This page contains a list of seminars that I am co-organizing within the Department of Computer Science and Department of Applied Mathematics
at CU Boulder. For a list of seminars that I gave, please see my CV.

This series of talks aims at encouraging networking among postdocs and promoting the exchange of ideas for potential collaborations.
We have started this series of relatively informal seminars where the postdocs from the two Departments, and occasionally from other local universities,
can showcase their research and foster relationships and collaborations between the two Departments and other universities.

**Please note:** These seminars are given by postdocs, but are intended for all types of audience (students are welcome!).

**APPM + CS Postdoc Seminar:**

**Fri. Feb. 15, 2019:**

**Time:**10:30 am

**Location:**ECCR 257 (Newton's Lab)

**Speaker: Valeria Barra**, Department of Computer Science, CU Boulder

**Title:**

*Efficient representation of high-order finite element operators*

**Abstract:**We present an extensible low-level library that provides a versatile algebraic interface and optimized implementations suitable for high-order operators: libCEED. This library aims to overcome the challenges in high-order methods that use global sparse matrices as operator representations. In fact, one of the challenges with high-order methods is that a global sparse matrix is no longer a good representation of a high-order operator, both with respect to the FLOPs needed for its evaluation, as well as the memory transfer needed for simple matrix-vector multiplies. Thus, high-order methods require a new "format" that represents a linear (or more generally non-linear) operator, not associated with a sparse matrix. The goal of libCEED is to propose such a format, as well as supporting implementations and data structures, that enable efficient operator evaluation and composition, on a variety of computational device types (CPUs, GPUs, etc.) and enables portable performance through nearly optimal memory transfers and FLOPs for operator evaluation. We investigate operator composition and design of coupled solvers in the context of atmospheric modeling, providing examples of the usage of libCEED with PETSc. We will show examples of solutions of the advection equation and the full compressible Navier-Stokes equations, to investigate the dynamics of density currents in the stratified atmosphere.

For the remainder of the talk, I am going to show some of my past research in the field of Computational Fluid Dynamics, regarding numerical simulations of the dynamics of free-boundary/interfacial flows of thin viscoelastic liquid films and membranes of Maxwell and Jeffreys type.

**Fri. Feb. 1, 2019:**

**Time:**11 am

**Location:**ECOT 831

**Speaker: Tahra Lucene Eissa**, Department of Applied Mathematics, CU Boulder

**Title:**

*Interactions between hierarchical decision-making processes in dynamic environments*

**Abstract:**In a constantly changing world, accurate decisions require flexible evidence accumulation where old information is discounted at a rate adapted to the frequency of environmental changes. However, sometimes humans and other animals must simultaneously infer the state of the environment and its volatility (hazard rate). To probe how these estimates impact one another when performed hierarchically, we develop and analyze a model of an ideal observer who makes noisy measurements of a two-state environment with an initially unknown hazard rate that is either high (changes happen often) or low (changes are rare). Using log-likelihood ratios of the state and hazard rate to represent the observer’s beliefs about the environment, we track how the observer’s estimates evolve over time. We find that the accuracy of the hazard rate estimate builds up slowly, with information at change points (CPs) providing evidence for a high hazard rate and the time between CPs suggesting the hazard rate is low. In contrast, state estimation accuracy drops immediately after CPs when the observer has yet to track the change and recovers at a rate dependent on the observer’s estimated hazard rate. Quantifying this recovery rate, we find that there is a tradeoff between recovery speed and overall state accuracy and that the speed of post-CP recovery changes with trial duration as the observer becomes more confident about their hazard rate estimate. We then compare our model that includes hazard rate inference to results from a normative model with a known hazard rate to assess how hierarchical inference processes impact state belief. We analyze the normative model using a set of nonlinear partial differential equations (PDEs), leading to faster and more accurate estimates than sampling methods. Comparing our model to this gold standard for state inference, we find that our model’s state inference improves over trial duration to match normative models as the hazard rate is learned. Thus, our setup can be used to identify situations that utilize hierarchical inference strategies and improve dynamic decision-making task design.

**Fri. Jan. 18, 2019:**

**Time:**11 am

**Location:**ECOT 831

**Speaker: Olena Burkovska**, Florida State University, Visiting Scholar at the Department of Applied Mathematics, CU Boulder

**Title:**

*Approximation of parametrized kernels arising in nonlocal and fractional Laplace models*

**Abstract:**We consider parametrized linear and obstacle problems driven by a spatially nonlocal integral operator. These problems have a broad impact on current developments in different fields such as, e.g., peridynamics, contact mechanics, and finance. We focus on integral kernels with nonlocal interactions limited to a ball of radius greater than 0 or (truncated) fractional Laplace kernels, which are also parametrized by the fractional power s ∈ (0,1). Compared to the fractional problems with infinite horizon of interaction, these type of problems are of independent interest, since they form a connection between purely nonlocal and classical local PDE problems. Our goal is to provide an efficient and reliable approximation of the solution for different values of the kernel parameters. To reduce the high computational cost associated with multi-query solution evaluations, we employ the reduced basis method (RBM) as a parametric model order reduction approach. A major difficulty in the construction of the method arises in the non-affinity of the integral kernel w.r.t. the parameters, which can not be directly treated by empirical interpolation due to the singularity and a lack of continuity of the kernel. This substantially affects the efficiency of the RBM. As a remedy, we propose suitable approximations of the kernel, based on the parametric regularity of the bilinear form and the improved spatial regularity of the solution. The results we provide are of independent interest for other approximation techniques and applications such as, e.g., optimization or parameter identification. Finally, we certify the RBM by providing reliable a posteriori error estimators and support the theoretical findings by numerical experiments.

**Fri. Dec. 14, 2018:**

**Time:**1 pm

**Location:**ECOT 831

**Speaker: Jeffrey Hokanson**, Department of Computer Science, CU Boulder

**Title:**

*H2-optimal Model Order Reduction Using Projected Nonlinear Least Squares*

**Abstract:**In many applications throughout science and engineering, model reduction plays an important role replacing expensive large-scale linear dynamical systems by inexpensive reduced order models that capture key features of the original, full order model. One approach to model reduction is to find reduced order models that are locally optimal approximations in the H2 norm, an approach taken by the Iterative Rational Krylov Algorithm (IRKA) and several others. Here we introduce a new approach for H2-optimal model reduction using the projected nonlinear least squares framework. At each iteration, we project the H2 optimization problem onto a finite-dimensional subspace yielding a weighted least rational approximation problem. Subsequent iterations append this subspace such that the least squares rational approximant asymptotically satisfies the first order necessary conditions of the original, H2 optimization problem. This enables us to build reduced order models with similar error in the H2 norm as competing methods but using far fewer evaluations of the expensive, full order model. Moreover our new algorithm only requires access to the transfer function of the full order model, unlike IRKA which requires a state-space representation or TF-IRKA which requires both the transfer function and its derivative. This application of projected nonlinear least squares to the H2-optimal model reduction problem suggests extensions of this approach related model reduction problems.

**Fri. Nov. 30, 2018:**

**Time:**1 pm

**Location:**ECOT 831

**Speaker: Tahra Lucene Eissa**, Department of Applied Mathematics, CU Boulder

**Title:**

*Spatiotemporal Dynamics of Neocortical Seizure Activity*

**Abstract:**Seizures are defined as sudden, abnormal electrical disturbances in the brain. Patients diagnosed with epilepsy have chronic, recurrent seizures and often require clinical intervention to prevent these episodes. Unfortunately, a large portion of epilepsy patients do not respond to current treatment options, in part due to a lack of understanding on how seizures develop in the brain. This talk will discuss some of the complex dynamics associated with seizure activity and how these dynamics can educate epilepsy treatment. Using a combination of human electrical recordings, biological experiments and computational modeling, we studied the dynamics of seizures at various spatial scales, ranging from a single neuron up to large neuronal networks (centimeter scale). At each scale, we analyzed the interactions between the seizure-producing neurons and the surrounding tissue to determine how the interactions can define a seizure's trajectory and the activity observed clinically. The findings were then used to identify representative electrical markers that could be applied to clinical treatment.

**Fri. Nov. 16, 2018:**

**Time:**1 pm

**Location:**ECOT 831

**Speaker: Giacomo Capodaglio**, Florida State University, Visiting Scholar at the Department of Applied Mathematics, CU Boulder

**Title:**

*Approximation of probability density functions for SPDEs using truncated series expansions*

**Abstract:**The probability density function (PDF) of a random variable associated with the solution of a stochastic partial differential equation (SPDE) is approximated using a truncated series expansion. The SPDE is solved using two stochastic finite element (SFEM) methods, Monte Carlo sampling and the stochastic Galerkin method with global polynomials. The random variable is a functional of the solution of the SPDE, such as the average over the physical domain. The truncated series are obtained considering a finite number of terms in the Gram-Charlier (GC) or Edgeworth (ED) series expansions. These expansions approximate the PDF of a random variable in terms of another PDF, and involve coefficients that are functions of the known cumulants of the random variable. While the GC and ED series have been employed in a variety of fields such as chemistry, astrophysics and finance, their use in the framework of SPDEs has not yet been explored. This is a joint work with Max Gunzburger and Henry P. Wynn.