We propose a Mixed Integer Partial Differential Equation Constrained Optimization (MIPDECO) formulation of the topological optimization for electromagnetic cloaking. Our formulation introduces binary variables to indicate the presence/absence of metamaterial at a given location within the cloaking device. The cloaking device is discretized on a 20x20 and 40x40 domain of squared material locations, and has two to…

The issue of parameter identifiability is a pervasive one in determining model parameters from data, specifically in trying to answer whether unique parameter estimation is possible for a given problem. Many related definitions of identifiability with subtle distinctions can be found in existing literature, and in this talk, we highlight some of the most utilized…

Accurate simulations of neutron transport within nuclear reactors are an important component in developing safe and efficient reactors and operation protocols. However, high-fidelity simulations of an entire core are often too costly for use in multi-query applications, such as multi-physics coupling, uncertainty quantification, or optimal experimental design. To facilitate efficient simulations, we utilize a simulation…

Variance-based global sensitivity analysis (GSA) provides useful measures, Sobol' indices, of how important individual input variables are to the output of a mathematical model. Traditional estimation of Sobol' indices by Monte Carlo methods can be unfeasible for models which are computationally expensive to evaluate. An appealing approach is to instead use a surrogate whose Sobol'…

We consider an optimal control problem subject to a poro-visco-elastic model with applications to fluid flows through biological tissues. Our goal is to optimize the fluid pressure and solid displacement using distributed or boundary control. We discuss an application of this problem to a tissue in the human eye. Previous literature on well- posedness of…

Many computational problems depend on solving systems of linear equations. The Conjugate Gradient method (CG) is a widely used iterative method that solves systems of linear equations. Early termination of CG sacrifices accuracy to save computational resources. The Bayesian Conjugate Gradient method (BayesCG) is a probabilistic generalization of CG that solves systems of linear equations…

Many inference problems relate to the dynamical system, x'=f(x). One primary problem in applications is that of system identification, i.e., how should the user accurately and efficiently identify the model f(x), including its functional family or parameter values, from discrete time-series data? One of the most successful algorithms to this end is the Sparse Identification of…

In a Take-Away Game on hypergraphs, two players take turns to remove the vertices and the hyperedges of the hypergraphs. In each turn, a player must remove either only one vertex or only one hyperedge. When a player chooses to remove one vertex, all of the hyperedges that contain the chosen vertex are also removed.…

A significant challenge in the development of drugs to treat central nervous system (CNS) disorders is to attain sufficient delivery of antibodies across blood-brain barriers (BBB). Since not all antibodies can pass through BBB, it is crucial to understand antibody exposure in the CNS quantitatively to construct drug characteristics and identify proper dosing regimens. We…

Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models. A well-known Achilles' heel of this approach is its computational cost which often renders it unfeasible in practice. An appealing alternative is to analyze instead the sensitivity of a surrogate model with the goal of lowering computational costs while…

Galerkin reduced-order models (ROMs) approximate computational fluid simulations by reducing snapshot data to a basis of proper orthogonal decomposition (POD) modes and solving for modal coefficients with ordinary differential equations. Galerkin ROMs reduce computational cost and can approximate flows with alternate Reynolds numbers, while parametric reduced order models allow adjustment of other system parameters. However,…

Given the inability to directly observe the conditions of a fault line, inversion of parameters describing them has been a subject of practical interest for the past couple of decades. To resolve this under a linear elasticity forward model, we consider Bayesian inference in the infinite dimensional setting given some surface displacement measurements, resulting in…

If you are interested in learning more about applied math research from your fellow students, or you want a friendly and constructive environment to practice presenting your own applied math research, AMGSS is for you! This is an informational and sign-up meeting, so come to learn more about AMGSS and/or to sign up to present…

In this talk we develop a method for efficient computation of reduced-order nonlinear solutions (RONS). RONS is a framework to create reduced-order models for time-dependent partial differential equations (PDEs) where the reduced-order solution has nonlinear dependence on time-varying parameters. With RONS we obtain an explicit set of ordinary differential equations (ODEs) to evolve the parameters.…

We consider sensitivity analysis of Bayesian inverse problems with respect to modeling uncertainties. To this end, we consider sensitivity analysis of the information gain, as measured by the Kullback-Leibler divergence from the posterior to the prior. This choice provides a principled approach that leverages key structures within the Bayesian inverse problem. Also, the information gain…

Extreme events are events that have an extremely low probability of occurring, but often have immense consequences. For this presentation, we focus on extreme events in climate change and wildfires. In the context of climate change, we examine the avoidance of so-called climate tipping points, which are climate regimes where small changes significantly alter the…

Zombies are popularly presented in media as resulting from an infectious outbreak. Various modeling assumptions for zombification as an infectious disease are discussed. Populations during the outbreak are then modeled with infectious disease compartment models accounting for various effects such as latent infectious populations, quarantining, etc. Equilibrium and stability conditions for these dynamics are determined,…

Talk 1: Low-cost Quantification of Fluid Flow Parameter Sensitivity using Reduced-order Modeling - Abstract 1: Sensitivity analysis for computational fluid dynamics (CFD) simulations is a complicated procedure, which still relies, in many cases, on engineering judgment and factors of safety. This is, in part, because the computational cost of quantifying the simulation's sensitivity to all…

- Presenter: William Anderson - Title: Fast and Scalable Computation of Reduced-Order Nonlinear Solutions for PDEs - Abstract: We develop a method for fast and scalable computation of reduced-order nonlinear solutions (RONS). RONS is a framework to build reduced-order models for time-dependent partial differential equations (PDEs), where the reduced-order solution depends nonlinearly on time-varying parameters. With…

Of primary importance in computational science and applications is quantification and improvement of predictive capabilities of large-scale parameterized models, which often require the use of multi-query techniques that are intractable for computationally expensive models. This research focuses on three primary thrusts: sensitivity analysis, reduced-order modeling, and uncertainty quantification and algorithm and implementation choices that scale favorably…