Abstract: There is currently a considerable spread in climate models regarding their outputs. This study analyzes the impact of soil parameters in the Community Land Model version 5 (CLM5) in simulating soil moisture across the Continental United States (CONUS) region using Empirical Orthogonal Function (EOF) and Self-Organizing Maps (SOM) analysis. We seek to understand the complex relationship between soil properties and moisture dynamics in the CONUS. Through EOF and SOM, the study identifies and categorizes distinct patterns in soil moisture, focusing on the influence of soil texture and hydraulic properties.

Abstract: In recent years, there has been a ton of hype around Deep Learning and Deep Neural Networks and it is hard to separate the buzz from the science. In my talk, I will explain how DNNs for unstructured data can be viewed as a fairly straightforward extension of classical methods such as logistic regression. As time allows, I will also discuss how these methods can be adapted to account for the intrinsic structure of the data in various settings such as graphs and images.

Abstract: Hyper dual numbers are generalized complex numbers consisting of one real part and three non-real parts. Hyper dual numbers allow us to easily extract exact first and second derivatives of a function when evaluated at a hyper dual number. This can be extended to the multivariable setting as well. In this project, we use a hyper dual class written in python to extract the first and second partial derivatives of parametric surface functions evaluated at hyper dual numbers. We then use those partial derivatives to compute the mean and Gaussian curvature at each point on a Dupin cyclide and then plot the surface, coloring it according to these curvature values. 

Abstract: In this talk, I will explore the pivotal role of cloud microphysics in governing Earth’s energy equilibrium and precipitation dynamics. I will discuss the difficulties associated with microphysics parameterization schemes, particularly emphasizing bulk and bin schemes. Besides that, I will compare the sensitivity of the weather research and forecasting model (WRF) subject to four microphysics schemes against ground-based measurement and satellite imagery in estimating snow height and snow water equivalent (SWE) in the Boise region.

Abstract: Recommending movies is an important part of any streaming service. In this talk, I will describe why and how to measure the similarity between two movies using their synopsis and metrics such as Cosine similarity and Jaccard similarity. Then I will describe how I made a database of the similarities between all movies in a real-world dataset and how I interacted with the database to obtain the 10 movies that are most similar to a given movie. I will also describe the distribution of similarity metrics for all of my data and specific movies within a genre such as horror or action.  

Abstract: Recently, numerical experiments demonstrated the remarkable efficiency of using deep neural networks to solve high-dimensional parametric partial differential equations (PDEs) in various contexts such as control and optimization problems, inverse problems, risk assessment, and uncertainty quantification, etc. In this talk, we will discuss how problems that involve PDEs can be solved using deep neural networks. 

Abstract: The Generalized Poisson's equation (GPe) arises when we model, in the Density Functional Theory (DFT) sense, the relationship between the electrostatic potential and charge density in wet environments.  In this talk, we present the approach to solving the  (GPe)  within the framework of DFT using the Immersed Interface Method. We demonstrate the effectiveness of this technique in handling complex material boundaries, interfaces, and irregular geometries, which are often encountered in real-world DFT simulations. This talk will give a general idea of how the GPe comes into play, a general introduction to the IIM method, how the correction term is formulated, and how it affects the accuracy of the numerical solution. 

Abstract: The transport equation models the concentration of a substance and we use it in a preliminary study of wildfire smoke transport.  Although the transport equation forms a strong foundation for estimating PM2.5 concentrations, numerous unknowns are associated with wildfire emissions. Therefore, we assume the model is inexact and employ the weak constraint 4D-Var data assimilation to estimate the time-evolving state. State estimates can vary significantly depending on the choice of data and model error variances. Rather than use heuristics to estimate prior errors, we use regularization methods, such as the chi-square method and the L-curve, to specify error covariances.  We will show 4D-Var results from the one- and two-dimensional transport equation. 

Abstract: We estimate PM2.5 concentrations from wildfire smoke by simulating the regional transport of wildfire smoke in the atmosphere. However, the transport processes are marred by errors attributed to parameterization and limited fundamental physics. We overcome this complexity by integrating error terms into model dynamics, observational data, and initial conditions. As a result, a cost functional associated with the errors evolves, leading to a system of coupled Euler-Lagrange (E-L) equations via the calculus of variations. The decomposition of the E-L system gives rise to two equations: a forward equation and a backward (adjoint)  equation. The adjoint solution obtained by integrating backward in time is used in the forward problem, which makes use of representer functions to yield PM2.5 estimates that match observations in an optimal sense. The representer functions are responses to unit impulses in space and time.  To efficiently and accurately solve for the representer functions, we use dynamic adaptive mesh refinement, available in our computational model Smoke3d.  In this talk, we will describe how we use Smoke3d to solve for the representer functions. In particular, we discuss the representation of numerical Dirac delta functions and resulting accuracy.  

Abstract: In this talk, we will present GeoFlood, a new open-source software package for solving shallow water equations (SWE) on a mapped, logically Cartesian grid managed by the parallel, adaptive library ForestClaw (Calhoun and Burstedde, 2017). The GeoFlood model is validated using standard benchmark tests from Néelz and Pender (2013) and against George (2011) results obtained from the GeoClaw software (Clawpack Development Team, 2020) for the historical Malpasset dam break problem.  The benchmark test results are compared against GeoClaw and a standard software HEC-RAS (Hydraulic Engineering Center - River Analysis System) results (Brunner, 2018). This comparison demonstrates the capability of GeoFlood to accurately and efficiently predict flood wave propagation on complex terrain. The results from comparisons with the Malpasset dam break show good agreement with the GeoClaw results and are consistent with the historical records of the event. 

Abstract: The separation of fast (barotropic) and slow (baroclinic) motions into subsystems through barotropic-baroclinic splitting has been widely adopted in layered ocean circulation models. In numerical modeling, finite difference and volume methods are frequently employed alongside this splitting technique. In this work, I will present an extension of the work in Higdon (2015) to two horizontal directions using an arbitrary high-order nodal discontinuous Galerkin (DG) method for the resulting splitting subsystems derived from layered shallow water equations with a two-level time integration method. The two-level time integration method consists of prediction and correction steps for the barotropic and baroclinic subsystems, allowing different time steps for the two subsystems, each satisfying their respective CFL conditions for numerical stability. Furthermore, any numerical inconsistencies arising from the discretization due to the splitting are addressed through a reconciliation process involving carefully computed flux deficits. Numerical tests are carried out to demonstrate the model’s performance of the proposed schemes.

Abstract: In this talk I will start with fundamental conservation laws and derive the Navier Stokes equations which govern the dynamics of fluids in motion. I will then introduce a number of simplifications often used in modeling and discuss incompressible flows, shallow water equations and hydrostatic equations. I will illustrate the talk with simulation results. 

Abstract: Tensor rank is an important question in various areas of science and mathematics. I will describe some simple applications motivated by statistics. Then, I will describe some of my research on ranks for symmetric tensors. Symmetric tensors are equivalent to polynomials, and can be studied using algebraic geometry.  

Abstract: This will be an interactive discussion, with audience participation, on the analytical and numerical techniques for solving a classic problem of potato bug pursuit (Part 2).

Abstract: This will be an interactive discussion, with audience participation, on the analytical and numerical techniques for solving a classic problem of potato bug pursuit (Part 1).