Deep Particle Algorithms and Advection-Reaction-Diffusion Transport Problems

深层粒子算法与平流反应扩散传输问题

• 批准号: 2309520
• 负责人: Jack Xin
• 金额: $ 39万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2309520&HistoricalAwards=false
• 关键词: Deep; Particle; Algorithms; Advection; Reaction

The project studies computational methods for learning and generating distributions of stochastic interacting particle representations of mathematical models in physics and biology. A new class of computational tools integrating particle simulation and machine learning will be developed for a wide range of applications in science and engineering such as modeling and prediction of large scale pattern formation of bacteria and insects, cancer cell invasion, wildfire spreading, and turbulent combustion in energy production. The light weight deep neural networks trained from data generated by particle simulations speed up prediction significantly, and potentially extend to field data in various domains with broader impacts. The planned education and out-reach activities help students, especially under-represented students, on multiple campuses to pursue advanced degrees and careers.The mathematical models under study are three space dimensional time dependent advection-reaction-diffusion partial differential equations challenging to compute by traditional mesh based methods especially when their solutions develop large gradients or concentrations at unknown locations. The project aims to address this challenge through an integrated framework of deep learning, optimal transport, and field-coupled stochastic interacting particle dynamics, the so called Deep Particle. The approach is mesh free, self-adaptive and does not require particle distributions to have invertible mappings between them. The project also investigates convergence and acceleration aspects of the resulting algorithms.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.

该项目研究用于学习和生成物理学和生物学中数学模型的随机相互作用粒子表示的分布的计算方法。一类新的计算工具集成粒子模拟和机器学习将被开发用于科学和工程领域的广泛应用，例如细菌和昆虫的大规模模式形成，癌细胞入侵，野火蔓延和能源生产中的湍流燃烧的建模和预测。根据粒子模拟生成的数据训练的轻量级深度神经网络显著加快了预测速度，并可能扩展到具有更广泛影响的各个领域的现场数据。计划中的教育和外展活动帮助学生，特别是代表性不足的学生，在多个校区追求更高的学位和职业生涯。正在研究的数学模型是三维空间依赖于时间的对流反应扩散偏微分方程，具有挑战性的计算传统的网格为基础的方法，特别是当他们的解决方案开发大梯度或浓度在未知的位置。该项目旨在通过深度学习，最佳传输和场耦合随机相互作用粒子动力学（所谓的深度粒子）的集成框架来解决这一挑战。该方法是无网格的，自适应的，不需要粒子分布之间有可逆的映射。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。