Stellarators are magnetic confinement devices under active development to deliver steady-state carbon-free fusion energy. Their design involves a high-dimensional, constrained optimization problem that requires expensive physics simulations and significant domain expertise. Recent advances in plasma physics and open-source tools have made stellarator optimization more accessible. However, broader community progress is currently bottlenecked by the lack of standardized optimization problems with strong baselines and datasets that enable data-driven approaches, particularly for quasi-isodynamic (QI) stellarator configurations, considered as a promising path to commercial fusion due to their inherent resilience to current-driven disruptions. Here, we release an open dataset of diverse QI-like stellarator plasma boundary shapes, paired with their ideal magnetohydrodynamic (MHD) equilibria and performance metrics. We generated this dataset by sampling a variety of QI fields and optimizing corresponding stellarator plasma boundaries. We introduce three optimization benchmarks of increasing complexity: (1) a single-objective geometric optimization problem, (2) a "simple-to-build" QI stellarator, and (3) a multi-objective ideal-MHD stable QI stellarator that investigates trade-offs between compactness and coil simplicity. For every benchmark, we provide reference code, evaluation scripts, and strong baselines based on classical optimization techniques. Finally, we show how learned models trained on our dataset can efficiently generate novel, feasible configurations without querying expensive physics oracles. By openly releasing the dataset (https://huggingface.co/datasets/proxima-fusion/constellaration) along with benchmark problems and baselines (https://github.com/proximafusion/constellaration), we aim to lower the entry barrier for optimization and machine learning researchers to engage in stellarator design and to accelerate cross-disciplinary progress toward bringing fusion energy to the grid.

Abstract The Large Hadron Collider (LHC) at CERN has generated a vast amount of information from physics events, reaching peaks of TB of data per day which are then sent to large storage facilities. Traditionally, data processing workflows in the High Energy Physics (HEP) field have leveraged grid computing resources. In this context, users have been responsible for manually parallelising the analysis, sending tasks to computing nodes and aggregating the partial results. Analysis environments in this field have had a common building block in the ROOT software framework. This is the de facto standard tool for storing, processing and visualising HEP data. ROOT offers a modern analysis tool called RDataFrame, which can parallelise computations from a single machine to a distributed cluster while hiding most of the scheduling and result aggregation complexity from users. This is currently done by leveraging Apache Spark as the distributed execution engine, but other alternatives are being explored by HEP research groups. Notably, Dask has rapidly gained popularity thanks to its ability to interface with batch queuing systems, widespread in HEP grid computing facilities. Furthermore, future upgrades of the LHC are expected to bring a dramatic increase in data volumes. This paper presents a novel implementation of the Dask backend for the distributed RDataFrame tool in order to address the aforementioned future trends. The scalability of the tool with both the new backend and the already available Spark backend is demonstrated for the first time on more than two thousand cores, testing a real HEP analysis.

We combine two popular optimization approaches to derive learning algorithms for generative models: variational optimization and evolutionary algorithms. The combination is realized for generative models with discrete latents by using truncated posteriors as the family of variational distributions. The variational parameters of truncated posteriors are sets of latent states. By interpreting these states as genomes of individuals and by using the variational lower bound to define a fitness, we can apply evolutionary algorithms to realize the variational loop. The used variational distributions are very flexible and we show that evolutionary algorithms can effectively and efficiently optimize the variational bound. Furthermore, the variational loop is generally applicable (“black box”) with no analytical derivations required. To show general applicability, we apply the approach to three generative models (we use Noisy-OR Bayes Nets, Binary Sparse Coding, and Spike-and-Slab Sparse Coding). To demonstrate effectiveness and efficiency of the novel variational approach, we use the standard competitive benchmarks of image denoising and inpainting. The benchmarks allow quantitative comparisons to a wide range of methods including probabilistic approaches, deep deterministic and generative networks, and non-local image processing methods. In the category of “zero-shot” learning (when only the corrupted image is used for training), we observed the evolutionary variational algorithm to significantly improve the state-of-the-art in many benchmark settings. For one well-known inpainting benchmark, we also observed state-of-the-art performance across all categories of algorithms although we only train on the corrupted image. In general, our investigations highlight the importance of research on optimization methods for generative models to achieve performance improvements.

We establish a link between evolutionary algorithms (EAs) and learning of probabilistic generative models with binary hidden variables. Learning is formulated as approximate maximum likelihood optimization using variational expectation maximization. When choosing truncated posteriors as variational distributions, the variational parameters take the form of sets of latent states. By (A) identifying these sets with populations of genomes, and by (B) defining the fitness of individuals as the joint probability of the chosen generative model, the sets of latent states can be optimized using EAs. We obtain scalable learning algorithms that effectively improve the tractable free energy objective of truncated posteriors. While this novel approach is applicable to any model with binary latents and tractable joint probability, as a proof of concept, we here apply it to the optimization of parameters of noisy-OR Bayes Nets (modeling binary data) and Binary Sparse Coding (modelling continuous data). We find that the data likelihood is efficiently improved by employing genetic algorithms with point mutations and single-point cross-over as EAs. In general we believe that, with the novel link established here, standard as well as recent results in evolutionary optimization can be leveraged to address the difficult problem of parameter optimization in generative models.