Abstract:While standard generative adversarial networks (GANs) rely solely on training data to learn unknown probability distributions, physics-informed GANs (PI-GANs) encode physical laws in the form of stochastic partial differential equations (PDEs) using auto differentiation. By relating observed data to unobserved quantities of interest through PDEs, PI-GANs allow for the estimation of underlying probability distributions without their direct measurement (i.e. inverse problems). The scalable nature of GANs allows high-dimensional, spatially-dependent probability distributions (i.e., random fields) to be inferred, while incorporating prior information through PDEs allows the training datasets to be relatively small. In this work, PI-GANs are demonstrated for the application of elastic modulus estimation in mechanical testing. Given measured deformation data, the underlying probability distribution of spatially-varying elastic modulus (stiffness) is learned. Two feed-forward deep neural network generators are used to model the deformation and material stiffness across a two dimensional domain. Wasserstein GANs with gradient penalty are employed for enhanced stability. In the absence of explicit training data, it is demonstrated that the PI-GAN learns to generate realistic, physically-admissible realizations of material stiffness by incorporating the PDE that relates it to the measured deformation. It is shown that the statistics (mean, standard deviation, point-wise distributions, correlation length) of these generated stiffness samples have good agreement with the true distribution.
Abstract:Capsule Networks have great potential to tackle problems in structural biology because of their attention to hierarchical relationships. This paper describes the implementation and application of a Capsule Network architecture to the classification of RAS protein family structures on GPU-based computational resources. The proposed Capsule Network trained on 2D and 3D structural encodings can successfully classify HRAS and KRAS structures. The Capsule Network can also classify a protein-based dataset derived from a PSI-BLAST search on sequences of KRAS and HRAS mutations. Our results show an accuracy improvement compared to traditional convolutional networks, while improving interpretability through visualization of activation vectors.