Physics-integrated generative modeling is a class of hybrid or grey-box modeling in which we augment the the data-driven model with the physics knowledge governing the data distribution. The use of physics knowledge allows the generative model to produce output in a controlled way, so that the output, by construction, complies with the physical laws. It imparts improved generalization ability to extrapolate beyond the training distribution as well as improved interpretability because the model is partly grounded in firm domain knowledge. In this work, we aim to improve the fidelity of reconstruction and robustness to noise in the physics integrated generative model. To this end, we use variational-autoencoder as a generative model. To improve the reconstruction results of the decoder, we propose to learn the latent posterior distribution of both the physics as well as the trainable data-driven components using planar normalizng flow. Normalizng flow based posterior distribution harnesses the inherent dynamical structure of the data distribution, hence the learned model gets closer to the true underlying data distribution. To improve the robustness of generative model against noise injected in the model, we propose a modification in the encoder part of the normalizing flow based VAE. We designed the encoder to incorporate scaled dot product attention based contextual information in the noisy latent vector which will mitigate the adverse effect of noise in the latent vector and make the model more robust. We empirically evaluated our models on human locomotion dataset [33] and the results validate the efficacy of our proposed models in terms of improvement in reconstruction quality as well as robustness against noise injected in the model.

翻译：物理集成生成式建模是一类混合或灰盒建模方法，通过在数据驱动模型中融入控制数据分布的物理知识，使生成模型的输出在构造上自然遵循物理定律。物理知识的引入不仅增强了模型超越训练数据分布的外推能力，还因其部分基于坚实的领域知识而提升了可解释性。本研究旨在提升物理集成生成式模型的重建保真度与噪声鲁棒性。为此，我们采用变分自编码器作为生成模型。为改进解码器的重建结果，我们提出利用平面归一化流同时学习物理组件与可训练数据驱动组件的潜变量后验分布。基于归一化流的后验分布能有效捕获数据分布的内在动态结构，使学习模型更逼近真实数据分布。针对注入模型的噪声对生成模型鲁棒性的影响，我们在基于归一化流的变分自编码器编码器部分提出改进：设计编码器在含噪潜向量中融入基于缩放点积注意力的上下文信息，从而缓解潜向量中的噪声负面效应并增强模型鲁棒性。基于人体运动数据集[33]的实验验证了所提模型在重建质量提升与噪声鲁棒性方面的有效性。