Horea Ilieş

Mohammad Mahdi Behzadi, Horea T. Ilies

Many machine learning methods have been recently developed to circumvent the high computational cost of the gradient-based topology optimization. These methods typically require extensive and costly datasets for training, have a difficult time generalizing to unseen boundary and loading conditions and to new domains, and do not take into consideration topological constraints of the predictions, which produces predictions with inconsistent topologies. We present a deep learning method based on generative adversarial networks for generative design exploration. The proposed method combines the generative power of conditional GANs with the knowledge transfer capabilities of transfer learning methods to predict optimal topologies for unseen boundary conditions. We also show that the knowledge transfer capabilities embedded in the design of the proposed algorithm significantly reduces the size of the training dataset compared to the traditional deep learning neural or adversarial networks. Moreover, we formulate a topological loss function based on the bottleneck distance obtained from the persistent diagram of the structures and demonstrate a significant improvement in the topological connectivity of the predicted structures. We use numerous examples to explore the efficiency and accuracy of the proposed approach for both seen and unseen boundary conditions in 2D.

Reed M. Williams, Horea T. Ilieş

Current point cloud processing algorithms do not have the capability to automatically extract semantic information from the observed scenes, except in very specialized cases. Furthermore, existing mesh analysis paradigms cannot be directly employed to automatically perform typical shape analysis tasks directly on point cloud models. We present a potent framework for shape analysis, similarity, and segmentation of noisy point cloud models for real objects of engineering interest, models that may be incomplete. The proposed framework relies on spectral methods and the heat diffusion kernel to construct compact shape signatures, and we show that the framework supports a variety of clustering techniques that have traditionally been applied only on mesh models. We developed and implemented one practical and convergent estimate of the Laplace-Beltrami operator for point clouds as well as a number of clustering techniques adapted to work directly on point clouds to produce geometric features of engineering interest. The key advantage of this framework is that it supports practical shape analysis capabilities that operate directly on point cloud models of objects without requiring surface reconstruction or global meshing. We show that the proposed technique is robust against typical noise present in possibly incomplete point clouds, and segment point clouds scanned by depth cameras (e.g. Kinect) into semantically-meaningful sub-shapes.

Pouya Tavousi, Morad Behandish, Horea T. Ilies et al.

A reliable prediction of 3D protein structures from sequence data remains a big challenge due to both theoretical and computational difficulties. We have previously shown that our kinetostatic compliance method (KCM) implemented into the Protofold package can overcome some of the key difficulties faced by other de novo structure prediction methods, such as the very small time steps required by the molecular dynamics (MD) approaches or the very large number of samples needed by the Monte Carlo (MC) sampling techniques. In this article, we improve the free energy formulation used in Protofold by including the typically underrated entropic effects, imparted due to differences in hydrophobicity of the chemical groups, which dominate the folding of most water-soluble proteins. In addition to the model enhancement, we revisit the numerical implementation by redesigning the algorithms and introducing efficient data structures that reduce the expected complexity from quadratic to linear. Moreover, we develop and optimize parallel implementations of the algorithms on both central and graphics processing units (CPU/GPU) achieving speed-ups up to two orders of magnitude on the GPU. Our simulations are consistent with the general behavior observed in the folding process in aqueous solvent, confirming the effectiveness of model improvements. We report on the folding process at multiple levels; namely, the formation of secondary structural elements and tertiary interactions between secondary elements or across larger domains. We also observe significant enhancements in running times that make the folding simulation tractable for large molecules.