We demonstrate that we can carry over the strategy of Finite Element Exterior Calculus (FEEC) to Summation-by-Parts (SBP) Finite Difference (FD) methods to achieve divergence- and curl-free discretizations. This is not obvious at first sight, as for SBP-FD no basis functions are known, but only values and derivatives at points. The key is a remarkable analytic relationship that enables us to construct compatible operators using integral and nodal degrees of free- dom. Pre-existing SBP-FD matrix operators can then be used to obtain nodal values from the integral degrees of freedom to derive a scheme with the desired properties.
High-order Discontinuous Galerkin (DG) methods offer excellent accuracy for turbulent flow simulations and are increasingly attractive on modern GPU-oriented architectures, where high polynomial orders can improve arithmetic intensity for sufficiently large workloads. However, very high-order under-resolved simulations remain sensitive to the balance between numerical and modeled dissipation. Here, we investigate how explicit Vreman subgrid-scale (SGS) modeling interacts with the dissipation introduced by split-form stabilization and Riemann solvers in a DGSEM framework. Using the three-dimensional Taylor-Green vortex at Re = 1600 and an in-viscid case (Re -> infinity), we evaluate kinetic energy dissipation, spectral accuracy, and numerical stability across well-resolved, under-resolved viscous, and strongly under-resolved regimes, comparing lower-and very high-polynomial-order configurations at comparable degrees of freedom. Our results show that the usefulness of explicit SGS modeling depends strongly on the resolution regime, polynomial order, and numerical dissipation already present in the scheme. For the well-resolved configurations considered here, adding a Vreman model does not improve accuracy because the wavenumber range where the model acts overlaps with the inherent numerical dissipation of the DG scheme. Using a similar number of degrees of freedom, we observe that lower-order simulations introduce stronger numerical damping near the smallest represented scales, whereas very high-order simulations retain more spectral content but are more prone to highwavenumber energy accumulation when insufficient dissipation is present. In contrast, when the resolution is insufficient, a suitably weak SGS contribution can help control this high-wavenumber energy accumulation, whereas excessive SGS dissipation degrades intermediate scales. These findings identify regimes in which explicit SGS modeling is beneficial, neutral, or detrimental, and provide practical guidance for choosing dissipation mechanisms in very high-order DG turbulence simulations, which are well suited to modern GPU architectures.
This paper introduces a new type of probabilistic semiparametric model that takes advantage of data binning to reduce the computational cost of kernel density estimation in nonparametric distributions. Two new conditional probability distributions are developed for the new binned semiparametric Bayesian networks: the sparse binned kernel density estimation and the Fourier kernel density estimation. These two probability distributions address the curse of dimensionality, which typically impacts binned models, by using sparse tensors and restricting the number of parent nodes in conditional probability calculations. To evaluate the proposal, we perform a complexity analysis and conduct several comparative experiments using synthetic data and datasets from the UCI Machine Learning Repository. The experiments include different binning rules, parent restrictions, grid sizes, and sample sizes to obtain a holistic view of the model's behavior. As a result, our binned semiparametric Bayesian networks achieve structural learning and log-likelihood estimations with no statistically significant differences compared to standard semiparametric Bayesian networks, but at significantly higher speeds. Thus, the new binned semiparametric Bayesian networks prove to be a reliable and more efficient alternative to their non-binned counterparts.
This study proposes a solar-driven methane pyrolysis system in which a particle-based concentrating solar power (CSP) plant supplies heat directly to an array of molten-salt (MnCl2–KCl) bubble-column reactors through the reactor wall, without an intermediate heat-transfer fluid or electric heating step. An hourly-resolved CSP model over a full year, comprising a heliostat field, a free-falling particle receiver, and two-bin thermal energy storage, is coupled to a reactor model that includes reaction kinetics, bubble hydrodynamics, particle-to-salt heat transfer, and equipment sizing. The integrated plant is assessed through a techno-economic analysis for a site in Daggett, California. At the baseline design (hot and cold particle temperatures of 1100 and 950 °C, 14 h of storage), the bulk salt temperature is 936 °C, the plant reaches a capacity factor of 69% and a single-pass methane conversion of 45%, and it produces about 6700 t/yr of hydrogen at a levelized cost of hydrogen (LCOH2) of $3.87/kg without carbon credit and $3.52/kg with credit for the co-produced carbon. Raising the reactor temperature increases the cost of solar heat but lowers LCOH2 through faster kinetics and fewer reactor modules, so the CSP and reactor subsystems must be designed jointly. Natural gas accounts for about 54% of LCOH2, and the particle-to-wall heat transfer coefficient is the most influential design parameter. At an assumed hydrogen price of $4/kg, the project has a positive 30-year net present value of $53 M with the carbon credit and without Section 45 V or LCFS policy support. At a gas price of $6/GJ and a hot-particle temperature of 1200 °C (bulk salt temperature of 1021 °C), approaching the conditions of earlier studies, LCOH2 falls to $1.9–2.3/kg depending on the carbon credit. The configuration is a conceptual design: experimental validation of the particle-to-wall heat transfer, corrosion, creep, thermal cycling, abrasion, and liner compatibility in molten chloride is required.
Driven by advances in machine learning and sensors, data-driven state estimation has become a key technology for supporting operational decisions in safety-critical systems. However, a single point estimate fails to reveal the uncertainty and confidence associated with a prediction, which can lead to overconfident decisions; as reliance on such estimates grows, the quantification and management of uncertainty becomes a prerequisite for reliable operation. This comprehensive review analyzes uncertainty management in data-driven state estimation, taking battery state estimation, in which current state estimation and future state prediction coexist, as a representative case study. This paper organizes uncertainty along two axes, its source (Aleatoric/Epistemic) and the mechanism that handles it (memory-based before modeling, model-based within the model), and applies this taxonomy to analyze how the dominant source and the management strategy suited to it shift along the prediction horizon. In doing so, it goes beyond a simple classification of techniques to present the correspondence between uncertainty sources and management strategies, and it summarizes the main open challenges and future research directions. The insights of this paper provide a foundation for reliable and risk-aware decision-making in predictive maintenance and safety-critical systems beyond batteries.
