In the realm of brittle fracture animation, generating realistic destruction
animations with physics simulation techniques can be computationally expensive.
Although methods using Voronoi diagrams or pre-fractured patterns work for
real-time applications, they often lack realism in portraying brittle
fractures. This paper introduces a novel learning-based approach for seamlessly
merging realistic brittle fracture animations with rigid-body simulations. Our
method utilizes BEM brittle fracture simulations to create fractured patterns
and collision conditions for a given shape, which serve as training data for
the learning process. To effectively integrate collision conditions and
fractured shapes into a deep learning framework, we introduce the concept of
latent impulse representation and geometrically-segmented signed distance
function (GS-SDF). The latent impulse representation serves as input, capturing
information about impact forces on the shape's surface. Simultaneously, a
GS-SDF is used as the output representation of the fractured shape. To address
the challenge of optimizing multiple fractured pattern targets with a single
latent code, we propose an eight-dimensional latent space based on a normal
distribution code within our latent impulse representation design. This
adaptation effectively transforms our neural network into a generative one. Our
experimental results demonstrate that our approach can generate significantly
more detailed brittle fractures compared to existing techniques, all while
maintaining commendable computational efficiency during run-time.

在脆性断裂动画领域，本文引入了一种新颖的基于学习的方法，将逼真的脆性断裂动画与刚体模拟相融合，通过 BEM 脆性断裂模拟和几何分割有符号距离函数（GS-SDF）作为训练数据，采用潜在冲量表示法作为输入，在保持计算效率的同时生成更详细的脆性断裂。

DeepFracture：一种预测脆性断裂的生成方法

DeepFracture: A Generative Approach for Predicting Brittle Fractures

Numerical modeling of localizations is a challenging task due to the evolving
rough solution in which the localization paths are not predefined. Despite
decades of efforts, there is a need for innovative discretization-independent
computational methods to predict the evolution of localizations. In this work,
an improved version of the neural network-enhanced Reproducing Kernel Particle
Method (NN-RKPM) is proposed for modeling brittle fracture. In the proposed
method, a background reproducing kernel (RK) approximation defined on a coarse
and uniform discretization is enriched by a neural network (NN) approximation
under a Partition of Unity framework. In the NN approximation, the deep neural
network automatically locates and inserts regularized discontinuities in the
function space. The NN-based enrichment functions are then patched together
with RK approximation functions using RK as a Partition of Unity patching
function. The optimum NN parameters defining the location, orientation, and
displacement distribution across location together with RK approximation
coefficients are obtained via the energy-based loss function minimization. To
regularize the NN-RK approximation, a constraint on the spatial gradient of the
parametric coordinates is imposed in the loss function. Analysis of the
convergence properties shows that the solution convergence of the proposed
method is guaranteed. The effectiveness of the proposed method is demonstrated
by a series of numerical examples involving damage propagation and branching.

本文提出了一种改进的神经网络增强再生核粒子法（NN-RKPM）来建模脆性断裂，实现了离散化无关的计算方法，并通过一系列数值算例展示了其有效性。

基于神经网络的再生核逼近增强方法用于脆性断裂建模

A Neural Network-Based Enrichment of Reproducing Kernel Approximation  for Modeling Brittle Fracture

We present a new physics informed neural network (PINN) algorithm for solving
brittle fracture problems. While most of the PINN algorithms available in the
literature minimize the residual of the governing partial differential
equation, the proposed approach takes a different path by minimizing the
variational energy of the system. Additionally, we modify the neural network
output such that the boundary conditions associated with the problem are
exactly satisfied. Compared to conventional residual based PINN, the proposed
approach has two major advantages. First, the imposition of boundary conditions
is relatively simpler and more robust. Second, the order of derivatives present
in the functional form of the variational energy is of lower order than in the
residual form. Hence, training the network is faster. To compute the total
variational energy of the system, an efficient scheme that takes as input a
geometry described by spline based CAD model and employs Gauss quadrature rules
for numerical integration has been proposed. Moreover, we utilize the concept
of transfer learning to obtain the crack path in an efficient manner. The
proposed approach is used to solve four fracture mechanics problems. For all
the examples, results obtained using the proposed approach match closely with
the results available in the literature. For the first two examples, we compare
the results obtained using the proposed approach with the conventional residual
based neural network results. For both the problems, the proposed approach is
found to yield better accuracy compared to conventional residual based PINN
algorithms.

本文提出一种基于物理知识的神经网络（PINN）算法，通过最小化系统的变分能量来求解脆性断裂问题，同时对神经网络输出进行修改以满足边界条件并采用迭代学习模式。通过在四个断裂力学问题上的验证，证明了该方法相对于常规的残差 PINN 算法具有更好的准确性和相对简单鲁棒的重要优势。