Physics-integrated generative modeling using attentive planar
  normalizing flow based variational autoencoder
Sheikh Waqas Akhtar
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.