发表机构
Swiss Data Science Center; ETH Zurich; EPFL; CERN（瑞士数据科学中心; 苏黎世联邦理工学院; 洛桑联邦理工学院; 欧洲核子研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对大规模科学应用中先进机器学习方法计算不可行的问题，提出一种经验贝叶斯方法自动调整谱归一化神经高斯过程超参数，在大型强子对撞机动态孔径预测中实现低计算成本下的高精度与良好不确定性校准。
AI 中文摘要
我们解决了大规模科学应用中可扩展不确定性量化的挑战，在这些应用中，复杂的先进机器学习方法通常在计算上不可行。我们的主要贡献是一种简单而有效的经验贝叶斯方法，用于自动调整灵活的、异方差的谱归一化神经高斯过程的超参数。该方法保留了半贝叶斯神经模型的表达能力和不确定性感知能力，同时通过将超参数学习直接集成到训练循环中，显著降低了计算负担。我们展示了该方法在估算环形粒子加速器中动态孔径这一高能物理对撞机和存储环中的基本问题上的实际影响，使用了欧洲核子研究中心大型强子对撞机的模拟数据。传统的动态孔径估算方法需要大量的粒子跟踪模拟，这些模拟耗时且资源密集，令人望而却步。我们的结果表明，所提出的方法在计算成本远低于先进方法的情况下，实现了具有竞争力的预测性能和良好校准的不确定性估计。我们强调，除了这一应用之外，所提出的经验贝叶斯框架为在手动超参数调整不切实际的情况下训练异方差神经模型提供了一种通用解决方案。因此，我们预计该框架可以应用于其他面临类似计算限制的领域。
英文摘要
We address the challenge of scalable uncertainty quantification in large-scale scientific applications, where complex state-of-the-art machine learning methods are often computationally infeasible. Our primary contribution is a simple yet effective empirical Bayes method for automatically tuning the hyperparameters of a flexible, heteroscedastic Spectral-normalized Neural Gaussian Process. This approach retains the expressiveness and uncertainty-awareness of semi-Bayesian neural models while significantly reducing the computational burden by integrating hyperparameter learning directly into the training loop. We demonstrate the practical impact of our method on the task of estimating the dynamic aperture in circular particle accelerators, a fundamental problem in high-energy physics colliders and storage rings, using simulation data from the case of the Large Hadron Collider at CERN. Traditional approaches to DA estimation require extensive particle-tracking simulations, which are prohibitively time-consuming and resource-intensive. Our results show that the proposed method achieves competitive predictive performance and well-calibrated uncertainty estimates at much lower computational cost than state-of-the-art approaches. We stress that, beyond this application, the proposed empirical Bayes framework offers a general solution for training heteroscedastic neural models in situations where manual hyperparameter tuning is impractical. Accordingly, we anticipate that this framework can be applied to other domains that encounter comparable computational limitations.
