In-context operator networks (ICON) are a class of operator learning methods based on the novel architectures of foundation models. Trained on a diverse set of datasets of initial and boundary conditions paired with corresponding solutions to ordinary and partial differential equations (ODEs and PDEs), ICON learns to map example condition-solution pairs of a given differential equation to an approximation of its solution operator. Here, we present a probabilistic framework that reveals ICON as implicitly performing Bayesian inference, where it computes the mean of the posterior predictive distribution over solution operators conditioned on the provided context, i.e., example condition-solution pairs. The formalism of random differential equations provides the probabilistic framework for describing the tasks ICON accomplishes while also providing a basis for understanding other multi-operator learning methods. This probabilistic perspective provides a basis for extending ICON to \emph{generative} settings, where one can sample from the posterior predictive distribution of solution operators. The generative formulation of ICON (GenICON) captures the underlying uncertainty in the solution operator, which enables principled uncertainty quantification in the solution predictions in operator learning.

--Nonnegative matrix factorization (NMF) is a known unsupervised data-reduction method. The principle of the common cause (PCC) is a basic methodological approach in probabilistic causality, which seeks an independent mixture model for the joint probability of two dependent random variables. It turns out that these two concepts are closely related. This relationship is explored reciprocally for several datasets of gray-scale images, which are conveniently mapped into probability models. On one hand, PCC provides a predictability tool that leads to a robust estimation of the effective rank of NMF . Unlike other estimates (e.g., those based on the Bayesian Information Criteria), our estimate of the rank is stable against weak noise. We show that NMF implemented around this rank produces features (basis images) that are also stable against noise and against seeds of local optimization, thereby effectively resolving the NMF nonidentifiability problem. On the other hand, NMF provides an interesting possibility of implementing PCC in an approximate way, where larger and positively correlated joint probabilities tend to be explained better via the independent mixture model. We work out a clustering method, where data points with the same common cause are grouped into the same cluster . We also show how NMF can be employed for data denoising. Nonnegative matrix factorization (NMF) was proposed and developed in data science [1]-[3].

Abstract--As long-endurance and seafloor-resident AUVs become more capable, there is an increasing need for extended, real-time interpretation of seafloor imagery to enable adaptive missions and optimise communication efficiency. Although offline image analysis methods are well established, they rely on access to complete datasets and human-labelled examples to manage the strong influence of environmental and operational conditions on seafloor image appearance--requirements that cannot be met in real-time settings. T o address this, we introduce an online clustering framework (OCF) capable of interpreting seafloor imagery without supervision, that is designed to operate in real-time on continuous data streams in a scalable, adaptive, and self-consistent manner . The method enables the efficient review and consolidation of common patterns across the entire data history in constant time by identifying and maintaining a set of representative samples that capture the evolving feature distribution, supporting dynamic cluster merging and splitting without reprocessing the full image history. We evaluate the framework on three diverse seafloor image datasets, analysing the impact of different representative sampling strategies on both clustering accuracy and computational cost. The OCF achieves the highest average F1 score of 0.68 across the three datasets among all comparative online clustering approaches, with a standard deviation of 3% across three distinct survey trajectories, demonstrating its superior clustering capability and robustness to trajectory variation. In addition, it maintains consistently lower and bounded computational time as the data volume increases. Compared to offline clustering methods, it strikes a favourable balance between accuracy and efficiency. These properties are beneficial for generating survey data summaries and supporting informative path planning in long-term, persistent autonomous marine exploration.

In supply chain management, decision-making often involves balancing multiple conflicting objectives, such as cost reduction, service level improvement, and environmental sustainability. Traditional multi-objective optimization methods, such as linear programming and evolutionary algorithms, struggle to adapt in real-time to the dynamic nature of supply chains. In this paper, we propose an approach that combines Reinforcement Learning (RL) and Multi-Objective Evolutionary Algorithms (MOEAs) to address these challenges for dynamic multi-objective optimization under uncertainty. Our method leverages MOEAs to search the parameter space of policy neural networks, generating a Pareto front of policies. This provides decision-makers with a diverse population of policies that can be dynamically switched based on the current system objectives, ensuring flexibility and adaptability in real-time decision-making. We also introduce Conditional Value-at-Risk (CVaR) to incorporate risk-sensitive decision-making, enhancing resilience in uncertain environments. We demonstrate the effectiveness of our approach through case studies, showcasing its ability to respond to supply chain dynamics and outperforming state-of-the-art methods in an inventory management case study. The proposed strategy not only improves decision-making efficiency but also offers a more robust framework for managing uncertainty and optimizing performance in supply chains.

Legged robots must achieve both robust locomotion and energy efficiency to be practical in real-world environments. Yet controllers trained in simulation often fail to transfer reliably, and most existing approaches neglect actuator-specific energy losses or depend on complex, hand-tuned reward formulations. We propose a framework that integrates sim-to-real reinforcement learning with a physics-grounded energy model for permanent magnet synchronous motors. The framework requires a minimal parameter set to capture the simulation-to-reality gap and employs a compact four-term reward with a first-principle-based energetic loss formulation that balances electrical and mechanical dissipation. We evaluate and validate the approach through a bottom-up dynamic parameter identification study, spanning actuators, full-robot in-air trajectories and on-ground locomotion. The framework is tested on three primary platforms and deployed on ten additional robots, demonstrating reliable policy transfer without randomization of dynamic parameters. Our method improves energetic efficiency over state-of-the-art methods, achieving a 32 percent reduction in the full Cost of Transport of ANYmal (value 1.27). All code, models, and datasets will be released.

The rapid expansion of scientific literature makes it increasingly difficult to acquire new knowledge, particularly in specialized domains where reasoning is complex, full-text access is restricted, and target references are sparse among a large set of candidates. We present a Deep Reinforcement Learning framework for sparse reference selection that emulates human knowledge construction, prioritizing which papers to read under limited time and cost. Evaluated on drug--gene relation discovery with access restricted to titles and abstracts, our approach demonstrates that both humans and machines can construct knowledge effectively from partial information.

While queueing network models are powerful tools for analyzing service systems, they traditionally require substantial human effort and domain expertise to construct. To make this modeling approach more scalable and accessible, we propose a data-driven framework for queueing network modeling and simulation based on autoregressive sequence models trained on event-stream data. Instead of explicitly specifying arrival processes, service mechanisms, or routing logic, our approach learns the conditional distributions of event types and event times, recasting the modeling task as a problem of sequence distribution learning. We show that Transformer-style architectures can effectively parameterize these distributions, enabling automated construction of high-fidelity simulators. As a proof of concept, we validate our framework on event tables generated from diverse queueing networks, showcasing its utility in simulation, uncertainty quantification, and counterfactual evaluation. Leveraging advances in artificial intelligence and the growing availability of data, our framework takes a step toward more automated, data-driven modeling pipelines to support broader adoption of queueing network models across service domains.

Data collection is crucial for learning robust world models in model-based reinforcement learning. The most prevalent strategies are to actively collect trajectories by interacting with the environment during online training or training on offline datasets. At first glance, the nature of learning task-agnostic environment dynamics makes world models a good candidate for effective offline training. However, the effects of online vs. offline data on world models and thus on the resulting task performance have not been thoroughly studied in the literature. In this work, we investigate both paradigms in model-based settings, conducting experiments on 31 different environments. First, we showcase that online agents outperform their offline counterparts. We identify a key challenge behind performance degradation of offline agents: encountering Out-Of-Distribution states at test time. This issue arises because, without the self-correction mechanism in online agents, offline datasets with limited state space coverage induce a mismatch between the agent's imagination and real rollouts, compromising policy training. We demonstrate that this issue can be mitigated by allowing for additional online interactions in a fixed or adaptive schedule, restoring the performance of online training with limited interaction data. We also showcase that incorporating exploration data helps mitigate the performance degradation of offline agents. Based on our insights, we recommend adding exploration data when collecting large datasets, as current efforts predominantly focus on expert data alone.

Aerial remote sensing using multispectral and RGB imagers has provided a critical impetus to precision agriculture. Analysis of the hyperspectral images with limited or no labels is challenging. This paper focuses on self-supervised learning to create neural network embeddings reflecting vegetation properties of trees from aerial hyperspectral images of crop fields. Experimental results demonstrate that a constructed tree representation, using a vegetation property-related embedding space, performs better in downstream machine learning tasks compared to the direct use of hyperspectral vegetation properties as tree representations.

We present a Reinforcement Learning (RL)-based locomotion system for Cosmo, a custom-built humanoid robot designed for entertainment applications. Unlike traditional humanoids, entertainment robots present unique challenges due to aesthetic-driven design choices. Cosmo embodies these with a disproportionately large head (16% of total mass), limited sensing, and protective shells that considerably restrict movement. To address these challenges, we apply Adversarial Motion Priors (AMP) to enable the robot to learn natural-looking movements while maintaining physical stability. We develop tailored domain randomization techniques and specialized reward structures to ensure safe sim-to-real, protecting valuable hardware components during deployment. Our experiments demonstrate that AMP generates stable standing and walking behaviors despite Cosmo's extreme mass distribution and movement constraints. These results establish a promising direction for robots that balance aesthetic appeal with functional performance, suggesting that learning-based methods can effectively adapt to aesthetic-driven design constraints.