Nonlinear and Large Deformation Formulations of the Parametric HFGMC Micromechanics for Soft and Hard Tissues
Rami Haj-Ali
The Nathan Cummings Chair in Mechanics
Faculty of Engineering, Tel-Aviv University, Israel, rami98@tau.ac.il

The parametric high fidelity generalized method of cells (HFGMC) micromechanical framework is presented for the three-dimensional (3D) modeling of multi-phase heterogeneous materials.   Nonlinear and strain-softening constitutive modeling along with large deformation formulations will be discussed and shown to be effective in simulating both damage in aerospace composites and mechanical behavior of soft or hard tissues.  In the framework of HFGMC, the multi-phase heterogeneous composite (e.g. tissue) is assumed to possess a periodic microstructure.  The detailed interactions between the constituents are explicitly accounted for. For the case of multiphase soft tissue, the constituents are considered to be hyperelastic, and the overall behavior of the composite tissue is established along with the field distributions within the constituents. For hard bone tissue, the HFGMC-based multiscale micromechanical model is employed for predicting the overall effective and damage mechanical behavior of vertebral trabecular bones (VTBs). Thus, the hierarchical VTB micromodeling is composed of three-levels: two 3D-HFGMC analyses as well as the 3D-sublaminate-model.  At the nano-scale level, the 3D-HFGMC method is applied to obtain the effective properties representing the mineral collagen fibrils composite. Next, at the sub-micron scale level, the 3D sublaminate-model is used to generate the effective properties of a repeated stack of multi-layered lamellae demonstrating the nature of the trabeculae (bone-wall). Thirdly, at the micron-scale level, the 3D-HFGMC method is used again on a representative unit-cell of the highly porous VTB microstructure. The soft HFGMC tissue model is calibrated using available experimental data of artery layers.  The results from this model are also compared to the well-known anisotropic constitutive model proposed by Holzapfel and coworkers.  Similarly, the hard-tissue HFGMC model is applied for VTB microstructures taken from micro-computed tomography (μCT) scans. The predicted overall anisotropic properties for native VTBs are examined and compared with reported values of moduli found in the literature.  In conclusion, the HFGMC is shown to be an effective and viable micromechanical modeling approach for a wide range of soft and hard tissues.

Bio-Sketch

Rami Haj-Ali is the Nathan Cummings Professor of Mechanics at Tel-Aviv University.  He received his BSc-ME from the Technion, MSc from Tel-Aviv University (TAU), and Ph.D. from the University of Illinois at Urbana-Champaign (UIUC) in 1996.  He was an Assistant, Associate and Full Professor at Georgia Institute of Technology (Georgia Tech) from 1997-2010 and from 2008-current as a Full Professor in Mechanical Engineering at Tel-Aviv University.  Dr. Haj-Ali has published over 150 research papers and technical reports, and over 75 refereed archival publications. His research interests include: Nonlinear and damage modeling of composite materials and structures, Micromechanics, Computational Mechanics, Bio-materials, and Biomechanics of Aortic Valves (AVs). His research attracted support from several competitive and industrial sponsors, including the US National Science Foundation (NSF), Israel Ministry of Science (MOST), German-Israel Foundation (GIF), European Union (EU-FP7), NASA, Lockheed Martin, Rafael, IMI, Edwards Lifesciences Co., among others. He has won numerous awards, including the Chester P. Siess Award for outstanding PhD and research, University of Illinois at Urbana-Champaign (1997), the National Science Foundation (NSF-USA) CAREER award (1999), the Maof Fellow from PBC-Kahanoff Foundation (2008) and the Marie Curie Fellow from the EU-IRG-FP7 (2009), and the Nathan Cummings Endowed Chair of Mechanics at TAU (2016).

ההרצאה תתקיים ביום ראשון 31.12.17, בשעה 14:00
בחדר 315, הבניין הרב תחומי, אוניברסיטת תל אביב

(The talk will be given in English)

Speaker:     Dr. Amichai Paisky
                   Massachusetts Institute of Technology

Monday, December 25^th, 2017
15:00 - 16:00

Room 011, Kitot Bldg., Faculty of Engineering

Universal Loss and Gaussian Learning Bounds

Abstract

In this talk I address two fundamental predictive modeling problems: choosing a universal loss function, and how to approach non-linear learning problems with linear means.

A loss function quantifies the difference between the true values and the estimated fits, for a given instance of data. Different loss functions correspond to a variety of merits, and the choice of a "correct" loss could sometimes be questionable. Here, I show that for binary classification problems, the Bernoulli log-likelihood loss (log-loss) is universal with respect to practical alternatives. In other words, I show that by minimizing the log-loss we minimize an upper bound to any smooth, convex and unbiased binary loss function. This property justifies the broad use of log-loss in regression, in decision trees, as an InfoMax criterion (cross-entropy minimization) and in many other applications.

I then address a Gaussian representation problem which utilizes the log-loss. In this problem we look for an embedding of an arbitrary data which maximizes its "Gaussian part" while preserving the original dependence between the variables and the target. This embedding provides an efficient (and practical) representation as it allows us to consider the favorable properties of a Gaussian distribution. I introduce different methods and show that the optimal Gaussian embedding is governed by the non-linear canonical correlations of the data. This result provides a primary limit for our ability to Gaussianize arbitrary data-sets and solve complex problems by linear means.

Bio
Amichai Painsky is a Post-Doctoral Fellow, co-affiliated with the Israeli Center for Research Excellence in Algorithms (I-CORE ALGO) at the Hebrew University, and the Signals, Information and Algorithms (SIA) Laboratory at MIT. Amichai received his B.Sc. in Electrical Engineering from Tel Aviv University (2007), his M.Eng. in Electrical Engineering from Princeton University (2009) and his Ph.D. in Statistics from Tel Aviv University (2016). He is a recipient an outstanding Ph.D. students award from the school of Mathematical Sciences, the Weinstein Institute of Signal Processing and the Marejn Foundation. Previously, he received a Brain Return Ph.D. Scholarship from the Israeli Center for Returning Scientists.

(The talk will be given in English)

Speaker:     Dr. Roi Livni
                   Department of Computer Science, Princeton University

Wednesday, December 20^th, 2017
15:00 - 16:00

Room 011, Kitot Bldg., Faculty of Engineering

Overcoming Intractability in Learning

Abstract

Machine learning has recently been revolutionized by the introduction of Deep Neural Networks. However, from a theoretical viewpoint these methods are still poorly understood. Indeed the key challenge in Machine Learning today is to derive rigorous results for optimization and generalization in deep learning. In this talk I will present several tractable approaches to training neural networks. At the second part I will discuss a new sequential algorithm for decision making that can take into account metric structure in the action space and avoids erratic behavior which often makes MAB algorithm impractical.

I will present our work that provides some of the first positive results and yield new, provably efficient, and practical algorithms for training certain types of neural networks. In a second work I will present a new online algorithm that learns by sequentially sampling random networks and asymptotically converges, in performance, to the optimal network. Our approach improves on previous random features based learning in terms of sample/computational complexity, and expressiveness. In a more recent work we take a different perspective on this problem. I will provide sufficient conditions that guarantee tractable learning, using the notion of refutation complexity. I will then discuss how this new idea can lead to new interesting generalization bounds that can potentially explain generalization in settings that are not always captured by classical theory.

In the setting of reinforcement learning I will present a recently developed new algorithm for decision making in a metrical action space. As an application, we consider a dynamic pricing problem in which a seller is faced with a stream of patient buyers. Existing MAB algorithms often ignore the structure in the action space, and they are led to an erratic behavior that leads to sub-optimal regret in face of a strategic environment. Our algorithm achieves an optimal regret, and improves on previously known regret bound.

Bio
Roi Livni is a research instructor at the computer science department in Princeton University. He is a recipient of the Eric and Wendy Schmidt fellowship for strategic innovation, and a Yad Hanadiv fellow for postdoctoral position.
He completed his PhD at the Hebrew University, during which he was a recipient of a Google Europe fellowship in learning theory. He also served, during his graduate studies, as a long term intern at Microsoft Research. His graduate work won a Best paper award in ICML'13, and a best student paper award in COLT'13.

School of Mechanical Engineering Seminar
Monday, January 8, 2018 at 14:00
Wolfson Building of Mechanical Engineering, Room 206

Suspension-Colloidal Transport in Porous Media: Petroleum and Environmental Applications

Prof. Pavel Bedrikovetsky

Australian School of Petroleum

University of Adelaide

Flow of suspensions and colloids in porous media with particle capture, detachment and consequent permeability alteration occurs in aquifers and subterranean basins during exploitation of artesian wells, disposal of industrial wastes in aquifers and consequent contamination, fresh and hot water storage in aquifers and geothermal reservoirs, ocean water invasion into aquifers, industrial filtering, as well as exploitation of oil and gas production and injection wells.

We discuss the particulate transport in rocks with fines attachment and detachment accounting for particle- and pore size distributions. The basic equations form a stochastic population-balance system. The system can be upscaled in the cases of mono-sized particles and of small-concentrations. 1D linear and axi-symmetric problems for suspension injection or detachment of natural reservoir fines allow for exact solutions. The solutions allow analysing the propagation of concentration waves of injected colloids or lifted suspensions, its effects on well injectivity and productivity. The exact solutions allow also for downscaling, i.e. restauration of the micro-scale behaviour. Another application of the exact solutions is regularisation of inverse problems, allowing interpreting laboratory experiments and tuning the model parameters. We show simple lab and field devices for complete characterisation of suspension-colloidal system and lab-based reservoir-scale predictions.

The talk is completed by exploration of random-walk and Boltzmann’s models, and of two-phase suspension-colloidal transport.

Bio: Pavel is a Professor of Petroleum Engineering at the University of Adelaide. His research covers suspension and multiphase transport in porous media, including exact integration, upscaling, inverse problems, and technologies of enhanced gas and oil recovery. He authors a seminal book on reservoir engineering and 230 papers in academic journals and Society of Petroleum Engineers (SPE). He is 2008-2009 and 2016-2017 SPE Distinguished Lecturer.