Monolithic matrix-free solver for fluid-structure interaction problems.

We are excited to announce the KAUST Research Conference on Flow simulation at the exascale: Opportunities, challenges, and its application in the industry, which will be held on March 28 – March 30, 2022 (#ExaCFDKAUST). The conference aims to bring together experts in flow simulation, computational mathematics, and high-performance computing. The goal is to define a research agenda and path forward that will enable scientists and engineers to continually leverage, engage, and direct advances in computational systems on the path to exascale computing and beyond. The conference will give space for presentations and discussions of computational fluid dynamics. As part of this event, we are accepting poster abstract submissions. The poster should present high-quality research contributions describing original and unpublished results of conceptual, constructive, empirical, experimental, or theoretical work in all areas of Computational Fluid Dynamics. For more information please visit the conference website.

Abstract

In this talk we will present two classes of regression models.

A standard way to move particles in a SMC sampler is to apply several steps of a MCMC (Markov chain Monte Carlo) kernel. Unfortunately, it is not clear how many steps need to be performed for optimal performance. In addition, the output of the intermediate steps are discarded and thus wasted somehow. We propose a new, waste-free SMC algorithm which uses the outputs of all these intermediate MCMC steps as particles. We establish that its output is consistent and asymptotically normal. We use the expression of the asymptotic variance to develop various insights on how to implement the algorithm in practice. We develop in particular a method to estimate, from a single run of the algorithm, the asymptotic variance of any particle estimate. We show empirically, through a range of numerical examples, that waste-free SMC tends to outperform standard SMC samplers, and especially so in situations where the mixing of the considered MCMC kernels decrease across iterations (as in tempering or rare event problems).

With the algorithm's suitability for exploiting current petascale and next-generation exascale supercomputers, stable and structure-preserving properties are necessary to develop predictive computational tools. This dissertation uses the mimetic properties of SBP-SAT operators and the structure-preserving property of a new relaxation procedure for Runge--Kutta schemes to construct nonlinearly stable full discretizations for non-reactive compressible computational fluid dynamics (CFD) and reaction-diffusion models.

The Maxwell-Stefan system is a system of equations commonly used to describe diffusion processes of multi-component systems. In this talk (i) I will describe modeling of multi-component systems, which leads to extensions of the Euler compressible dynamics system with mass and thermal diffusion. (ii) Will describe how the Maxwell-Stefan system emerges in the high-friction limit of multi-component Euler flows. (iii) Discuss some mathematical questions that this model raises and on the construction of numerical schemes for the Maxwell-Stefan system associated with the minimization of frictional dissipation.

I will present some recent work in collaboration with Elisa Davoli (TU Wien) and Katerina Nik (University of Vienna) on a three-dimensional quasistatic morpholelastic model. The mechanical response of the body and its growth are modeled by the interplay of hyperelastic energy minimization and growth dynamics. An existence result is obtained by regularization and time-discretization, also taking advantage of an exponential-update scheme. Then, we allow the growth dynamics to depend on an additional scalar field describing a nutrient, and formulate an optimal control problem. Eventually, we tackle the existence of coupled morphoelastic and nutrient solutions, when the latter is allowed to diffuse and interact with the growing body. The preprint is available as arXiv:2110.05566.

In recent years, machine learning has proven to be efficient in solving various physical problems through data-driven approaches. For example, in wave physics, models based on analytical and numerical schemes employ intensive trial-and-error tuning of material (and geometrical) parameters for 'on demand' wave properties, which require deep understanding of the physics and are computationally expensive.  As a result, it is desired to develop intelligent models that learn the bidirectional mapping between different physical quantities and automate technological device design. In this presentation, I will discuss novel generative models for forward and inverse predictions that outperform human performance. In particular, I will show how machine learning can be used to design broadband acoustic cloaks, unidirectional non-Hermitian structures, and for solving the inverse scattering problem of shape recognition.

This talk focuses on a 'particle MCMC' method known as the conditional particle filter (CPF), or the particle Gibbs. The CPF is a slight algorithmic variant of the original particle filter, but serves a different purpose: it defines an MCMC transition targeting the HMM smoothing distribution. The empirical evidence suggests that certain variants of the CPF mix well even in high dimensions (with long observation records). We review some theoretical insights that consolidate such empirical findings, and justify why the CPF is often efficient for HMM inference.

Dynamic programming is an efficient technique to solve optimization problems. It is based on decomposing the initial problem into simpler ones and solving these sub-problems beginning from the simplest ones. A conventional dynamic programming algorithm returns an optimal object from a given set of objects. We developed extensions of dynamic programming which allow us (i) to describe the set of objects under consideration, (ii) to perform a multi-stage optimization of objects relative to different criteria, (iii) to count the number of optimal objects, (iv) to find the set of Pareto optimal points for the bi-criteria optimization problem, and (v) to study the relationships between two criteria. The considered applications include optimization of decision trees and decision rule systems as algorithms for problem-solving, as ways for knowledge representation, and as classifiers, optimization of element partition trees for rectangular meshes which are used in finite element methods for solving PDEs, and multi-stage optimization for such classic combinatorial optimization problems as matrix chain multiplication, binary search trees, global sequence alignment, and shortest paths.

Models of physical phenomena include important qualitative properties, and any useful approximate solution of the model must respect these properties. Such properties include conservation or dissipation of energy, as well as positivity of quantities like mass, probability, or concentration.  Preservation of these properties in computationally affordable numerical solutions of complex physical models remains a major challenge today. I will describe some recent advances in numerical methods for general dynamical systems that enable preservation of system dynamics and of bounds on the state, in the context of high-order accurate and efficient discretizations. The power of these methods will be demonstrated through applications in the area of surface water waves.

Spatially misaligned data are becoming increasingly common due to advances in both data collection and management in a wide range of scientific disciplines including the epidemiological, ecological and environmental fields. Here, we present a Bayesian geostatistical model for fusion of data obtained at point and areal resolutions. The model assumes that underlying all observations there is a spatially continuous variable that can be modeled using a Gaussian random field process.

Terahertz (THz) frequency electromagnetic fields have numerous applications ranging from wireless communications to imaging systems and nondestructive testing, to material characterization. One of the main obstacles in the way of widespread industrial use of THz technologies is the difficulty of implementing compact and frequency-stable THz sources that can operate at room temperatures. Among a variety of possible options, photoconductive devices (PCDs) satisfy these conditions. Indeed, they have become one of the most promising candidates for THz source generation since recent advances in fabrication techniques, such as metasurface integration and nanostructured surface inclusions have significantly increased their optical-to-THz conversion efficiency and made them polarization insensitive.

Biological systems are distinguished by their enormous complexity and variability. That is why mathematical modelling and computational simulation of those systems is very difficult, in particular thinking of detailed models which are based on first principles. The difficulties start with geometric modelling  which needs to extract basic structures from highly complex and variable phenotypes, on the other hand also has to take the statistic variability into account.

It is now fairly common to use Sequential Monte Carlo (SMC) algorithms for normalizing constant estimation of high-dimensional, complex distributions without any particular structure. In order for the algorithm to give reasonable accuracy, it is well known empirically that one must introduce appropriate intermediate distributions that allow the particle system to “gradually evolve” from a simple initial distribution to the complex target distribution, and one must also specify an appropriate number of particles to control the error. Since both the number of intermediate distributions and the number of particles affect the computational cost of the algorithm, it is crucial to study and attempt to minimize the computational cost of the algorithm subject to constraints on the error.

Advances in imaging technology have given neuroscientists unprecedented access to examine various facets of how the brain “works”. Brain activity is complex. A full understanding of brain activity requires careful study of its multi-scale spatial-temporal organization (from neurons to regions of interest; and from transient events to long-term temporal dynamics). Motivated by these challenges, we will explore some characterizations of dependence between components of a multivariate time series and then apply these to the study of brain functional connectivity.  This is potentially interesting for brain scientists because functional brain networks are associated with cognitive function and mental and neurological diseases.

A variational model in the context of the gradient theory for fluid-fluid phase transitions with small scale heterogeneities is studied. In the case where the scale of the small heterogeneities is of the same order of the scale governing the phase transition, the interaction between homogenization and the phase transitions process leads to an anisotropic interfacial energy. Bounds on the homogenized surface tension are established. In addition, a characterization of the large-scale limiting behavior of viscosity solutions to non-degenerate and periodic Eikonal equations in half-spaces is given. This is joint work with Riccardo Cristoferi (Radboud University, The Netherlands), Adrian Hagerty (USA), Cristina Popovici (USA), Rustum Choksi (McGill, Canada), Jessica Lin (McGill, Canada), and Raghavendra Venkatraman (NYU, USA).

Together with the algorithm suitability to exploit current petascale and next-generation exascale supercomputers, robust, accurate, and structure-preserving discretizations are necessary for developing predictive computational tools. The research carried out in the Advanced Numerical Algorithms and Numerical Simulations Laboratory (AANSLab) leverages a multidisciplinary platform that integrates numerical analysis, physics, and high-performance computing. In particular, we focus on the analysis and development of novel numerical methods for ordinary and partial differential equations with provable properties such as nonlinear stability and conservation, and structure-preserving techniques. These properties are critical for designing reliable, efficient, and self-adaptive solvers for complex geometries – an essential cornerstone for next-generation computational frameworks. Current classes of partial differential equations that we are working on are the compressible Navier–Stokes equations, the Eulerian model for compressible heat-conducting flows, and the diffusion-reaction and convection-diffusion-reaction equations for molecular communication. We also use deep learning to complement and speed up the process of solving efficiently large-scale PDE-based problems. In this talk, I will summarize the progress we made in the last five years in the following areas: - Numerical analysis and algorithm development for robust, smart compressible flow solvers. - Development from the ground up of a new scalable hp-adaptive computational fluid dynamics (CFD) framework that places KAUST a few years ahead of the NASA CFD 2030 vision: o Applications and impact in the automotive and aerospace industry. o Improving knowledge of flow physics: Examples in detonation and aeroacoustics. - Advection-reaction-diffusion algorithms for molecular communication. Finally, I'll discuss our translational work to solve industrially relevant flow problems in partnership with Boeing, NASA Langley Research Center, and McLaren F1 Racing Team, and my future research plans.

Abstract

In many research fields such as meteorology, eco

Over 4000 exoplanets - planets beyond the Solar System - have been discovered since the first Nobel prize-winning exoplanet detection around a Sun-like star in 1995. The majority of these exoplanets have been detected by indirect methods, inferring the presence of the exoplanet by observing the star.

Elliptic PDEs are ubiquitous both in Mathematics and in applications of Mathematics. Regularity of generalized solutions is a fundamental issue necessary to handle in proper way if one want to obtain qualitative information about solutions. My goal is to introduce the audience to the topic of regularity for elliptic PDEs under assumptions on the coefficients that are of minimal requirements.

Elliptic PDEs are ubiquitous both in Mathematics and in applications of Mathematics. Regularity of generalized solutions is a fundamental issue necessary to handle in proper way if one want to obtain qualitative information about solutions. My goal is to introduce the audience to the topic of regularity for elliptic PDEs under assumptions on the coefficients that are of minimal requirements.

In this talk an inversion-based control approach is presented for the generation and stabilization of a periodic orbit in a multi-link triple pendulum on a cart. To this end, a nominal trajectory is generated by formulating the posture transition problem as a two-point Boundary Value Problem (BVP) in an input-output representation. For solvability of the BVP, a setup function is introduced such that additional parameters are provided in the differential equation of the internal dynamics. Based on the linearized dynamics about the nominal trajectory, a linear-quadratic-Gaussian controller is implemented to compensate for measurement noise, model uncertainties, and external disturbances. This way we force a triple pendulum to move along a non-trivial periodic orbit and render it attractive. The high performance and accuracy of our approach is illustrated on an experimental setup.

Backward induction, the cornerstone of dynamic game theory, is the classical algorithm applied to solve finite dynamic games with perfect and complete information. While theoretically sound and beautiful in its simplicity, backward induction does not perform so well when it comes to predicting human behavior. The objective of this seminar is twofold. First, we will understand what backward induction is and how to apply it on game-theoretic trees. Second, we will answer the question of whether backward induction is a good model of how people make choices in dynamic interactions.