arXiv subjects

Markus Kaiser

Publications and source records attributed to Markus Kaiser.

10 recordsLinked to original sources

arXiv2025

ConStellaration: A dataset of QI-like stellarator plasma boundaries and optimization benchmarks

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 along with benchmark problems and baselines, 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.

cs.LG↗

arXiv2023

Multi-fidelity experimental design for ice-sheet simulation

Computer simulations are becoming an essential tool in many scientific fields from molecular dynamics to aeronautics. In glaciology, future predictions of sea level change require input from ice sheet models. Due to uncertainties in the forcings and the parameter choices for such models, many different realisations of the model are needed in order to produce probabilistic forecasts of sea level change. For these reasons, producing robust probabilistic forecasts from an ensemble of model simulations over regions of interest can be extremely expensive for many ice sheet models. Multi-fidelity experimental design (MFED) is a strategy that models the high-fidelity output of the simulator by combining information from various resolutions in an attempt to minimize the computational costs of the process and maximize the accuracy of the posterior. In this paper, we present an application of MFED to an ice-sheet simulatorand demonstrate potential computational savings by modelling the relationship between spatial resolutions. We also analyze the behavior of MFED strategies using theoretical results from sub-modular maximization.

physics.comp-ph↗

arXiv2022

A locally time-invariant metric for climate model ensemble predictions of extreme risk

Adaptation-relevant predictions of climate change are often derived by combining climate model simulations in a multi-model ensemble. Model evaluation methods used in performance-based ensemble weighting schemes have limitations in the context of high-impact extreme events. We introduce a locally time-invariant method for evaluating climate model simulations with a focus on assessing the simulation of extremes. We explore the behaviour of the proposed method in predicting extreme heat days in Nairobi and provide comparative results for eight additional cities.

physics.ao-ph↗

arXiv2022

Ice Core Dating using Probabilistic Programming

Ice cores record crucial information about past climate. However, before ice core data can have scientific value, the chronology must be inferred by estimating the age as a function of depth. Under certain conditions, chemicals locked in the ice display quasi-periodic cycles that delineate annual layers. Manually counting these noisy seasonal patterns to infer the chronology can be an imperfect and time-consuming process, and does not capture uncertainty in a principled fashion. In addition, several ice cores may be collected from a region, introducing an aspect of spatial correlation between them. We present an exploration of the use of probabilistic models for automatic dating of ice cores, using probabilistic programming to showcase its use for prototyping, automatic inference and maintainability, and demonstrate common failure modes of these tools.

stat.ML↗

arXiv2019

Compositional uncertainty in deep Gaussian processes

Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a posterior distribution of compositions of multiple functions giving rise to the observations. However, exact Bayesian inference is intractable for DGPs, motivating the use of various approximations. We show that the application of simplifying mean-field assumptions across the hierarchy leads to the layers of a DGP collapsing to near-deterministic transformations. We argue that such an inference scheme is suboptimal, not taking advantage of the potential of the model to discover the compositional structure in the data. To address this issue, we examine alternative variational inference schemes allowing for dependencies across different layers and discuss their advantages and limitations.

stat.ML↗

arXiv2019

Interpretable Dynamics Models for Data-Efficient Reinforcement Learning

In this paper, we present a Bayesian view on model-based reinforcement learning. We use expert knowledge to impose structure on the transition model and present an efficient learning scheme based on variational inference. This scheme is applied to a heteroskedastic and bimodal benchmark problem on which we compare our results to NFQ and show how our approach yields human-interpretable insight about the underlying dynamics while also increasing data-efficiency.

cs.LG↗

arXiv2019

Modulating Surrogates for Bayesian Optimization

Bayesian optimization (BO) methods often rely on the assumption that the objective function is well-behaved, but in practice, this is seldom true for real-world objectives even if noise-free observations can be collected. Common approaches, which try to model the objective as precisely as possible, often fail to make progress by spending too many evaluations modeling irrelevant details. We address this issue by proposing surrogate models that focus on the well-behaved structure in the objective function, which is informative for search, while ignoring detrimental structure that is challenging to model from few observations. First, we demonstrate that surrogate models with appropriate noise distributions can absorb challenging structures in the objective function by treating them as irreducible uncertainty. Secondly, we show that a latent Gaussian process is an excellent surrogate for this purpose, comparing with Gaussian processes with standard noise distributions. We perform numerous experiments on a range of BO benchmarks and find that our approach improves reliability and performance when faced with challenging objective functions.

stat.ML↗

arXiv2018

Data Association with Gaussian Processes

The data association problem is concerned with separating data coming from different generating processes, for example when data come from different data sources, contain significant noise, or exhibit multimodality. We present a fully Bayesian approach to this problem. Our model is capable of simultaneously solving the data association problem and the induced supervised learning problems. Underpinning our approach is the use of Gaussian process priors to encode the structure of both the data and the data associations. We present an efficient learning scheme based on doubly stochastic variational inference and discuss how it can be applied to deep Gaussian process priors.

stat.ML↗

arXiv2017

Bayesian Alignments of Warped Multi-Output Gaussian Processes

We propose a novel Bayesian approach to modelling nonlinear alignments of time series based on latent shared information. We apply the method to the real-world problem of finding common structure in the sensor data of wind turbines introduced by the underlying latent and turbulent wind field. The proposed model allows for both arbitrary alignments of the inputs and non-parametric output warpings to transform the observations. This gives rise to multiple deep Gaussian process models connected via latent generating processes. We present an efficient variational approximation based on nested variational compression and show how the model can be used to extract shared information between dependent time series, recovering an interpretable functional decomposition of the learning problem. We show results for an artificial data set and real-world data of two wind turbines.

stat.ML↗

arXiv2012

Programming errors in traversal programs over structured data

Traversal strategies á la Stratego (also á la Strafunski and 'Scrap Your Boilerplate') provide an exceptionally versatile and uniform means of querying and transforming deeply nested and heterogeneously structured data including terms in functional programming and rewriting, objects in OO programming, and XML documents in XML programming. However, the resulting traversal programs are prone to programming errors. We are specifically concerned with errors that go beyond conservative type errors; examples we examine include divergent traversals, prematurely terminated traversals, and traversals with dead code. Based on an inventory of possible programming errors we explore options of static typing and static analysis so that some categories of errors can be avoided. This exploration generates suggestions for improvements to strategy libraries as well as their underlying programming languages. Haskell is used for illustrations and specifications with sufficient explanations to make the presentation comprehensible to the non-specialist. The overall ideas are language-agnostic and they are summarized accordingly.

cs.PL↗