An extendable, efficient and explainable Machine Learning approach is
proposed to represent cyclic plasticity and replace conventional material
models based on the Radial Return Mapping algorithm. High accuracy and
stability by means of a limited amount of training data is achieved by
implementing physics-informed regularizations and the back stress information.
The off-loading of the Neural Network is applied to the maximal extent. The
proposed model architecture is simpler and more efficient compared to existing
solutions from the literature, while representing a complete three-dimensional
material model. The validation of the approach is carried out by means of
surrogate data obtained with the Armstrong-Frederick kinematic hardening model.
The Mean Squared Error is assumed as the loss function which stipulates several
restrictions: deviatoric character of internal variables, compliance with the
flow rule, the differentiation of elastic and plastic steps and the
associativity of the flow rule. The latter, however, has a minor impact on the
accuracy, which implies the generalizability of the model for a broad spectrum
of evolution laws for internal variables. Numerical tests simulating several
load cases are shown in detail and validated for accuracy and stability.

提出了一种可扩展、高效且可解释的机器学习方法来表示循环塑性并替代基于径向返回映射算法的传统材料模型，通过实现物理信息正规化和背应力信息，以及最大程度上对神经网络的卸载，实现了在有限的训练数据量下的高精度和稳定性。该模型结构相对于文献中现有的解决方案更简单、更高效，并能表示完整的三维材料模型。通过采用 Armstrong-Frederick 运动硬化模型获得的替代数据进行了验证，均方误差被作为损失函数，该函数规定了几个限制条件：内部变量的去杂化特性，与流动规则的一致性，弹性和塑性步骤的区分以及流动规则的关联性，然而，后者对准确性的影响较小，这意味着该模型适用于广泛的内部变量演化规律。详细展示了模拟多个载荷情况的数值测试，并进行了准确性和稳定性的验证。

基于混合数据驱动和物理信息的正则化学习循环塑性与神经网络

Hybrid data-driven and physics-informed regularized learning of cyclic  plasticity with Neural Networks

We consider the challenging problem of predicting intrinsic object properties
from a single image by exploiting differentiable renderers. Many previous
learning-based approaches for inverse graphics adopt rasterization-based
renderers and assume naive lighting and material models, which often fail to
account for non-Lambertian, specular reflections commonly observed in the wild.
In this work, we propose DIBR++, a hybrid differentiable renderer which
supports these photorealistic effects by combining rasterization and
ray-tracing, taking the advantage of their respective strengths -- speed and
realism. Our renderer incorporates environmental lighting and spatially-varying
material models to efficiently approximate light transport, either through
direct estimation or via spherical basis functions. Compared to more advanced
physics-based differentiable renderers leveraging path tracing, DIBR++ is
highly performant due to its compact and expressive shading model, which
enables easy integration with learning frameworks for geometry, reflectance and
lighting prediction from a single image without requiring any ground-truth. We
experimentally demonstrate that our approach achieves superior material and
lighting disentanglement on synthetic and real data compared to existing
rasterization-based approaches and showcase several artistic applications
including material editing and relighting.

该论文提出了一种混合不同 iable 引擎，它支持光照和材质等照片级别的效果，甚至可以处理一些 “非兰伯特” 和 “高光” 等效果。拥有优秀的性能并且不需要任何地面真实数据，可以从单个图像中实现几何、反射和光照预测。