Neural Green’s function for Laplacian systems

Tang, Jingwei; Azevedo, Vinícius; Cordonnier, Guillaume; Solenthaler, Barbara

doi:10.1016/j.cag.2022.07.016

Cited by 4 publications

(2 citation statements)

References 37 publications

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“…With the rapid improvement of neural network inference performance, many data-driven models have been proposed [21], [23], [45]. Tang et al [46] regressed a Green's function solution for 2D Laplacian systems aided by the fully-connected networks. Yang et al [47] used a fully connected network to replace the local solution of PCG for accelerating 3D smoke simulation.…”

Section: Data-driven Fluid Modelingmentioning

confidence: 99%

MPMNet: A Data-Driven MPM Framework for Dynamic Fluid-Solid Interaction

Gao

et al. 2024

IEEE Trans. Visual. Comput. Graphics

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High-accuracy, high-efficiency physics-based fluid-solid interaction is essential for reality modeling and computer animation in online games or real-time Virtual Reality (VR) systems. However, the large-scale simulation of incompressible fluid and its interaction with the surrounding solid environment is either time-consuming or suffering from the reduced time/space resolution due to the complicated iterative nature pertinent to numerical computations of involved Partial Differential Equations (PDEs). In recent years, we have witnessed significant growth in exploring a different, alternative data-driven approach to addressing some of the existing technical challenges in conventional model-centric graphics and animation methods. This paper showcases some of our exploratory efforts in this direction. One technical concern of our research is to address the central key challenge of how to best construct the numerical solver effectively and how to best integrate spatiotemporal/dimensional neural networks with the available MPM's pressure solvers. In particular, we devise the MPMNet, a hybrid data-driven framework supporting the popular and powerful Material Point Method (MPM), to combine the comprehensive properties of MPM in numerically handling physical behaviors ranging from fluid to deformable solids and the high efficiency of data-driven models. At the architectural level, our MPMNet comprises three primary components: A data processing module to describe the physical properties by way of the input fields; A deep neural network group to learn the spatiotemporal features; And an iterative refinement process to continue to reduce possible numerical errors. The goal of these special technical developments is to aim at involved numerical acceleration while preserving physical accuracy, realizing efficient and accurate fluid-solid interactions in a data-driven fashion. The extensive experimental results verify that our MPMNet can tremendously speed up the computation compared with the popular numerical methods as the complexity of interaction scenes increases while better retaining the numerical accuracy.

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Section: Data-driven Fluid Modelingmentioning

confidence: 99%

MPMNet: A Data-Driven MPM Framework for Dynamic Fluid-Solid Interaction

Gao

et al. 2024

IEEE Trans. Visual. Comput. Graphics

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“…With rapid advancements in neural network inference performance, data-driven models have emerged as a promising alternative. Researchers like Tang et al [31] have utilized fully connected networks to regress Green's function solutions for 2D Laplacian systems, while Yang et al [32] employed fully connected networks to accelerate 3D smoke simulation by replacing local PCG solutions. These approaches have achieved impressive speedups in pressure calculation, surpassing traditional methods by more than tenfold without the need for multithreaded computation.…”

Section: Introductionmentioning

confidence: 99%

Material Point Method-Based Simulation Techniques for Medical Applications

Sung,

Kim,

Shin

2024

Electronics

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We propose a method for recognizing fragment objects to model the detailed tearing of elastic objects like human organs. Traditional methods require high-performance GPUs for real-time calculations to accurately simulate the detailed fragmentation of rapidly deforming objects or create random fragments to improve visual effects with minimal computation. The proposed method utilizes a deep neural network (DNN) to produce physically accurate results without requiring high-performance GPUs. Physically parameterized material point method (MPM) simulation data were used to learn small-scale detailed fragments. The tearing process is segmented and learned based on various training data from different spaces and external forces. The inference algorithm classifies the fragments from the training data and modifies the deformation gradient using a modifier. An experiment was conducted to compare the proposed method and the traditional MPM in the same environment. As a result, it was confirmed that visual fidelity for the tearing of elastic objects has been improved. This supports the simulation of various incision types in a virtual surgery.

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Editorial Note

Jorge¹

2022

Computers & Graphics

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Neural Green’s function for Laplacian systems

Cited by 4 publications

References 37 publications

MPMNet: A Data-Driven MPM Framework for Dynamic Fluid-Solid Interaction

MPMNet: A Data-Driven MPM Framework for Dynamic Fluid-Solid Interaction

Material Point Method-Based Simulation Techniques for Medical Applications

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