and curated analysis-ready datasets. Earth observation datasets comprehensively monitor ecosystem dynamics and responses to climatic extremes, yet the data complexity can challenge the effectiveness of machine learning models. Despite recent progress in deep learning to ecosystem monitoring, there is a need for datasets specifically designed to analyse compound heatwave and drought extreme impact. Here, we introduce the DeepExtremeCubes database, tailored to map around these extremes, focusing on persistent natural vegetation. It comprises over 40,000 spatially sampled small data cubes (i.e. minicubes) globally, with a spatial coverage of 2.5 by 2.5 km. Each minicube includes (i) Sentinel-2 L2A images, (ii) ERA5-Land variables and generated extreme event cube covering 2016 to 2022, and (iii) ancillary land cover and topography maps. The paper aims to (1) streamline data accessibility, structuring, pre-processing, and enhance scientific reproducibility, and (2) facilitate biosphere dynamics forecasting in response to compound extremes.

Kai-Hendrik Cohrs, Gherardo Varando, Emiliano Diaz et al.

Causality is essential for understanding complex systems, such as the economy, the brain, and the climate. Constructing causal graphs often relies on either data-driven or expert-driven approaches, both fraught with challenges. The former methods, like the celebrated PC algorithm, face issues with data requirements and assumptions of causal sufficiency, while the latter demand substantial time and domain knowledge. This work explores the capabilities of Large Language Models (LLMs) as an alternative to domain experts for causal graph generation. We frame conditional independence queries as prompts to LLMs and employ the PC algorithm with the answers. The performance of the LLM-based conditional independence oracle on systems with known causal graphs shows a high degree of variability. We improve the performance through a proposed statistical-inspired voting schema that allows some control over false-positive and false-negative rates. Inspecting the chain-of-thought argumentation, we find causal reasoning to justify its answer to a probabilistic query. We show evidence that knowledge-based CIT could eventually become a complementary tool for data-driven causal discovery.

Homer Durand, Gherardo Varando, Nathan Mankovich et al.

We propose a regularisation strategy of classical machine learning algorithms rooted in causality that ensures robustness against distribution shifts. Building upon the anchor regression framework, we demonstrate how incorporating a straightforward regularisation term into the loss function of classical multivariate analysis algorithms, such as (orthonormalized) partial least squares, reduced-rank regression, and multiple linear regression, enables out-of-distribution generalisation. Our framework allows users to efficiently verify the compatibility of a loss function with the regularisation strategy. Estimators for selected algorithms are provided, showcasing consistency and efficacy in synthetic and real-world climate science problems. The empirical validation highlights the versatility of anchor regularisation, emphasizing its compatibility with multivariate analysis approaches and its role in enhancing replicability while guarding against distribution shifts. The extended anchor framework advances causal inference methodologies, addressing the need for reliable out-of-distribution generalisation.

Gustau Camps-Valls, Andreas Gerhardus, Urmi Ninad et al.

Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.

Devis Tuia, Konrad Schindler, Begüm Demir et al.

Earth observation (EO) is a prime instrument for monitoring land and ocean processes, studying the dynamics at work, and taking the pulse of our planet. This article gives a bird's eye view of the essential scientific tools and approaches informing and supporting the transition from raw EO data to usable EO-based information. The promises, as well as the current challenges of these developments, are highlighted under dedicated sections. Specifically, we cover the impact of (i) Computer vision; (ii) Machine learning; (iii) Advanced processing and computing; (iv) Knowledge-based AI; (v) Explainable AI and causal inference; (vi) Physics-aware models; (vii) User-centric approaches; and (viii) the much-needed discussion of ethical and societal issues related to the massive use of ML technologies in EO.

Kai Jeggle, David Neubauer, Gustau Camps-Valls et al.

Cirrus clouds are key modulators of Earth's climate. Their dependencies on meteorological and aerosol conditions are among the largest uncertainties in global climate models. This work uses three years of satellite and reanalysis data to study the link between cirrus drivers and cloud properties. We use a gradient-boosted machine learning model and a Long Short-Term Memory (LSTM) network with an attention layer to predict the ice water content and ice crystal number concentration. The models show that meteorological and aerosol conditions can predict cirrus properties with $R^2 = 0.49$. Feature attributions are calculated with SHapley Additive exPlanations (SHAP) to quantify the link between meteorological and aerosol conditions and cirrus properties. For instance, the minimum concentration of supermicron-sized dust particles required to cause a decrease in ice crystal number concentration predictions is $2 \times 10^{-4}$ mg m\textsuperscript{-3}. The last 15 hours before the observation predict all cirrus properties.

Gulsen Taskin, Gustau Camps-Valls

Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent classification, regression, or unmixing. Manifold learning methods have shown excellent performance to deal with hyperspectral image (HSI) analysis but, unless specifically designed, they cannot provide an explicit embedding map readily applicable to out-of-sample data. A common assumption to deal with the problem is that the transformation between the high-dimensional input space and the (typically low) latent space is linear. This is a particularly strong assumption, especially when dealing with hyperspectral images due to the well-known nonlinear nature of the data. To address this problem, a manifold learning method based on High Dimensional Model Representation (HDMR) is proposed, which enables to present a nonlinear embedding function to project out-of-sample samples into the latent space. The proposed method is compared to manifold learning methods along with its linear counterparts and achieves promising performance in terms of classification accuracy of a representative set of hyperspectral images.

Ioannis Prapas, Spyros Kondylatos, Ioannis Papoutsis et al.

Wildfire forecasting is of paramount importance for disaster risk reduction and environmental sustainability. We approach daily fire danger prediction as a machine learning task, using historical Earth observation data from the last decade to predict next-day's fire danger. To that end, we collect, pre-process and harmonize an open-access datacube, featuring a set of covariates that jointly affect the fire occurrence and spread, such as weather conditions, satellite-derived products, topography features and variables related to human activity. We implement a variety of Deep Learning (DL) models to capture the spatial, temporal or spatio-temporal context and compare them against a Random Forest (RF) baseline. We find that either spatial or temporal context is enough to surpass the RF, while a ConvLSTM that exploits the spatio-temporal context performs best with a test Area Under the Receiver Operating Characteristic of 0.926. Our DL-based proof-of-concept provides national-scale daily fire danger maps at a much higher spatial resolution than existing operational solutions.

Luca Martino, Víctor Elvira, Javier López-Santiago et al.

In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model selection or uncertainty quantification. Bayesian inference requires the approximation of complicated integrals involving (often costly) posterior distributions. Generally, this approximation is obtained by means of Monte Carlo (MC) methods. In order to reduce the computational cost of the corresponding technique, surrogate models (also called emulators) are often employed. Another alternative approach is the so-called Approximate Bayesian Computation (ABC) scheme. ABC does not require the evaluation of the costly model but the ability to simulate artificial data according to that model. Moreover, in ABC, the choice of a suitable distance between real and artificial data is also required. In this work, we introduce a novel approach where the expensive model is evaluated only in some well-chosen samples. The selection of these nodes is based on the so-called compressed Monte Carlo (CMC) scheme. We provide theoretical results supporting the novel algorithms and give empirical evidence of the performance of the proposed method in several numerical experiments. Two of them are real-world applications in astronomy and satellite remote sensing.

Daniel Heestermans Svendsen, Maria Piles, Jordi Muñoz-Marí et al.

The modelling of Earth observation data is a challenging problem, typically approached by either purely mechanistic or purely data-driven methods. Mechanistic models encode the domain knowledge and physical rules governing the system. Such models, however, need the correct specification of all interactions between variables in the problem and the appropriate parameterization is a challenge in itself. On the other hand, machine learning approaches are flexible data-driven tools, able to approximate arbitrarily complex functions, but lack interpretability and struggle when data is scarce or in extrapolation regimes. In this paper, we argue that hybrid learning schemes that combine both approaches can address all these issues efficiently. We introduce Gaussian process (GP) convolution models for hybrid modelling in Earth observation (EO) problems. We specifically propose the use of a class of GP convolution models called latent force models (LFMs) for EO time series modelling, analysis and understanding. LFMs are hybrid models that incorporate physical knowledge encoded in differential equations into a multioutput GP model. LFMs can transfer information across time-series, cope with missing observations, infer explicit latent functions forcing the system, and learn parameterizations which are very helpful for system analysis and interpretability. We consider time series of soil moisture from active (ASCAT) and passive (SMOS, AMSR2) microwave satellites. We show how assuming a first order differential equation as governing equation, the model automatically estimates the e-folding time or decay rate related to soil moisture persistence and discovers latent forces related to precipitation. The proposed hybrid methodology reconciles the two main approaches in remote sensing parameter estimation by blending statistical learning and mechanistic modeling.

Daniel Heestermans Svendsen, Pablo Morales-Alvarez, Ana Belen Ruescas et al.

Parameter retrieval and model inversion are key problems in remote sensing and Earth observation. Currently, different approximations exist: a direct, yet costly, inversion of radiative transfer models (RTMs); the statistical inversion with in situ data that often results in problems with extrapolation outside the study area; and the most widely adopted hybrid modeling by which statistical models, mostly nonlinear and non-parametric machine learning algorithms, are applied to invert RTM simulations. We will focus on the latter. Among the different existing algorithms, in the last decade kernel based methods, and Gaussian Processes (GPs) in particular, have provided useful and informative solutions to such RTM inversion problems. This is in large part due to the confidence intervals they provide, and their predictive accuracy. However, RTMs are very complex, highly nonlinear, and typically hierarchical models, so that often a shallow GP model cannot capture complex feature relations for inversion. This motivates the use of deeper hierarchical architectures, while still preserving the desirable properties of GPs. This paper introduces the use of deep Gaussian Processes (DGPs) for bio-geo-physical model inversion. Unlike shallow GP models, DGPs account for complicated (modular, hierarchical) processes, provide an efficient solution that scales well to big datasets, and improve prediction accuracy over their single layer counterpart. In the experimental section, we provide empirical evidence of performance for the estimation of surface temperature and dew point temperature from infrared sounding data, as well as for the prediction of chlorophyll content, inorganic suspended matter, and coloured dissolved matter from multispectral data acquired by the Sentinel-3 OLCI sensor. The presented methodology allows for more expressive forms of GPs in remote sensing model inversion problems.

Devis Tuia, Michele Volpi, Maxime Trolliet et al.

We introduce a method for manifold alignment of different modalities (or domains) of remote sensing images. The problem is recurrent when a set of multitemporal, multisource, multisensor and multiangular images is available. In these situations, images should ideally be spatially coregistred, corrected and compensated for differences in the image domains. Such procedures require the interaction of the user, involve tuning of many parameters and heuristics, and are usually applied separately. Changes of sensors and acquisition conditions translate into shifts, twists, warps and foldings of the image distributions (or manifolds). The proposed semisupervised manifold alignment (SS-MA) method aligns the images working directly on their manifolds, and is thus not restricted to images of the same resolutions, either spectral or spatial. SS-MA pulls close together samples of the same class while pushing those of different classes apart. At the same time, it preserves the geometry of each manifold along the transformation. The method builds a linear invertible transformation to a latent space where all images are alike, and reduces to solving a generalized eigenproblem of moderate size. We study the performance of SS-MA in toy examples and in real multiangular, multitemporal, and multisource image classification problems. The method performs well for strong deformations and leads to accurate classification for all domains.

Devis Tuia, Ribana Roscher, Jan Dirk Wegner et al.

In the last years we have witnessed the fields of geosciences and remote sensing and artificial intelligence to become closer. Thanks to both the massive availability of observational data, improved simulations, and algorithmic advances, these disciplines have found common objectives and challenges to advance the modeling and understanding of the Earth system. Despite such great opportunities, we also observed a worrying tendency to remain in disciplinary comfort zones applying recent advances from artificial intelligence on well resolved remote sensing problems. Here we take a position on research directions where we think the interface between these fields will have the most impact and become potential game changers. In our declared agenda for AI on Earth sciences, we aim to inspire researchers, especially the younger generations, to tackle these challenges for a real advance of remote sensing and the geosciences.

Ana B. Ruescas, Martin Hieronymi, Sampsa Koponen et al.

The coloured dissolved organic matter (CDOM) concentration is the standard measure of humic substance in natural waters. CDOM measurements by remote sensing is calculated using the absorption coefficient (a) at a certain wavelength (e.g. 440nm). This paper presents a comparison of four machine learning methods for the retrieval of CDOM from remote sensing signals: regularized linear regression (RLR), random forest (RF), kernel ridge regression (KRR) and Gaussian process regression (GPR). Results are compared with the established polynomial regression algorithms. RLR is revealed as the simplest and most efficient method, followed closely by its nonlinear counterpart KRR.

Fernando Mateo, Jordi Munoz-Mari, Valero Laparra et al.

Gaussian Processes (GPs) has experienced tremendous success in geoscience in general and for bio-geophysical parameter retrieval in the last years. GPs constitute a solid Bayesian framework to formulate many function approximation problems consistently. This paper reviews the main theoretical GP developments in the field. We review new algorithms that respect the signal and noise characteristics, that provide feature rankings automatically, and that allow applicability of associated uncertainty intervals to transport GP models in space and time. All these developments are illustrated in the field of geoscience and remote sensing at a local and global scales through a set of illustrative examples.

Anna Mateo-Sanchis, Jordi Munoz-Mari, Manuel Campos-Taberner et al.

In this work we evaluate multi-output (MO) Gaussian Process (GP) models based on the linear model of coregionalization (LMC) for estimation of biophysical parameter variables under a gap filling setup. In particular, we focus on LAI and fAPAR over rice areas. We show how this problem cannot be solved with standard single-output (SO) GP models, and how the proposed MO-GP models are able to successfully predict these variables even in high missing data regimes, by implicitly performing an across-domain information transfer.

Gonzalo Mateo-García, Luis Gómez-Chova, Gustau Camps-Valls

Convolutional neural networks (CNN) have proven to be state of the art methods for many image classification tasks and their use is rapidly increasing in remote sensing problems. One of their major strengths is that, when enough data is available, CNN perform an end-to-end learning without the need of custom feature extraction methods. In this work, we study the use of different CNN architectures for cloud masking of Proba-V multispectral images. We compare such methods with the more classical machine learning approach based on feature extraction plus supervised classification. Experimental results suggest that CNN are a promising alternative for solving cloud masking problems.

Luis Gómez-Chova, Gonzalo Mateo-García, Jordi Muñoz-Marí et al.

This paper presents the development and implementation of a cloud detection algorithm for Proba-V. Accurate and automatic detection of clouds in satellite scenes is a key issue for a wide range of remote sensing applications. With no accurate cloud masking, undetected clouds are one of the most significant sources of error in both sea and land cover biophysical parameter retrieval. The objective of the algorithms presented in this paper is to detect clouds accurately providing a cloud flag per pixel. For this purpose, the method exploits the information of Proba-V using statistical machine learning techniques to identify the clouds present in Proba-V products. The effectiveness of the proposed method is successfully illustrated using a large number of real Proba-V images.

Juan Emmanuel Johnson, Valero Laparra, Gustau Camps-Valls

Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems, especially in parameter retrieval. An addition to a predictive mean function, GPs come equipped with a useful property: the predictive variance function which provides confidence intervals for the predictions. The GP formulation usually assumes that there is no input noise in the training and testing points, only in the observations. However, this is often not the case in Earth observation problems where an accurate assessment of the instrument error is usually available. In this paper, we showcase how the derivative of a GP model can be used to provide an analytical error propagation formulation and we analyze the predictive variance and the propagated error terms in a temperature prediction problem from infrared sounding data.

Anna Mateo-Sanchis, Jordi Muñoz-Marí, Adrián Pérez-Suay et al.

This paper introduces warped Gaussian processes (WGP) regression in remote sensing applications. WGP models output observations as a parametric nonlinear transformation of a GP. The parameters of such prior model are then learned via standard maximum likelihood. We show the good performance of the proposed model for the estimation of oceanic chlorophyll content from multispectral data, vegetation parameters (chlorophyll, leaf area index, and fractional vegetation cover) from hyperspectral data, and in the detection of the causal direction in a collection of 28 bivariate geoscience and remote sensing causal problems. The model consistently performs better than the standard GP and the more advanced heteroscedastic GP model, both in terms of accuracy and more sensible confidence intervals.

Emiliano Díaz, Adrián Pérez-Suay, Valero Laparra et al.

This paper introduces a novel statistical regression framework that allows the incorporation of consistency constraints. A linear and nonlinear (kernel-based) formulation are introduced, and both imply closed-form analytical solutions. The models exploit all the information from a set of drivers while being maximally independent of a set of auxiliary, protected variables. We successfully illustrate the performance in the estimation of chlorophyll content.