This paper presents estimates of the European High Voltage circuit breaker population and its SF6 inventory. Data on power system topology obtained from the OpenStreetMap database are used in conjunction with TSO and industry input to obtain estimates for the present-day population and inventory, offering an alternative to estimates based on uncertain or incomplete reported inventories. Three strategies for replacing the existing population of circuit breakers are defined and compared based on their resulting need for new circuit breakers and total future emissions of SF6. Two of these strategies are phase-out strategies aiming to eliminate SF6 from the circuit breaker population completely, while the third is based on a continued use of SF6 in circuit breakers. An accelerated transition to SF6-free operation brings the largest reduction of emissions, but incurs economic and logistic penalties due to more circuit breakers to be commissioned. Future emissions are estimated to be 30 and 37 Megatonnes CO2e with the accelerated and gradual phase-out strategies, respectively. The accelerated phase-out requires approximately 30–50% more circuit breakers to be commissioned across all voltage levels by 2050.
Proposed future solar thermal power plant technologies commonly feature high-temperature supercritical CO2 (sCO2) power cycles due to predicted high thermal efficiencies and low capital costs. However, as the technology also poses significant challenges, a detailed techno-economic comparison is needed to assess potential benefits over state-of-the-art steam cycles. In this study, detailed thermodynamic models of six sCO2 cycles and a reference steam cycle as well as cost correlations for their main components were developed. The models were used for hourly simulations to derive the plants’ annual energy yields and levelized cost of electricity. Results show that the levelized cost of any sCO2 process is at least 9% higher than that of the reference system. Although there is considerable uncertainty in some of the components’ cost models, even lowering the costs of most sCO2-specific components by 50% did not lead to cost parity. This indicates that the development of next-generation solar thermal plants should include modern steam power cycles.
Partial differential equations (PDEs) govern physical phenomena across the full range of scientific scales, yet their computational solution remains one of the defining challenges of modern science. This critical review examines two mature but epistemologically distinct paradigms for PDE solution, classical numerical methods and machine learning approaches, through a unified evaluative framework structured around six fundamental computational challenges: high dimensionality, nonlinearity, geometric complexity, discontinuities, multiscale phenomena, and multiphysics coupling. Classical methods, including finite difference, finite element, finite volume, and spectral discretizations, are assessed for their structure-preserving properties, rigorous convergence theory, and scalable solver design; their persistent limitations in high-dimensional and geometrically complex settings are characterized in detail. Machine learning approaches, including physics-informed neural networks, neural operators, graph architectures, transformers, generative models, and hybrid frameworks, are evaluated under a taxonomy organized by the degree to which physical knowledge is incorporated, and subjected to the same critical assessment applied to classical methods. The central finding is that classical methods are deductive: errors are bounded by quantities derivable from PDE structure and discretization parameters. Machine learning methods are inductive: accuracy depends on statistical proximity to the training distribution. This distinction determines not which paradigm is superior, but what each can certify, and therefore where each should be deployed. Epistemological character, rather than computational speed, is the primary criterion governing responsible method selection. We identify three genuine complementarities between the paradigms and develop principles for hybrid design, including a framework for the structure inheritance problem and an error budget decomposition that separates discretization, neural approximation, and coupling contributions. We further assess emerging frontiers, including foundation models for scientific computing, differentiable programming for inverse design, quantum algorithms, and exascale co-design, evaluating each against the structural constraints that determine whether current barriers are fundamental or contingent on engineering progress. The conclusion is not that one paradigm supersedes the other, but that their principled integration, grounded in the complementary strengths each provides, offers the most credible path toward computationally tractable solutions to the most consequential open problems that neither can address alone.
Generative learning generates high dimensional data based on low dimensional conditions, also called prompts. Therefore, generative learning algorithms are eligible for solving (Bayesian) inverse problems. In this article we compare a traditional Bayesian inverse approach based on a forward regression model and a prior sampled with the Markov Chain Monte Carlo method with three state of the art generative learning models, namely conditional Generative Adversarial Networks, Invertible Neural Networks and Conditional Flow Matching. We apply them to a problem of gas turbine combustor design where we map six independent design parameters to three performance labels. We propose several metrics for the evaluation of this inverse design approaches and measure the accuracy of the labels of the generated designs along with the diversity. We also study the performance as a function of the training dataset size. Our benchmark has a clear winner, as Conditional Flow Matching consistently outperforms all competing approaches.
Anomalies in time series can be a symptom of an incoming failure. Thus, the detection of anomalous data can both reduce maintenance actions and asset unscheduled stops. To tackle this challenge, we exploit the capabilities of convolutional neural networks (CNNs), fed with images obtained from multivariate time series data, transformed by means of two different approaches. Two CNN architectures are investigated, i.e., VGG-19 and SqueezeNet. The performance of both CNNs fed with images is compared to that of (i) a temporal convolutional network (TCN) fed with time series data and (ii) a support vector machine (SVM) model. In this paper, we present the comprehensive framework, which starts from time series transformation, goes through CNN development and ends with anomaly detection. The framework is applied to field data taken during normal operation of ten SGT-800 gas turbines, located in two different regions. The normal data covers 150 days of operation. Spike faults are implanted in two out of the 20 available measured variables, i.e., compressor discharge temperature and compressor discharge pressure, by considering different combinations of maximum fault magnitude and number of implanted spikes in each time series. The results demonstrate that both CNNs fed with images achieve significantly higher classification accuracy than both a TCN model fed with time series data and an SVM model. Moreover, the Markov transition field (MTF) method always proves more robust than Gramian angular summation field (GASF) method, and also allows higher accuracy values, in the range from 0.85 to 0.99.
