Computational methods involving differential equations in computer graphics, machine learning and inference problems

计算机图形学、机器学习和推理问题中涉及微分方程的计算方法

基本信息

批准号：
RGPIN-2022-03327
负责人：
Ascher, Uri
金额：
$ 2.99万
依托单位：
University of British Columbia
依托单位国家：
加拿大
项目类别：
Discovery Grants Program - Individual
财政年份：
2022
资助国家：
加拿大
起止时间：
2022-01-01 至 2023-12-31
项目状态：
已结题

来源：
https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=749778
关键词：
Computational methods involving differential equations

项目摘要

The general objective of my research is to develop efficient and reliable computational algorithms for large-scale models involving learning (neural networks), physics-based simulation in computer graphics and robotics, partial differential equations in applications, inference problems, and optimization. The focus is on methods for constrained differential problems in time and space, data driven learning and inference (inverse) problems, neural nets, nonlinear optimization algorithms, and data assimilation approaches. Such problems arise in physics-based simulation in computer graphics, image processing, finance, model calibration, and distributed parameter estimation. I have a lifelong interest in exploring the relationship between discrete and continuous processes, and I'm also interested in geometric integration, including conservative discretizations for time--dependent differential problems. While my research focuses on the transfer of knowledge and expertise amongst different areas of application, emphasis will be placed within this framework on particular applications that arise in areas such as computer graphics, vision, biology, and finance. Over the next five years I expect to work on the following topics: 1. Differential equation models for optimization algorithms and neural nets 2. Neural net methods for capturing structure and solution detail of constrained differential equations 3. Numerical integrators for physics-based simulations in computer animation 4. Handling contact and friction in physics--based animation 5. Learning deformable object properties and other inverse problems Almost all of my activities are collaborative and involve HQP.

我的研究的一般目标是为涉及学习（神经网络），计算机图形和机器人技术的基于物理的模拟，应用程序中的部分微分方程，推理问题和优化的大规模模型开发有效且可靠的计算算法。重点是在时间和空间，数据驱动的学习和推理（逆）问题，神经网，非线性优化算法和数据同化方法的差异问题的方法上。这些问题是在计算机图形，图像处理，金融，模型校准和分布式参数估计中基于物理学的仿真中出现的。我对探索离散和连续过程之间的关系有终生的兴趣，而且我也对几何整合感兴趣，包括对时间依赖的差异问题的保守离散化。尽管我的研究重点是在不同应用领域之间的知识和专业知识的转移，但该框架将重点放在计算机图形，视觉，生物学和金融等领域的特定应用程序中。在接下来的五年中，我期望在以下主题上进行：1。优化算法和神经网的微分方程模型2。用于捕获约束微分方程的结构和解决方案的神经网络方法3.计算机动画中基于物理的模拟的数值集成器4。基于物理动画的数值模拟4.基于物理学的动画中的接触和摩擦5。