We introduce a data-driven approach to learn a generalized kinetic collision operator directly from molecular dynamics. Unlike the conventional (e.g., Landau) models, the present operator takes an anisotropic form that accounts for a second energy transfer arising from the collective interactions between the pair of collision particles and the environment. Numerical results show that preserving the broadly overlooked anisotropic nature of the collision energy transfer is crucial for predicting the plasma kinetics with non-negligible correlations, where the Landau model shows limitations.

Probabilistic electricity price forecasting (PEPF) is a key task for market participants in short-term electricity markets. The increasing availability of high-frequency data and the need for real-time decision-making in energy markets require online estimation methods for efficient model updating. We present an online, multivariate, regularized distributional regression model, allowing for the modeling of all distribution parameters conditional on explanatory variables. Our approach is based on the combination of the multivariate distributional regression and an efficient online learning algorithm based on online coordinate descent for LASSO-type regularization. Additionally, we propose to regularize the estimation along a path of increasingly complex dependence structures of the multivariate distribution, allowing for parsimonious estimation and early stopping. We validate our approach through one of the first forecasting studies focusing on multivariate probabilistic forecasting in the German day-ahead electricity market while using only online estimation methods. We compare our approach to online LASSO-ARX-models with adaptive marginal distribution and to online univariate distributional models combined with an adaptive Copula. We show that the multivariate distributional regression, which allows modeling all distribution parameters - including the mean and the dependence structure - conditional on explanatory variables such as renewable in-feed or past prices provide superior forecasting performance compared to modeling of the marginals only and keeping a static/unconditional dependence structure. Additionally, online estimation yields a speed-up by a factor of 80 to over 400 times compared to batch fitting.

The representation of atomic configurations for machine learning models has led to the development of numerous descriptors, often to describe the local environment of atoms. However, many of these representations are incomplete and/or functionally dependent. Incomplete descriptor sets are unable to represent all meaningful changes in the atomic environment. Complete constructions of atomic environment descriptors, on the other hand, often suffer from a high degree of functional dependence, where some descriptors can be written as functions of the others. These redundant descriptors do not provide additional power to discriminate between different atomic environments and increase the computational burden. By employing techniques from the pattern recognition literature to existing atomistic representations, we remove descriptors that are functions of other descriptors to produce the smallest possible set that satisfies completeness. We apply this in two ways: first we refine an existing description, the Atomistic Cluster Expansion. We show that this yields a more efficient subset of descriptors. Second, we augment an incomplete construction based on a scalar neural network, yielding a new message-passing network architecture that can recognize up to 5-body patterns in each neuron by taking advantage of an optimal set of Cartesian tensor invariants. This architecture shows strong accuracy on state-of-the-art benchmarks while retaining low computational cost. Our results not only yield improved models, but point the way to classes of invariant bases that minimize cost while maximizing expressivity for a host of applications.

The Mean-Field Schrodinger Bridge (MFSB) problem is an optimization problem aiming to find the minimum effort control policy to drive a McKean-Vlassov stochastic differential equation from one probability measure to another. In the context of multiagent control, the objective is to control the configuration of a swarm of identical, interacting cooperative agents, as captured by the time-varying probability measure of their state. Available methods for solving this problem for distributions with continuous support rely either on spatial discretizations of the problem's domain or on approximating optimal solutions using neural networks trained through stochastic optimization schemes. For agents following Linear Time-Varying dynamics, and for Gaussian Mixture Model boundary distributions, we propose a highly efficient parameterization to approximate the solutions of the corresponding MFSB in closed form, without any learning steps. Our proposed approach consists of a mixture of elementary policies, each solving a Gaussian-to-Gaussian Covariance Steering problem from the components of the initial to the components of the terminal mixture. Leveraging the semidefinite formulation of the Covariance Steering problem, our proposed solver can handle probabilistic hard constraints on the system's state, while maintaining numerical tractability. We illustrate our approach on a variety of numerical examples.

Recent estimates put the carbon footprint of Bitcoin and Ethereum at an average of 64 and 26 million tonnes of CO2 per year, respectively. To address this growing problem, several possible approaches have been proposed in the literature: creating alternative blockchain consensus mechanisms, applying redundancy reduction techniques, utilizing renewable energy sources, and employing energy-efficient devices, etc. In this paper, we follow the second avenue and propose an efficient approach based on reinforcement learning that improves the block broadcasting scheme in blockchain networks. The analysis and experimental results confirmed that the proposed improvement of the block propagation scheme could cleverly handle network dynamics and achieve better results than the default approach. Additionally, our technical integration of the simulator and developed RL environment can be used as a complete solution for further study of new schemes and protocols that use RL or other ML techniques.

In recent years, proper scoring rules have emerged as a power ful general approach for estimating probability distributions. In addition to significantly ex panding the range of modeling techniques that can be applied in practice, this has also substantially broadened the conceptual understanding of estimation methods. Originally, proper scoring rules we re conceived in meteorology as summary statistics for describing the performance of probabilisti c forecasts ( Murphy and Winkler, 1984), but they also play an important role in economics as tools for bel ief elicitation ( Schotter and Trevino, 2014). A probabilistic forecast is a probability distribution ove r the space of the possible outcomes of the future event that is stated by the forecaster. The simple st and most popular case of probabilistic forecasts arises when the outcome is binary, so the probabilistic forecast reduces to issuing a predictive probability of success. Brier ( 1950) was the first to consider the problem of devising a scoring rule which could not be "played" by a dishonest fore casting agent. He introduced the quadratic scoring rule and showed that it incentivizes a for ecasting agent to state his most accurate probability estimate when faced with uncertainty.

This work has been submitted to the IEEE for possible publication. Active Learning Design: Modeling Force Output for Axisymmetric Soft Pneumatic Actuators Gregory M. Campbell, Gentian Muhaxheri, Leonardo Ferreira Guilhoto, Christian D. Santangelo, Paris Perdikaris, James Pikul, and Mark Yim Abstract --Soft pneumatic actuators (SPA) made from elas-tomeric materials can provide large strain and large force. The behavior of locally strain-restricted hyperelastic materials under inflation has been investigated thoroughly for shape reconfiguration, but requires further investigation for trajectories involving external force. In this work we model force-pressure-height relationships for a concentrically strain-limited class of soft pneumatic actuators and demonstrate the use of this model to design SPA response for object lifting. We predict relationships under different loadings by solving energy minimization equations and verify this theory by using an automated test rig to collect rich data for n=22 Ecoflex 00-30 membranes. We collect this data using an active learning pipeline to efficiently model the design space. We show that this learned material model outperforms the theory-based model and naive curve-fitting approaches. We use our model to optimize membrane design for different lift tasks and compare this performance to other designs. These contributions represent a step towards understanding the natural response for this class of actuator and embodying intelligent lifts in a single-pressure input actuator system. Keywords: Soft Robot Materials and Design, Hydraulic/Pneumatic Actuators, Active Learning, Hyperelastic Rubbers I. INTRODUCTION Soft actuators are promising for physical human-robot interaction in large part due to their compliance.

Multi-modal optimization involves identifying multiple global and local optima of a function, offering valuable insights into diverse optimal solutions within the search space. Evolutionary algorithms (EAs) excel at finding multiple solutions in a single run, providing a distinct advantage over classical optimization techniques that often require multiple restarts without guarantee of obtaining diverse solutions. Among these EAs, differential evolution (DE) stands out as a powerful and versatile optimizer for continuous parameter spaces. DE has shown significant success in multi-modal optimization by utilizing its population-based search to promote the formation of multiple stable subpopulations, each targeting different optima. Recent advancements in DE for multi-modal optimization have focused on niching methods, parameter adaptation, hybridization with other algorithms including machine learning, and applications across various domains. Given these developments, it is an opportune moment to present a critical review of the latest literature and identify key future research directions. This paper offers a comprehensive overview of recent DE advancements in multimodal optimization, including methods for handling multiple optima, hybridization with EAs, and machine learning, and highlights a range of real-world applications. Additionally, the paper outlines a set of compelling open problems and future research issues from multiple perspectives

Extracting structured information from unstructured text is crucial for modeling real-world processes, but traditional schema mining relies on semi-structured data, limiting scalability. This paper introduces schema-miner, a novel tool that combines large language models with human feedback to automate and refine schema extraction. Through an iterative workflow, it organizes properties from text, incorporates expert input, and integrates domain-specific ontologies for semantic depth. Applied to materials science--specifically atomic layer deposition-- schema-miner demonstrates that expert-guided LLMs generate semantically rich schemas suitable for diverse real-world applications.

Conformal prediction and scenario optimization constitute two important classes of statistical learning frameworks to certify decisions made using data. They have found numerous applications in control theory, machine learning and robotics. Despite intense research in both areas, and apparently similar results, a clear connection between these two frameworks has not been established. By focusing on the so-called vanilla conformal prediction, we show rigorously how to choose appropriate score functions and set predictor map to recover well-known bounds on the probability of constraint violation associated with scenario programs. We also show how to treat ranking of nonconformity scores as a one-dimensional scenario program with discarded constraints, and use such connection to recover vanilla conformal prediction guarantees on the validity of the set predictor. We also capitalize on the main developments of the scenario approach, and show how we could analyze calibration conditional conformal prediction under this lens. Our results establish a theoretical bridge between conformal prediction and scenario optimization.