CAREER: Modeling and Simulating Generalized Diffusion for Computer Graphics and Computational Science

职业：计算机图形学和计算科学的广义扩散建模和仿真

• 批准号: 2238955
• 负责人: Mridul Aanjaneya
• 金额: $ 50万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-04-01 至 2028-03-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2238955&HistoricalAwards=false
• 关键词: CAREER; Modeling; Simulating; Generalized; Diffusion

Many problems that arise in computer graphics (such as virtual painting and phase changes like ice formation and dendrite growth) are driven by diffusion as pigment, crystals, or neural branches spread. The predominant model employed to capture diffusion is Fourier's law. However, this formulation prevents the simulation of anomalous diffusive processes, where diffusion occurs either faster (super-diffusion) or slower (sub-diffusion) than the rate predicted by Fourier's law. Currently, there is a need for efficiently simulating and visualizing super-diffusive phenomena, such as the super-spreader events for disease propagation witnessed during the COVID-19 pandemic or the melting of the permafrost due to global warming. This project will push the frontiers of physics simulation in computer graphics by developing a general framework for efficiently simulating all kinds of diffusive processes in large-scale applications, thereby enabling for example characterization of diffusion parameters that lead to specific experimental observations in the real world or the design of policies for preventing disease outbreaks in moving crowds. Project outcomes will have broad impact by supporting the visualization of such complex physical processes at greatly expanded scales. Additional broad impact will derive from the ability to run high resolution simulations on commodity workstations, which will allow a broad audience, particularly students in STEM, to simulate large-scale problems on their own workstations that previously may have required less-accessible enterprise-grade computational resources. Outreach and educational activities such as workshops will leverage diversity programs at Rutgers University to recruit and support students from under-represented groups.This project will advance the state-of-the-art in computer graphics by developing a novel formulation for diffusion using fractional derivatives that can not only simulate sub- and super-diffusive processes but also recover the efficiency of the best-known solvers for traditional Fourier-based diffusion. A hybrid Lagrangian/Eulerian representation will be adopted for modeling both micro- and macroscopic interactions, the two being strongly coupled together while accounting for discontinuities such as cracks that may emerge. To scale to large problem sizes, an adaptive discretization scheme will be developed using spatial polynomial regions that can flexibly represent the diffusion fluxes in any irregular domain of arbitrary shape using polynomial functions. For fast numerical solutions, this project will develop an efficient solver using Multigrid methods that better utilize the hardware memory bandwidth by avoiding construction of the linear system while leading to fast convergence rates on modern workstations. The resulting framework will allow the simulation of diffusive phenomena such as super-diffusion that have either not been explored in computer graphics or are currently beyond the reach of existing methods. Implementations of the proposed methodology will be made available to the community as open-source software packages, along with a lightweight client that supports interactive user feedback from the browser while the computationally intensive simulation runs on a remote server thereby making this research broadly accessible, in particular to undergraduate and K-12 students, to cultivate their early interest in STEM.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.

计算机图形（例如虚拟绘画和诸如冰形成和树突生长之类的相变）中出现的许多问题都是由颜料，晶体或神经分支扩散的扩散驱动的。用于捕获扩散的主要模型是傅立叶定律。但是，该公式阻止了对异常扩散过程的模拟，在这种过程中，扩散发生的速度（超扩散）要么比傅立叶定律预测的速率更快（超扩散）或较慢（亚扩散）。目前，需要有效地模拟和可视化超排除现象，例如在19009年大流行期间见证的疾病传播的超级传播事件，或由于全球变暖而导致的永久冻土融化。该项目将通过开发一个通用框架来推动计算机图形中物理模拟的前沿，该框架有效地模拟了大规模应用中的各种扩散过程，从而有助于表征扩散参数的表征，从而在现实世界中进行特定的实验观察，或者在现实世界中进行特定的实验观察或预防疾病爆发疾病爆发的政策。通过支持大大扩展的量表，项目结果将通过支持这种复杂的物理过程的可视化，从而产生广泛的影响。额外的广泛影响将源于对商品工作站进行高分辨率模拟的能力，这将使广泛的受众，尤其是STEM的学生模拟自己的工作站上的大规模问题，这些问题以前可能需要较低的企业级计算资源。外展和教育活动（例如研讨会）将利用罗格斯大学的多样性计划来招募和支持来自代表性不足的群体的学生。该项目将通过开发新的计算衍生品扩散的表述来推动计算机图形的最先进，这些衍生剂不仅可以恢复过较大的差异，而且还可以恢复过较大的差异，以恢复过良好的效率。将采用混合拉格朗日/欧拉尔式的代表来建模微观和宏观相互作用，两者在考虑到可能出现的裂纹等不连续性的同时强烈耦合在一起。为了扩展到大问题，将使用空间多项式区域开发自适应离散方案，该方案可以灵活地表示使用多项式函数的任何任意形状的不规则域中的扩散通量。对于快速数值解决方案，该项目将使用多机方法来开发有效的求解器，通过避免构建线性系统，同时导致现代工作站上的快速收敛速度，从而更好地利用硬件存储器带宽。最终的框架将允许模拟扩散现象，例如在计算机图形学中未探索的超扩散，或者目前超出了现有方法的范围。所提出的方法的实施将作为开源软件包提供给社区，以及一个轻巧的客户，该客户支持浏览器的交互式用户反馈，而计算强度的模拟在远程服务器上运行，从而可以广泛地访问这项研究，从而使本科生和K-12的学生对STEM FATE的早期培养，并培养了对STEM的培养。基金会的智力优点和更广泛的影响审查标准。

项目成果

A Generalized Constitutive Model for Versatile MPM Simulation and Inverse Learning with Differentiable Physics

• DOI: 10.1145/3606925
• 发表时间: 2023-08
• 期刊: Proceedings of the ACM on Computer Graphics and Interactive Techniques
• 影响因子: 1.3
• 作者: Haozhe Su;Xuan Li;Tao Xue;Chenfanfu Jiang;Mridul Aanjaneya

An Interactive Framework for Visually Realistic 3D Motion Synthesis using Evolutionarily-trained Spiking Neural Networks

使用经过进化训练的尖峰神经网络进行视觉逼真 3D 运动合成的交互式框架

• DOI: 10.1145/3585509
• 发表时间: 2023
• 期刊: Proceedings of the ACM on Computer Graphics and Interactive Techniques
• 影响因子: 1.3
• 作者: Polykretis, Ioannis;Patil, Aditi;Aanjaneya, Mridul;Michmizos, Konstantinos
• 通讯作者: Michmizos, Konstantinos

Real-time Height-field Simulation of Sand and Water Mixtures

• DOI: 10.1145/3610548.3618159
• 发表时间: 2023-12
• 期刊: SIGGRAPH Asia 2023 Conference Papers
• 作者: Haozhe Su;Siyu Zhang;Zherong Pan;Mridul Aanjaneya;Xifeng Gao;Kui Wu