Abstract
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.
Abstract (translated)
物理集成生成建模是一种混合或灰色盒模型，其中我们通过添加指导数据分布的物理知识来增强数据驱动模型。利用物理知识可以使生成模型以可控的方式产生输出，从而使输出本质上符合物理定律。它赋予了扩展训练分布以外的高置信度能力，并提高了可解释性，因为模型的部分基础是固有领域知识。在这项工作中，我们旨在提高物理集成生成模型的重建精度和对噪声的鲁棒性。为此，我们使用变分自编码器作为生成模型。为了提高解码器的重建结果，我们提出了一种使用平滑正态分布来学习物理和可训练数据驱动组件的后验分布的计划。平滑正态分布的后验分布利用了数据分布的固有动态结构，因此所学习到的模型更接近于真实的数据分布。为了提高生成模型对模型内噪声的鲁棒性，我们在平滑正态分布的编码器部分进行了修改，基于上下文信息进行缩放点积注意。这将减轻噪声在 latent 向量上的不利影响，使模型更加鲁棒。我们对人类运动数据集 [33] 进行了实证评估，结果证实了我们在建模方面的提议，即提高重建质量和模型对噪声的鲁棒性。
URL
https://arxiv.org/abs/2404.12267
