Mauro Dalla Mura

Anthony Frion, Lucas Drumetz, Mauro Dalla Mura et al.

With the increasing availability of large scale datasets, computational power and tools like automatic differentiation and expressive neural network architectures, sequential data are now often treated in a data-driven way, with a dynamical model trained from the observation data. While neural networks are often seen as uninterpretable black-box architectures, they can still benefit from physical priors on the data and from mathematical knowledge. In this paper, we use a neural network architecture which leverages the long-known Koopman operator theory to embed dynamical systems in latent spaces where their dynamics can be described linearly, enabling a number of appealing features. We introduce methods that enable to train such a model for long-term continuous reconstruction, even in difficult contexts where the data comes in irregularly-sampled time series. The potential for self-supervised learning is also demonstrated, as we show the promising use of trained dynamical models as priors for variational data assimilation techniques, with applications to e.g. time series interpolation and forecasting.

Anthony Frion, Lucas Drumetz, Mauro Dalla Mura et al.

Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where the dynamics of the underlying phenomenon can be described by a linear operator, based on the Koopman operator theory. However, despite being able to provide reliable long-term predictions for some dynamical systems in ideal situations, the methods proposed so far have limitations, such as requiring to discretize intrinsically continuous dynamical systems, leading to data loss, especially when handling incomplete or sparsely sampled data. Here, we propose a new deep Koopman framework that represents dynamics in an intrinsically continuous way, leading to better performance on limited training data, as exemplified on several datasets arising from dynamical systems.

Andrea Marinoni, Pietro Lio', Erik Cambria et al.

The strong and continuous increase of AI-based services leads to the steady proliferation of AI data centres worldwide with the unavoidable escalation of their power consumption. It is unknown how this energy demand for computational purposes will impact the surrounding environment. Here, we focus our attention on the heat dissipation of AI hyperscalers. Taking advantage of land surface temperature measurements acquired by remote sensing platforms over the last decades, we are able to obtain a robust assessment of the temperature increase recorded in the areas surrounding AI data centres globally. We estimate that the land surface temperature increases by 2°C on average after the start of operations of an AI data centre, inducing local microclimate zones, which we call the data heat island effect. We assess the impact on the communities, quantifying that more than 340 million people could be affected by this temperature increase. Our results show that the data heat island effect could have a remarkable influence on communities and regional welfare in the future, hence becoming part of the conversation around environmentally sustainable AI worldwide.

Anthony Frion, Lucas Drumetz, Guillaume Tochon et al.

In the context of an increasing popularity of data-driven models to represent dynamical systems, many machine learning-based implementations of the Koopman operator have recently been proposed. However, the vast majority of those works are limited to deterministic predictions, while the knowledge of uncertainty is critical in fields like meteorology and climatology. In this work, we investigate the training of ensembles of models to produce stochastic outputs. We show through experiments on real remote sensing image time series that ensembles of independently trained models are highly overconfident and that using a training criterion that explicitly encourages the members to produce predictions with high inter-model variances greatly improves the uncertainty quantification of the ensembles.

Kebin Contreras, Luis Toscano-Palomino, Mauro Dalla Mura et al.

Recovering the past from present observations is an intriguing challenge with potential applications in forensics and scene analysis. Thermal imaging, operating in the infrared range, provides access to otherwise invisible information. Since humans are typically warmer (37 C -98.6 F) than their surroundings, interactions such as sitting, touching, or leaning leave residual heat traces. These fading imprints serve as passive temporal codes, allowing for the inference of recent events that exceed the capabilities of RGB cameras. This work proposes a time-reversed reconstruction framework that uses paired RGB and thermal images to recover scene states from a few seconds earlier. The proposed approach couples Visual-Language Models (VLMs) with a constrained diffusion process, where one VLM generates scene descriptions and another guides image reconstruction, ensuring semantic and structural consistency. The method is evaluated in three controlled scenarios, demonstrating the feasibility of reconstructing plausible past frames up to 120 seconds earlier, providing a first step toward time-reversed imaging from thermal traces.

Anthony Frion, Lucas Drumetz, Mauro Dalla Mura et al.

Following the introduction of Dynamic Mode Decomposition and its numerous extensions, many neural autoencoder-based implementations of the Koopman operator have recently been proposed. This class of methods appears to be of interest for modeling dynamical systems, either through direct long-term prediction of the evolution of the state or as a powerful embedding for downstream methods. In particular, a recent line of work has developed invertible Koopman autoencoders (IKAEs), which provide an exact reconstruction of the input state thanks to their analytically invertible encoder, based on coupling layer normalizing flow models. We identify that the conservation of the dimension imposed by the normalizing flows is a limitation for the IKAE models, and thus we propose to augment the latent state with a second, non-invertible encoder network. This results in our new model: the Augmented Invertible Koopman AutoEncoder (AIKAE). We demonstrate the relevance of the AIKAE through a series of long-term time series forecasting experiments, on satellite image time series as well as on a benchmark involving predictions based on a large lookback window of observations.

Giuseppe Costantino, Sophie Giffard-Roisin, Mauro Dalla Mura et al.

Geospatial data has been transformative for the monitoring of the Earth, yet, as in the case of (geo)physical monitoring, the measurements can have variable spatial and temporal sampling and may be associated with a significant level of perturbations degrading the signal quality. Denoising geospatial data is, therefore, essential, yet often challenging because the observations may comprise noise coming from different origins, including both environmental signals and instrumental artifacts, which are spatially and temporally correlated, thus hard to disentangle. This study addresses the denoising of multivariate time series acquired by irregularly distributed networks of sensors, requiring specific methods to handle the spatiotemporal correlation of the noise and the signal of interest. Specifically, our method focuses on the denoising of geodetic position time series, used to monitor ground displacement worldwide with centimeter- to-millimeter precision. Among the signals affecting GNSS data, slow slip events (SSEs) are of interest to seismologists. These are transients of deformation that are weakly emerging compared to other signals. Here, we design SSEdenoiser, a multi-station spatiotemporal graph-based attentive denoiser that learns latent characteristics of GNSS noise to reveal SSE-related displacement with sub-millimeter precision. It is based on the key combination of graph recurrent networks and spatiotemporal Transformers. The proposed method is applied to the Cascadia subduction zone, where SSEs occur along with bursts of tectonic tremors, a seismic rumbling identified from independent seismic recordings. The extracted events match the spatiotemporal evolution of tremors. This good space-time correlation of the denoised GNSS signals with the tremors validates the proposed denoising procedure.

Anthony Frion, Lucas Drumetz, Guillaume Tochon et al.

Over the last few years, massive amounts of satellite multispectral and hyperspectral images covering the Earth's surface have been made publicly available for scientific purpose, for example through the European Copernicus project. Simultaneously, the development of self-supervised learning (SSL) methods has sparked great interest in the remote sensing community, enabling to learn latent representations from unlabeled data to help treating downstream tasks for which there is few annotated examples, such as interpolation, forecasting or unmixing. Following this line, we train a deep learning model inspired from the Koopman operator theory to model long-term reflectance dynamics in an unsupervised way. We show that this trained model, being differentiable, can be used as a prior for data assimilation in a straightforward way. Our datasets, which are composed of Sentinel-2 multispectral image time series, are publicly released with several levels of treatment.

Keiller Nogueira, Jocelyn Chanussot, Mauro Dalla Mura et al.

The recent impressive results of deep learning-based methods on computer vision applications brought fresh air to the research and industrial community. This success is mainly due to the process that allows those methods to learn data-driven features, generally based upon linear operations. However, in some scenarios, such operations do not have a good performance because of their inherited process that blurs edges, losing notions of corners, borders, and geometry of objects. Overcoming this, non-linear operations, such as morphological ones, may preserve such properties of the objects, being preferable and even state-of-the-art in some applications. Encouraged by this, in this work, we propose a novel network, called Deep Morphological Network (DeepMorphNet), capable of doing non-linear morphological operations while performing the feature learning process by optimizing the structuring elements. The DeepMorphNets can be trained and optimized end-to-end using traditional existing techniques commonly employed in the training of deep learning approaches. A systematic evaluation of the proposed algorithm is conducted using two synthetic and two traditional image classification datasets. Results show that the proposed DeepMorphNets is a promising technique that can learn distinct features when compared to the ones learned by current deep learning methods.

Keiller Nogueira, Mauro Dalla Mura, Jocelyn Chanussot et al.

Semantic segmentation requires methods capable of learning high-level features while dealing with large volume of data. Towards such goal, Convolutional Networks can learn specific and adaptable features based on the data. However, these networks are not capable of processing a whole remote sensing image, given its huge size. To overcome such limitation, the image is processed using fixed size patches. The definition of the input patch size is usually performed empirically (evaluating several sizes) or imposed (by network constraint). Both strategies suffer from drawbacks and could not lead to the best patch size. To alleviate this problem, several works exploited multi-context information by combining networks or layers. This process increases the number of parameters resulting in a more difficult model to train. In this work, we propose a novel technique to perform semantic segmentation of remote sensing images that exploits a multi-context paradigm without increasing the number of parameters while defining, in training time, the best patch size. The main idea is to train a dilated network with distinct patch sizes, allowing it to capture multi-context characteristics from heterogeneous contexts. While processing these varying patches, the network provides a score for each patch size, helping in the definition of the best size for the current scenario. A systematic evaluation of the proposed algorithm is conducted using four high-resolution remote sensing datasets with very distinct properties. Our results show that the proposed algorithm provides improvements in pixelwise classification accuracy when compared to state-of-the-art methods.