Physics-integrated generative modeling using attentive planar normalizing flow based variational autoencoder
Sheikh Waqas Akhtar
TL;DR
The paper tackles the challenge of integrating physics knowledge into generative models to improve reconstruction fidelity and generalization under noise. It introduces a physics integrated variational autoencoder (NF-VAE) with planar normalizing flows to model two latent streams, one physics based and one data driven, and an attentive variant (Attentive NF-VAE) to inject context. The decoder combines a physics path via an ODE solver with a neural path, and learning is guided by an ELBO augmented with Takesaki-style regularizers. Experiments on human locomotion data show that NF-VAE and its attentive extension outperform baselines in reconstruction accuracy and robustness to feature noise, with NF-based posteriors providing the strongest performance gains. This approach offers a principled way to fuse domain physics with flexible probabilistic inference for dynamical systems.
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.