@unpublished{cao2023material,
  title = {Material Point Methods on Unstructured Tessellations: A Stable Kernel Approach With Continuous Gradient Reconstruction},
  author = {Cao, Yadi and Zhao, Yidong and Li, Minchen and Yang, Yin and Choo, Jinhyun and Terzopoulos, Demetri and Jiang, Chenfanfu},
  note = {arXiv:2312.10338},
  year = {2023},
  file = {cao2023material.pdf},
  doi = {2312.10338}
}

The Material Point Method (MPM) is a hybrid Eulerian-Lagrangian simulation technique for solid mechanics with significant deformation. Structured background grids are commonly employed in the standard MPM, but they may give rise to several accuracy problems in handling complex geometries. When using (2D) unstructured triangular or (3D) tetrahedral background elements, however, significant challenges arise (eg, cell-crossing error). Substantial numerical errors develop due to the inherent C0 continuity property of the interpolation function, which causes discontinuous gradients across element boundaries. Prior efforts in constructing C1 continuous interpolation functions have either not been adapted for unstructured grids or have only been applied to 2D triangular meshes. In this study, an Unstructured Moving Least Squares MPM (UMLS-MPM) is introduced to accommodate 2D and 3D simplex tessellation. The central idea is to incorporate a diminishing function into the sample weights of the MLS kernel, ensuring an analytically continuous velocity gradient estimation. Numerical analyses confirm the method’s capability in mitigating cell crossing inaccuracies and realizing expected convergence.

@article{fang2023augmented,
  title = {Augmented Incremental Potential Contact for Sticky Interactions},
  author = {Fang, Yu and Li, Minchen and Cao, Yadi and Li, Xuan and Wolper, Joshuah and Yang, Yin and Jiang, Chenfanfu},
  journal = {IEEE Transactions on Visualization and Computer Graphics},
  year = {2023},
  publisher = {IEEE},
  file = {fang2023augmented.pdf},
  doi = {10.1109/TVCG.2023.3295656}
}

We introduce a variational formulation for simulating sticky interactions between elastoplastic solids. Our method brings a wider range of material behaviors into the reach of the Incremental Potential Contact (IPC) solver recently developed by. Extending IPC requires several contributions. We first augment IPC with the classical Raous-Cangemi-Cocou (RCC) adhesion model. This allows us to robustly simulate the sticky interactions between arbitrary codimensional-0, 1, and 2 geometries. To enable user-friendly practical adoptions of our method, we further introduce a physically parametrized, easily controllable normal adhesion formulation based on the unsigned distance , which is fully compatible with IPC’s barrier formulation. Furthermore, we propose a smoothly clamped tangential adhesion model that naturally models intricate behaviors including debonding. Lastly, we perform benchmark studies comparing our method with the classical models as well as real-world experimental results to demonstrate the efficacy of our method.

@article{cao2022efficient,
  title = {An efficient b-spline lagrangian/eulerian method for compressible flow, shock waves, and fracturing solids},
  author = {Cao, Yadi and Chen, Yunuo and Li, Minchen and Yang, Yin and Zhang, Xinxin and Aanjaneya, Mridul and Jiang, Chenfanfu},
  journal = {ACM Transactions on Graphics (TOG)},
  volume = {41},
  number = {5},
  pages = {1--13},
  year = {2022},
  publisher = {ACM New York, NY},
  file = {cao2022efficient.pdf},
  doi = {https://doi.org/10.1145/3519595}
}

This study presents a new method for modeling the interaction between compressible flow, shock waves, and deformable structures, emphasizing destructive dynamics. Extending advances in time-splitting compressible flow and the Material Point Methods (MPM), we develop a hybrid Eulerian and Lagrangian/Eulerian scheme for monolithic flow-structure interactions. We adopt the second-order WENO scheme to advance the continuity equation. To stably resolve deforming boundaries with sub-cell particles, we propose a blending treatment of reflective and passable boundary conditions inspired by the theory of porous media. The strongly coupled velocity-pressure system is discretized with a new mixed-order finite element formulation employing B-spline shape functions. Shock wave propagation, temperature/density-induced buoyancy effects, and topology changes in solids are unitedly captured.

@article{cao2019liquid,
  title = {A liquid plug moving in an annular pipe--Heat transfer analysis},
  author = {Cao, Yadi and Gao, Xuan and Li, Ri},
  journal = {International Journal of Heat and Mass Transfer},
  volume = {139},
  pages = {1065--1076},
  year = {2019},
  publisher = {Elsevier},
  file = {cao2019liquid.pdf},
  doi = {https://doi.org/10.1016/j.ijheatmasstransfer.2019.05.088}
}

Different from a fully developed continuous flow in an annular pipe, a liquid plug moving in an annular pipe generates two toroidal vortexes, which cause radial transport that enhances heat transfer. The fully developed heat transfer of the concentric plug is studied for three types of thermal wall conditions: inner-flux, outer-flux, and isothermal. The fully developed heat transfer of the continuous flow is analytically solved for the same thermal wall conditions. The comparison of heat transfer is made between the plug and the continuous flow. Two heat transfer mechanisms, boundary layer transport and radial transport, are considered to explain the heat transfer enhancement. If the radial transport is weak, the plug shows similar heat transfer performance to the continuous flow, which is dominated by the boundary layer transport. The heat transfer enhancement relies on the radial transport, which increases with decreasing the inner radius, decreasing the plug length, and increasing the Peclet number.

@article{cao2018liquid,
  title = {A liquid plug moving in an annular pipe—Flow analysis},
  author = {Cao, Yadi and Li, Ri},
  journal = {Physics of Fluids},
  volume = {30},
  number = {9},
  year = {2018},
  publisher = {AIP Publishing},
  file = {cao2018liquid.pdf},
  doi = {https://doi.org/10.1063/1.5050258}
}

The flow in a liquid plug moving in an annular pipe is analytically solved. The interaction with the two concentric walls of the annular pipe results in two toroidal vortexes within the concentric plug. Focus is put on long plugs with aspect ratio larger than 2, which have vortex circulation flow rates and volume ratio independent of the plug length. Based on the analytical results, correlations are derived for the circulation flow rates of the plug and each vortex and for the volume ratio of the two vortexes. Correlations are also developed for evaluating the radial transport of the plug flow. The friction factor for concentric plugs is a function of the aspect ratio and the radius ratio. For very long plugs with, the friction factor approaches that of the fully developed continuous flow in the annular pipe.

@inproceedings{cao2023efficient,
  title = {Efficient Learning of Mesh-Based Physical Simulation with Bi-Stride Multi-Scale Graph Neural Network},
  author = {Cao, Yadi and Chai, Menglei and Li, Minchen and Jiang, Chenfanfu},
  booktitle = {Proceedings of the 40th International Conference on Machine Learning},
  pages = {3541--3558},
  year = {2023},
  volume = {202},
  publisher = {PMLR},
  file = {cao2023efficient.pdf}
}

Learning the long-range interactions on large-scale mesh-based physical systems with flat Graph Neural Networks (GNNs) and stacking Message Passings (MPs) is challenging due to the scaling complexity w.r.t. the number of nodes and over-smoothing. Therefore, there has been growing interest in the community to introduce multi-scale structures to GNNs for physics simulation. However, current state-of-the-art methods are limited by their reliance on the labor-heavy drawing of coarser meshes or building coarser levels based on spatial proximity, which can introduce wrong edges across geometry boundaries. Inspired by the bipartite graph determination, we propose a novel pooling strategy, bi-stride to tackle the aforementioned limitations. Bi-stride pools nodes on every other frontier of the Breadth-First-Search (BFS), without the need for the manual drawing of coarser meshes and, avoid wrong edges introduced by spatial proximity. Additionally, it enables a reduced number of MP times on each level and the non-parametrized pooling and unpooling by interpolations, similar to convolutional Neural Networks (CNNs), which significantly reduces computational requirements. Experiments show that the proposed framework, BSMS-GNN, significantly outperforms existing methods in terms of both accuracy and computational efficiency in representative physics-based simulation scenarios.

@inproceedings{huang2023tango,
  title = {{TANGO}: Time-reversal Latent Graph{ODE} for Multi-Agent Dynamical Systems},
  author = {Huang, Zijie and Zhao, Wanjia and Gao, Jingdong and Hu, Ziniu and Luo, Xiao and Cao, Yadi and Chen, Yuanzhou and Sun, Yizhou and Wang, Wei},
  booktitle = {The Symbiosis of Deep Learning and Differential Equations III},
  year = {2023},
  file = {huang2023tango.pdf}
}

Learning complex multi-agent system dynamics from data is crucial across many domains like physical simulations and material modeling. Existing physics-informed approaches, like Hamiltonian Neural Network, introduce inductive bias by strictly following energy conservation law. However, many real-world systems do not strictly conserve energy. Thus, we focus on Time-Reversal Symmetry, a broader physical principle indicating that system dynamics should remain invariant when time is reversed. This principle not only preserves energy in conservative systems but also serves as a strong inductive bias for non-conservative, reversible systems. In this paper, we propose a simple-yet-effective self-supervised regularization term as a soft constraint that aligns the forward and backward trajectories predicted by a continuous graph neural network-based ordinary differential equation (GraphODE). In addition, we theoretically show that our regularization essentially minimizes higher-order Taylor expansion terms during the ODE integration steps, which enables our model to be more noise-tolerant and even applicable to irreversible systems.

@inproceedings{li2022plasticitynet,
  title = {Plasticitynet: Learning to simulate metal, sand, and snow for optimization time integration},
  author = {Li, Xuan and Cao, Yadi and Li, Minchen and Yang, Yin and Schroeder, Craig and Jiang, Chenfanfu},
  journal = {Advances in Neural Information Processing Systems},
  volume = {35},
  pages = {27783--27796},
  year = {2022},
  file = {li2022plasticitynet.pdf}
}

In this paper, we propose a neural network-based approach for learning to represent the behavior of plastic solid materials ranging from rubber and metal to sand and snow. Unlike elastic forces such as spring forces, these plastic forces do not result from the positional gradient of any potential energy, imposing great challenges on the stability and flexibility of their simulation. Our method effectively resolves this issue by learning a generalizable plastic energy whose derivative closely matches the analytical behavior of plastic forces. Our method, for the first time, enables the simulation of a wide range of arbitrary elasticity-plasticity combinations using time step-independent, unconditionally stable optimization-based time integrators. We demonstrate the efficacy of our method by learning and producing challenging 2D and 3D effects of metal, sand, and snow with complex dynamics.

@inproceedings{cao2018liquidastfe,
  title = {Liquid Plug in Gas Flow in Annular Channel},
  author = {Cao, Yadi and Li, Ri},
  booktitle = {ASTFE Digital Library},
  year = {2018},
  organization = {Begel House Inc.},
  doi = {10.1615/TFEC2018.mph.024337}
}

Learning the long-range interactions on large-scale mesh-based physical systems with flat Graph Neural Networks (GNNs) and stacking Message Passings (MPs) is challenging due to the scaling complexity w.r.t. the number of nodes and over-smoothing. Therefore, there has been growing interest in the community to introduce multi-scale structures to GNNs for physics simulation. However, current state-of-the-art methods are limited by their reliance on the labor-heavy drawing of coarser meshes or building coarser levels based on spatial proximity, which can introduce wrong edges across geometry boundaries. Inspired by the bipartite graph determination, we propose a novel pooling strategy, bi-stride to tackle the aforementioned limitations. Bi-stride pools nodes on every other frontier of the Breadth-First-Search (BFS), without the need for the manual drawing of coarser meshes and, avoid wrong edges introduced by spatial proximity. Additionally, it enables a reduced number of MP times on each level and the non-parametrized pooling and unpooling by interpolations, similar to convolutional Neural Networks (CNNs), which significantly reduces computational requirements. Experiments show that the proposed framework, BSMS-GNN, significantly outperforms existing methods in terms of both accuracy and computational efficiency in representative physics-based simulation scenarios.