LEAPS-MPS: Deep Quasi-Reversibility Inversion for Source Localization Oncological Problems

脑肿瘤是最致命的癌症之一，影响全球数百万人。仅在美国，每年就有数千名成人和儿童接受原发性脑肿瘤诊断。肿瘤学家，神经学家和其他参与该领域的科学家的一个关键焦点是确定肿瘤的特定解剖起源部位。了解这个位点可能有助于了解肿瘤的行为方式，预测它可能引起的症状，以及识别与脑肿瘤高度相关的遗传综合征。因此，这些原始信息可以成为早期发现脑癌的重要辅助手段。本项目研究了一种可靠高效的反演算法，称为深度准可逆性方法（DQRM），可以快速重建原发肿瘤的位置。通过积极让本科生参与研究活动并促进机构之间的合作，该项目将有助于受脑肿瘤影响的个人的福祉，并有助于培养熟练的STEM劳动力。该项目是基于一个历史悠久的HBCU，从而提供了一个机会，以扩大研究参与STEM。该项目涉及数值和理论研究的建议DQRM解决源定位肿瘤学问题与不同程度的复杂性。DQRM是变分准可逆性（QR）方法和深度学习无网格算法的结合。 该设计融合了计算数学、偏微分方程和机器学习技术，可快速提供可靠且准确的准解。一方面，变分QR方法可以克服局部化的功能，高度动态的非线性，和重建过程中固有的指数不稳定性。另一方面，深度学习方法处理维度灾难和与数据测量相关的成本。该项目的第一个目标是研究逆求解器在处理与肿瘤细胞进化动力学相关的准线性抛物模型中的有效性。第二个是通过结合考虑年龄、大小和空间结构等因素的高级肿瘤生长模型来研究该算法的适用性。该项目的理论主题是围绕着神经网络逼近器向准解的收敛。该项目部分由历史上的黑人学院和大学-卓越研究（HBCU-EiR）计划资助。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

Brain tumors are among the most fatal cancers, affecting millions of individuals worldwide. In the United States alone, each year thousands of adults and children receive a primary brain tumor diagnosis. A key focus for oncologists, neurologists, and other scientists involved in the field is in determining the specific anatomical origin site of the tumor. Knowing this site might help in gaining insights in how the tumor behaves, in predicting the symptoms it is likely to cause, and in identifying genetic syndromes that have a high association with brain tumors. Therefore, this source information can be an important aid in the early detection of brain cancer. This project studies a reliable and efficient inversion algorithm called Deep Quasi-Reversibility Method (DQRM) that can quickly reconstruct the primary tumor’s location. By actively involving undergraduate students in research activities and fostering collaborations between institutions, the project will contribute to the well-being of individuals affected by brain tumors as well as help to cultivate a skilled STEM workforce. The project is based at a long-established HBCU, thus providing an opportunity to broadening research participating in STEM.The project involves numerical and theoretical studies of the proposed DQRM for solving the source localization oncological question with different levels of complexity. The DQRM is a combination of a variational quasi-reversibility (QR) method and a deep learning mesh-free-based algorithm. The design brings together techniques of computational mathematics, partial differential equations, and machine learning to fast deliver a reliable and accurate quasi-solution. On one hand, the variational QR approach can overcome localized features, highly dynamic nonlinearities, and the inherent exponential instability of the reconstruction process. On the other, the deep learning approach handles the curse of dimensionality and the costs associated with data measurement. The first objective of the project is to study the effectiveness of the inverse solver in tackling the quasi-linear parabolic models associated with the evolutionary dynamics of tumor cells. The second is to investigate the applicability of the algorithm by incorporating an advanced tumor growth model that considers factors such as age, size, and spatial structure. The theoretical theme is centered around the convergence of a neural network approximator towards the quasi-solution.This project is funded in part by the Historically Black Colleges and Universities - Excellence in Research (HBCU-EiR) program.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.