Tipping points are abrupt, drastic, and often irreversible changes in the evolution of non-stationary and chaotic dynamical systems. For instance, increased greenhouse gas concentrations are predicted to lead to drastic decreases in low cloud cover, referred to as a climatological tipping point. In this paper, we learn the evolution of such non-stationary dynamical systems using a novel recurrent neural operator (RNO), which learns mappings between function spaces. After training RNO on only the pre-tipping dynamics, we employ it to detect future tipping points using an uncertainty-based approach. In particular, we propose a conformal prediction framework to forecast tipping points by monitoring deviations from physics constraints (such as conserved quantities and partial differential equations), enabling forecasting of these abrupt changes along with a rigorous measure of uncertainty. We illustrate our proposed methodology on non-stationary ordinary and partial differential equations, such as the Lorenz-63 and Kuramoto-Sivashinsky equations. We also apply our methods to forecast a climate tipping point in stratocumulus cloud cover. In our experiments, we demonstrate that even partial or approximate physics constraints can be used to accurately forecast future tipping points.

Establishing a human settlement on Mars is an incredibly complex engineering problem. The inhospitable nature of the Martian environment requires any habitat to be largely self-sustaining. Beyond mining a few basic minerals and water, the colonizers will be dependent on Earth resupply and replenishment of necessities via technological means, i.e., splitting Martian water into oxygen for breathing and hydrogen for fuel. Beyond the technical and engineering challenges, future colonists will also face psychological and human behavior challenges. Our goal is to better understand the behavioral and psychological interactions of future Martian colonists through an Agent-Based Modeling (ABM simulation) approach. We seek to identify areas of consideration for planning a colony as well as propose a minimum initial population size required to create a stable colony. Accounting for engineering and technological limitations, we draw on research regarding high performing teams in isolated and high stress environments (ex: submarines, Arctic exploration, ISS, war) to include the 4 basic personality types within the ABM. Interactions between agents with different psychological profiles are modeled at the individual level, while global events such as accidents or delays in Earth resupply affect the colony as a whole. From our multiple simulations and scenarios (up to 28 Earth years), we found that an initial population of 22 was the minimum required to maintain a viable colony size over the long run. We also found that the agreeable personality type was the one more likely to survive. We find, contrary to other literature, that the minimum number of people with all personality types that can lead to a sustainable settlement is in the tens and not hundreds.

Thesis concerns the study and development of hierarchical representations for spatio-temporal visual attention modeling and understanding in video sequences. More specifically, we propose two computational models for visual attention. First, we present a generative probabilistic model for context-aware visual attention modeling and understanding. Secondly, we develop a deep network architecture for visual attention modeling, which first estimates top-down spatio-temporal visual attention, and ultimately serves for modeling attention in the temporal domain. The first part of the thesis introduces our first proposal: a generative probabilistic framework for spatio-temporal visual attention modeling and understanding.

Robotic underwater systems, e.g., Autonomous Underwater Vehicles (AUVs) and Remotely Operated Vehicles (ROVs), are promising tools for collecting biogeochemical data at the ice-water interface for scientific advancements. However, state estimation, i.e., localization, is a well-known problem for robotic systems, especially, for the ones that travel underwater. In this paper, we present a tightly-coupled multi-sensors fusion framework to increase localization accuracy that is robust to sensor failure. Visual images, Doppler Velocity Log (DVL), Inertial Measurement Unit (IMU) and Pressure sensor are integrated into the state-of-art Multi-State Constraint Kalman Filter (MSCKF) for state estimation. Besides that a new keyframe-based state clone mechanism and a new DVL-aided feature enhancement are presented to further improve the localization performance. The proposed method is validated with a data set collected in the field under frozen ice, and the result is compared with 6 other different sensor fusion setups. Overall, the result with the keyframe enabled and DVL-aided feature enhancement yields the best performance with a Root-mean-square error of less than 2 m compared to the ground truth path with a total traveling distance of about 200 m.

Hyperparameter tuning plays a crucial role in optimizing the performance of predictive learners. Cross--validation (CV) is a widely adopted technique for estimating the error of different hyperparameter settings. Repeated cross-validation (RCV) has been commonly employed to reduce the variability of CV errors. In this paper, we introduce a novel approach called blocked cross-validation (BCV), where the repetitions are blocked with respect to both CV partition and the random behavior of the learner. Theoretical analysis and empirical experiments demonstrate that BCV provides more precise error estimates compared to RCV, even with a significantly reduced number of runs. We present extensive examples using real--world data sets to showcase the effectiveness and efficiency of BCV in hyperparameter tuning. Our results indicate that BCV outperforms RCV in hyperparameter tuning, achieving greater precision with fewer computations.

Human-robot interaction will play an essential role in various industries and daily tasks, enabling robots to effectively collaborate with humans and reduce their physical workload. Most of the existing approaches for physical human-robot interaction focus on collaboration between a human and a single ground robot. In recent years, very little progress has been made in this research area when considering aerial robots, which offer increased versatility and mobility compared to their grounded counterparts. This paper proposes a novel approach for safe human-robot collaborative transportation and manipulation of a cable-suspended payload with multiple aerial robots. We leverage the proposed method to enable smooth and intuitive interaction between the transported objects and a human worker while considering safety constraints during operations by exploiting the redundancy of the internal transportation system. The key elements of our system are (a) a distributed payload external wrench estimator that does not rely on any force sensor; (b) a 6D admittance controller for human-aerial-robot collaborative transportation and manipulation; (c) a safety-aware controller that exploits the internal system redundancy to guarantee the execution of additional tasks devoted to preserving the human or robot safety without affecting the payload trajectory tracking or quality of interaction. We validate the approach through extensive simulation and real-world experiments. These include as well the robot team assisting the human in transporting and manipulating a load or the human helping the robot team navigate the environment. To the best of our knowledge, this work is the first to create an interactive and safety-aware approach for quadrotor teams that physically collaborate with a human operator during transportation and manipulation tasks.

Numerical data imputation algorithms replace missing values by estimates to leverage incomplete data sets. Current imputation methods seek to minimize the error between the unobserved ground truth and the imputed values. But this strategy can create artifacts leading to poor imputation in the presence of multimodal or complex distributions. To tackle this problem, we introduce the $k$NN$\times$KDE algorithm: a data imputation method combining nearest neighbor estimation ($k$NN) and density estimation with Gaussian kernels (KDE). We compare our method with previous data imputation methods using artificial and real-world data with different data missing scenarios and various data missing rates, and show that our method can cope with complex original data structure, yields lower data imputation errors, and provides probabilistic estimates with higher likelihood than current methods. We release the code in open-source for the community: https://github.com/DeltaFloflo/knnxkde

Visualization is a crucial step in exploratory data analysis. One possible approach is to train an autoencoder with low-dimensional latent space. Large network depth and width can help unfolding the data. However, such expressive networks can achieve low reconstruction error even when the latent representation is distorted. To avoid such misleading visualizations, we propose first a differential geometric perspective on the decoder, leading to insightful diagnostics for an embedding's distortion, and second a new regularizer mitigating such distortion. Our ``Geometric Autoencoder'' avoids stretching the embedding spuriously, so that the visualization captures the data structure more faithfully. It also flags areas where little distortion could not be achieved, thus guarding against misinterpretation.

Layer-wise relevance propagation (LRP) is a widely used and powerful technique to reveal insights into various artificial neural network (ANN) architectures. LRP is often used in the context of image classification. The aim is to understand, which parts of the input sample have highest relevance and hence most influence on the model prediction. Relevance can be traced back through the network to attribute a certain score to each input pixel. Relevance scores are then combined and displayed as heat maps and give humans an intuitive visual understanding of classification models. Opening the black box to understand the classification engine in great detail is essential for domain experts to gain trust in ANN models. However, there are pitfalls in terms of model-inherent artifacts included in the obtained relevance maps, that can easily be missed. But for a valid interpretation, these artifacts must not be ignored. Here, we apply and revise LRP on various ANN architectures trained as classifiers on geospatial and synthetic data. Depending on the network architecture, we show techniques to control model focus and give guidance to improve the quality of obtained relevance maps to separate facts from artifacts.

After more than a decade of searching, the IceCube neutrino detector in Antarctica has finally found high-energy particles from within the Milky Way. This discovery opens a window into how cosmic rays shape the universe. The disc of the Milky Way is incredibly bright in every wavelength of light – particularly in gamma rays, which tend to be accompanied by neutrinos. But any neutrinos from within our galaxy have historically been overwhelmed by stronger signals from other galaxies, so we haven't been able to observe them. "It took us 10 years to find the galactic plane in neutrinos," says IceCube head Francis Halzen at the University of Wisconsin-Madison.