This paper presents a learning-based framework for approximating an exact magnetic-field interaction model, supported by both numerical and experimental validation. High-fidelity magnetic-field interaction modeling is essential for achieving exceptional accuracy and responsiveness across a wide range of fields, including transportation, energy systems, medicine, biomedical robotics, and aerospace robotics. In aerospace engineering, magnetic actuation has been investigated as a fuel-free solution for multi-satellite attitude and formation control. Although the exact magnetic field can be computed from the Biot-Savart law, the associated computational cost is prohibitive, and prior studies have therefore relied on dipole approximations to improve efficiency. However, these approximations lose accuracy during proximity operations, leading to unstable behavior and even collisions. To address this limitation, we develop a learning-based approximation framework that faithfully reproduces the exact field while dramatically reducing computational cost. The proposed method additionally provides a certified error bound, derived from the number of training samples, ensuring reliable prediction accuracy. The learned model can also accommodate interactions between coils of different sizes through appropriate geometric transformations, without retraining. To verify the effectiveness of the proposed framework under challenging conditions, a spacecraft docking scenario is examined through both numerical simulations and experimental validation.

Multi-Agent Reinforcement Learning involves agents that learn together in a shared environment, leading to emergent dynamics sensitive to initial conditions and parameter variations. A Dynamical Systems approach, which studies the evolution of multi-component systems over time, has uncovered some of the underlying dynamics by constructing deterministic approximation models of stochastic algorithms. In this work, we demonstrate that even in the simplest case of independent Q-learning with a Boltzmann exploration policy, significant discrepancies arise between the actual algorithm and previous approximations. We elaborate why these models actually approximate interesting variants rather than the original incremental algorithm. To explain the discrepancies, we introduce a new discrete-time approximation model that explicitly accounts for agents' update frequencies within the learning process and show that its dynamics fundamentally differ from the simplified dynamics of prior models. We illustrate the usefulness of our approach by applying it to the question of spontaneous cooperation in social dilemmas, specifically the Prisoner's Dilemma as the simplest case study. We identify conditions under which the learning behaviour appears as long-term stable cooperation from an external perspective. However, our model shows that this behaviour is merely a metastable transient phase and not a true equilibrium, making it exploitable. We further exemplify how specific parameter settings can significantly exacerbate the moving target problem in independent learning. Through a systematic analysis of our model, we show that increasing the discount factor induces oscillations, preventing convergence to a joint policy. These oscillations arise from a supercritical Neimark-Sacker bifurcation, which transforms the unique stable fixed point into an unstable focus surrounded by a stable limit cycle.

In this paper the accuracy and robustness of quality measures for the assessment of machine learning models are investigated. The prediction quality of a machine learning model is evaluated model-independent based on a cross-validation approach, where the approximation error is estimated for unknown data. The presented measures quantify the amount of explained variation in the model prediction. The reliability of these measures is assessed by means of several numerical examples, where an additional data set for the verification of the estimated prediction error is available. Furthermore, the confidence bounds of the presented quality measures are estimated and local quality measures are derived from the prediction residuals obtained by the cross-validation approach.

In real case applications within the virtual prototyping process, it is not always possible to reduce the complexity of the physical models and to obtain numerical models which can be solved quickly. Usually, every single numerical simulation takes hours or even days. Although the progresses in numerical methods and high performance computing, in such cases, it is not possible to explore various model configurations, hence efficient surrogate models are required. Generally the available meta-model techniques show several advantages and disadvantages depending on the investigated problem. In this paper we present an automatic approach for the selection of the optimal suitable meta-model for the actual problem. Together with an automatic reduction of the variable space using advanced filter techniques an efficient approximation is enabled also for high dimensional problems. This filter techniques enable a reduction of the high dimensional variable space to a much smaller subspace where meta-model-based sensitivity analyses are carried out to assess the influence of important variables and to identify the optimal subspace with corresponding surrogate model which enables the most accurate probabilistic analysis. For this purpose we investigate variance-based and moment-free sensitivity measures in combination with advanced meta-models as moving least squares and kriging.

Modern-day time-domain photometric surveys collect a lot of observations of various astronomical objects and the coming era of large-scale surveys will provide even more information on their properties. Spectroscopic follow-ups are especially crucial for transients such as supernovae and most of these objects have not been subject to such studies. }{Flux time series are actively used as an affordable alternative for photometric classification and characterization, for instance, peak identifications and luminosity decline estimations. However, the collected time series are multidimensional and irregularly sampled, while also containing outliers and without any well-defined systematic uncertainties. This paper presents a search for the best-performing methods to approximate the observed light curves over time and wavelength for the purpose of generating time series with regular time steps in each passband.}{We examined several light curve approximation methods based on neural networks such as multilayer perceptrons, Bayesian neural networks, and normalizing flows to approximate observations of a single light curve. Test datasets include simulated PLAsTiCC and real Zwicky Transient Facility Bright Transient Survey light curves of transients.}{The tests demonstrate that even just a few observations are enough to fit the networks and improve the quality of approximation, compared to state-of-the-art models. The methods described in this work have a low computational complexity and are significantly faster than Gaussian processes. Additionally, we analyzed the performance of the approximation techniques from the perspective of further peak identification and transients classification. The study results have been released in an open and user-friendly Fulu Python library available on GitHub for the scientific community.

Inference from large autoregressive models like Transformers is slow - decoding K tokens takes K serial runs of the model. In this work we introduce speculative decoding - an algorithm to sample from autoregressive models faster without any changes to the outputs, by computing several tokens in parallel. At the heart of our approach lie the observations that (1) hard language-modeling tasks often include easier subtasks that can be approximated well by more efficient models, and (2) using speculative execution and a novel sampling method, we can make exact decoding from the large models faster, by running them in parallel on the outputs of the approximation models, potentially generating several tokens concurrently, and without changing the distribution. Our method can accelerate existing off-the-shelf models without retraining or architecture changes. We demonstrate it on T5-XXL and show a 2X-3X acceleration compared to the standard T5X implementation, with identical outputs.

Dynamic routing occurs when customers are not known in advance, e.g. for real-time routing. Two heuristics are proposed that solve the balanced dynamic multiple travelling salesmen problem (BD-mTSP). These heuristics represent operational (tactical) tools for dynamic (online, real-time) routing. Several types and scopes of dynamics are proposed. Particular attention is given to sequential dynamics. The balanced dynamic closest vehicle heuristic (BD-CVH) and the balanced dynamic assignment vehicle heuristic (BD-AVH) are applied to this type of dynamics. The algorithms are tested for instances in the Euclidean plane. Continuous approximation models for the BD-mTSP's are derived and serve as strategic tools for dynamic routing. The models express route lengths using vehicles, customers and dynamic scopes without the need of running an algorithm. A machine learning approach was used to obtain regression models. The mean-average-percentage error of two of these models is below 3%.

We consider the problem of quantifying the quality of a model selection problem for a graphical model. We discuss this by formulating the problem as a detection problem. Model selection problems usually minimize a distance between the original distribution and the model distribution. For the special case of Gaussian distributions, the model selection problem simplifies to the covariance selection problem which is widely discussed in literature by Dempster [2] where the likelihood criterion is maximized or equivalently the Kullback-Leibler (KL) divergence is minimized to compute the model covariance matrix. While this solution is optimal for Gaussian distributions in the sense of the KL divergence, it is not optimal when compared with other information divergences and criteria such as Area Under the Curve (AUC). In this paper, we analytically compute upper and lower bounds for the AUC and discuss the quality of model selection problem using the AUC and its bounds as an accuracy measure in detection problem. We define the correlation approximation matrix (CAM) and show that analytical computation of the KL divergence, the AUC and its bounds only depend on the eigenvalues of CAM. We also show the relationship between the AUC, the KL divergence and the ROC curve by optimizing with respect to the ROC curve. In the examples provided, we pick tree structures as the simplest graphical models. We perform simulations on fully-connected graphs and compute the tree structured models by applying the widely used Chow-Liu algorithm [3]. Examples show that the quality of tree approximation models are not good in general based on information divergences, the AUC and its bounds when the number of nodes in the graphical model is large. We show both analytically and by simulations that the 1-AUC for the tree approximation model decays exponentially as the dimension of graphical model increases.

Real-time strategy (RTS) games make heavy use of artificial intelligence (AI), especially in the design of computerized opponents. Because of the computational complexity involved in managing all aspects of these games, many AI opponents are designed to optimize only a few areas of playing style. In games like StarCraft 2, a very popular and recently released RTS, most AI strategies revolve around economic and building efficiency: AI opponents try to gather and spend all resources as quickly and effectively as possible while ensuring that no units are idle. The aim of this work was to help address the need for AI combat strategies that are not computationally intensive. Our goal was to produce a computationally efficient model that is accurate at predicting the results of complex battles between diverse armies, including which army will win and how many units will remain. Our results suggest it may be possible to develop a relatively simple approximation model of combat that can accurately predict many battles that do not involve micromanagement. Future designs of AI opponents may be able to incorporate such an approximation model into their decision and planning systems to provide a challenge that is strategically balanced across all aspects of play.