We construct a thermodynamic potential that can guide training of a generative model defined on a set of binary degrees of freedom. We argue that upon reduction in description, so as to make the generative model computationally-manageable, the potential develops multiple minima. This is mirrored by the emergence of multiple minima in the free energy proper of the generative model itself. The variety of training samples that employ N binary degrees of freedom is ordinarily much lower than the size 2^N of the full phase space. The non-represented configurations, we argue, should be thought of as comprising a high-temperature phase separated by an extensive energy gap from the configurations composing the training set. Thus, training amounts to sampling a free energy surface in the form of a library of distinct bound states, each of which breaks ergodicity. The ergodicity breaking prevents escape into the near continuum of states comprising the high-temperature phase; thus it is necessary for proper functionality. It may however have the side effect of limiting access to patterns that were underrepresented in the training set. At the same time, the ergodicity breaking within the library complicates both learning and retrieval. As a remedy, one may concurrently employ multiple generative models -- up to one model per free energy minimum.

Data-based methods have gained increasing importance in engineering, especially but not only driven by successes with deep artificial neural networks. Success stories are prevalent, e.g., in areas such as data-driven modeling, control and automation, as well as surrogate modeling for accelerated simulation. Beyond engineering, generative and large-language models are increasingly helping with tasks that, previously, were solely associated with creative human processes. Thus, it seems timely to seek artificial-intelligence-support for engineering design tasks to automate, help with, or accelerate purpose-built designs of engineering systems, e.g., in mechanics and dynamics, where design so far requires a lot of specialized knowledge. However, research-wise, compared to established, predominantly first-principles-based methods, the datasets used for training, validation, and test become an almost inherent part of the overall methodology. Thus, data publishing becomes just as important in (data-driven) engineering science as appropriate descriptions of conventional methodology in publications in the past. This article analyzes the value and challenges of data publishing in mechanics and dynamics, in particular regarding engineering design tasks, showing that the latter raise also challenges and considerations not typical in fields where data-driven methods have been booming originally. Possible ways to deal with these challenges are discussed and a set of examples from across different design problems shows how data publishing can be put into practice. The analysis, discussions, and examples are based on the research experience made in a priority program of the German research foundation focusing on research on artificially intelligent design assistants in mechanics and dynamics.

Assignment problems are a classic combinatorial optimization problem in which a group of agents must be assigned to a group of tasks such that maximum utility is achieved while satisfying assignment constraints. Given the utility of each agent completing each task, polynomial-time algorithms exist to solve a single assignment problem in its simplest form. However, in many modern-day applications such as satellite constellations, power grids, and mobile robot scheduling, assignment problems unfold over time, with the utility for a given assignment depending heavily on the state of the system. We apply multi-agent reinforcement learning to this problem, learning the value of assignments by bootstrapping from a known polynomial-time greedy solver and then learning from further experience. We then choose assignments using a distributed optimal assignment mechanism rather than by selecting them directly. We demonstrate that this algorithm is theoretically justified and avoids pitfalls experienced by other RL algorithms in this setting. Finally, we show that our algorithm significantly outperforms other methods in the literature, even while scaling to realistic scenarios with hundreds of agents and tasks.

In the context of uncertainty quantification (UQ) the curse of dimensionality, whereby quantification efficiency degrades drastistically with parameter dimension, is particular extreme with highly parameterized models such as neural networks (NNs). Fortunately, in many cases, these models are overparameterized in the sense that the number of parameters can be reduced with negligible effects on accuracy and sometimes improvements in generalization [1]. Furthermore, NNs often have parameterizations that have fungible parameters such that permutations of the values and connections lead to equivalent output responses. This suggests methods that simultaneously sparsify and characterize the uncertainty of a model, while handling and taking advantage of the symmetries inherent in the model, are potentially advantageous approaches. Although Markov chain Monte Carlo (MCMC) methods [2] have been the reference standard to generate samples for UQ methods, they can be temperamental and do not scale well for high dimensional models. More recently, there has been widespread use of variational inference methods (VI), which cast the parameter posterior sampling problem as an optimization of a surrogate posterior guided by a suitable objective, such as the Kullback-Liebler (KL) divergence between the predictive posterior and true posterior induced by the data. In particular, there is now a family of model ensemble methods based on Stein's identity [3], such as Stein variational gradient descent (SVGD) [4], projected SVGD [5], and Stein variational Newton's method [6]. These methods have advantages over MCMC methods by virtue of propagating in parallel a coordinated ensemble of particles that represent the empirical posterior.

Scaling the size of the memory for a 1.3 billion parameter base model (zero memory parameters corresponds to a dense model), trained to 1 trillion tokens. On the left, factual QA accuracy (exact match on NaturalQuestions and F1 score on TriviaQA), on the right task NLL (lower is better). Dashed lines show the performance of a 7B model trained on 2 trillion tokens with 10x more FLOPs. Pretrained language models encode vast amounts of information in their parameters (Roberts et al., 2020), and they can recall and use this information more accurately with increasing scale (Brown et al., 2020). For dense deep neural networks, which encode information primarily as weights of linear matrix transforms, this scaling of parameter size is directly coupled to an increase in computational and energy requirements. It is unclear if this is the most efficient solution to all information storage needs of language models. An important subset of information that language models need to learn are simple associations.

In complex scenes and varied conditions, effectively integrating spatial-temporal context is crucial for accurately identifying changes. However, current RS-CD methods lack a balanced consideration of performance and efficiency. CNNs lack global context, Transformers are computationally expensive, and Mambas face CUDA dependence and local correlation loss. In this paper, we propose CDXFormer, with a core component that is a powerful XLSTM-based feature enhancement layer, integrating the advantages of linear computational complexity, global context perception, and strong interpret-ability. Specifically, we introduce a scale-specific Feature Enhancer layer, incorporating a Cross-Temporal Global Perceptron customized for semantic-accurate deep features, and a Cross-Temporal Spatial Refiner customized for detail-rich shallow features. Additionally, we propose a Cross-Scale Interactive Fusion module to progressively interact global change representations with spatial responses. Extensive experimental results demonstrate that CDXFormer achieves state-of-the-art performance across three benchmark datasets, offering a compelling balance between efficiency and accuracy. Code is available at https://github.com/xwmaxwma/rschange.

This paper presents a novel deep learning framework for estimating multivariate joint extremes of metocean variables, based on the Semi-Parametric Angular-Radial (SPAR) model. When considered in polar coordinates, the problem of modelling multivariate extremes is transformed to one of modelling an angular density, and the tail of a univariate radial variable conditioned on angle. In the SPAR approach, the tail of the radial variable is modelled using a generalised Pareto (GP) distribution, providing a natural extension of univariate extreme value theory to the multivariate setting. In this work, we show how the method can be applied in higher dimensions, using a case study for five metocean variables: wind speed, wind direction, wave height, wave period and wave direction. The angular variable is modelled empirically, while the parameters of the GP model are approximated using fully-connected deep neural networks. Our data-driven approach provides great flexibility in the dependence structures that can be represented, together with computationally efficient routines for training the model. Furthermore, the application of the method requires fewer assumptions about the underlying distribution(s) compared to existing approaches, and an asymptotically justified means for extrapolating outside the range of observations. Using various diagnostic plots, we show that the fitted models provide a good description of the joint extremes of the metocean variables considered.

These lecture notes were developed for a Master's course in advanced machine learning at Erasmus University of Rotterdam. The course is designed for graduate students in mathematics, statistics and econometrics. The content follows a proposition-proof structure, making it suitable for students seeking a formal and rigorous understanding of the statistical theory underlying machine learning methods. At present, the notes focus on linear regression, with an in-depth exploration of the existence, uniqueness, relations, computation, and nonasymptotic properties of the most prominent estimators in this setting: least squares, ridgeless, ridge, and lasso. Background It is assumed that readers have a solid background in calculus, linear algebra, convex analysis, and probability theory.

Human reliability analysis (HRA) is crucial for evaluating and improving the safety of complex systems. Recent efforts have focused on estimating human error probability (HEP), but existing methods often rely heavily on expert knowledge,which can be subjective and time-consuming. Inspired by the success of large language models (LLMs) in natural language processing, this paper introduces a novel two-stage framework for knowledge-driven reliability analysis, integrating IDHEAS and LLMs (KRAIL). This innovative framework enables the semi-automated computation of base HEP values. Additionally, knowledge graphs are utilized as a form of retrieval-augmented generation (RAG) for enhancing the framework' s capability to retrieve and process relevant data efficiently. Experiments are systematically conducted and evaluated on authoritative datasets of human reliability. The experimental results of the proposed methodology demonstrate its superior performance on base HEP estimation under partial information for reliability assessment.

Forecasters using flexible neural networks (NN) in multi-horizon distributional regression setups often struggle to gain detailed insights into the underlying mechanisms that lead to the predicted feature-conditioned distribution parameters. In this work, we deploy a Neural Basis Model for Location, Scale and Shape, that blends the principled interpretability of GAMLSS with a computationally scalable shared basis decomposition, combined by linear projections supporting dedicated stepwise and parameter-wise feature shape functions aggregations. Experiments have been conducted on multiple market regions, achieving probabilistic forecasting performance comparable to that of distributional neural networks, while providing more insights into the model behavior through the learned nonlinear feature level maps to the distribution parameters across the prediction steps. Introduction Probabilistic forecasting of hourly electricity prices in day-ahead power markets (PEPF) is a complex problem with a significant impact. These enable informed decision-making in high-stakes scenarios such as trading strategies, resource scheduling, and optimal commitment by factoring in potential fluctuations and associated risks [2]. Moreover, electricity prices are characterized by high volatility and rapid changes driven by intricate factors, including distributed power demand, generation costs, and weather conditions [3].