EAGER: An Inference Methodology to Illuminate Nonlinear Neutrino Flavor Transformation for Nuclear Astrophysics

探索宇宙爆炸背后的物理学对于理解可见宇宙的组成至关重要。具体地说，大质量恒星的爆炸是一些重元素核合成的候选地点，重元素是包括地球上生命在内的结构的组成部分。与此同时，这些爆炸的重要物理方面很难通过核天体物理学的传统方法获得。这既是由于现有代码缺乏对所需数学框架的适应性，也是由于计算复杂性。此外，这些爆炸的重要特征仍然被人为地隐藏起来，不被用来描述它们的工具所描述。同时，推理是与机器学习技术相关的另一种方法论。在地球科学和神经生物学中，推理已经证明成功地阐明了类似于那些被认为阻碍核天体物理学进展的问题。推理解释这些问题的可能性很高，因此本项目将探索与这些问题有关的推理。在一个科学领域内培育的创新在应用于分散的领域时可能具有变革性。这项研究的一个组成部分是对本科生的培训，其中许多人的社会经济背景在科学界的代表性不足。学生们还参与喜剧科学的公共宣传活动。在这些高密度环境中，中微子味场中的方向变化后向散射被认为是传统技术所不能看到的物理现象。中微子是基本粒子，它的“味道”决定了它们与其他粒子相互作用的方式。味道在很大程度上决定了中子与质子的比率以及能量和熵的沉积，从而在一定程度上决定了爆炸和核合成的机制。改变方向的后向散射可以发生在味场中，并显著影响爆炸的形状，但它提出了一个两点边值问题：一个传统的数值积分不能处理的框架。本项目研究了统计数据同化(SDA)解释这一问题的能力。SDA是一种贝叶斯推理方法，为数值天气预报而发明，用于预测稀疏样本的非线性系统。原则上，SDA非常适合于求解边值问题，并有望在计算效率上优于积分。这个项目试图确定SDA是否可以在1)解决方向变化的后向散射问题和2)效率方面优于积分，从而避免牺牲物理细节。在初步结果中，SDA有效地恢复了在非后向散射区域中通过积分获得的解。这些发现要求对SDA处理后向散射问题的能力进行深入研究。这一裁决反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Probing the physics underlying cosmic explosions is vital for understanding the makeup of the observable Universe. Specifically, the explosions of massive stars are candidate sites for the nucleosynthesis of some heavy elements – the building blocks of structures including life on Earth. Meanwhile, important aspects of the physics of these explosions are difficult to access via traditional approaches in nuclear astrophysics. This is due both to a lack of adaptability of existing codes to the required mathematical framework and to computational complexity. Moreover, important features of these explosions remain artificially hidden from the tools built to describe them. Meanwhile, inference is an alternative methodology, related to machine learning techniques. In the geosciences and neurobiology, inference has demonstrated success in illuminating problems akin to those noted to hinder progress within nuclear astrophysics. The potential for inference to illuminate these problems is high, and thus this project will explore inference to bear upon them. Innovations cultivated within one scientific arena can be transformative when applied to disjoint fields. Integral to the research is the training of undergraduates, many with socio-economic backgrounds under-represented in science. Students also engage in comedic science public outreach. The physics noted as “artificially hidden” from traditional techniques is direction-changing backscattering in the neutrino flavor field in these high-density environments. Neutrinos are elementary particles whose “flavor” dictates the manner in which they interact with other particles. Flavor in large part sets the neutron-to-proton ratio as well as energy and entropy deposition, thereby in-part dictating the mechanism of explosion and nucleosynthesis. Direction-changing backscattering can occur in the flavor field and significantly shape the explosion, but it presents a two-point boundary-value problem: a framework that traditional numerical integration is ill-equipped to handle. This project investigates the ability of statistical data assimilation (SDA) to illuminate this problem. SDA is a Bayesian inference methodology, invented for numerical weather prediction, to predict sparsely-sampled nonlinear systems. In principle, SDA is well-suited for solving boundary-value problems, and it is expected to outperform integration in computational efficiency. This project seeks to establish whether SDA can outperform integration in terms of 1) solving the direction-changing backscattering problem, and 2) efficiency so as to avoid sacrificing physical detail. In preliminary results, SDA efficiently recovers solutions obtained by integration in the non-backscattering regime. These findings call for a deep examination of SDA’s ability to handle the back-scattering problem.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.