Department of Mathematical and Statistical Sciences, CU Denver

Join us for Tyler Spears’ MS in Applied Mathematics Project Presentation “Modeling Fire Risk in Hawai'i Using Satellite, Atmospheric and Geographic Data” on Friday December 6, 2024 from 12:30pm-2:30pm in Student Commons Building 4113. Title: Modeling Fire Risk in Hawai'i Using Satellite, Atmospheric and Geographic Data Abstract: Wildfires threaten ecosystems, communities, and property, underscoring the need for accurate predictive models for disaster management. This project develops a Deep Neural Network (DNN) to estimate wildfire occurrence probability by integrating meteorological data, satellite fire detection records, and static environmental features like topography and vegetation classifications. Using data since 2011, the model builds a sample from each satellite pixel, using meteorological, topographical, and fuel conditions as features and fire presence as the label. Temporal aggregation captures historical trends through averaged meteorological features. The DNN optimizes predictions using cross-entropy loss, producing spatial risk maps to support emergency planning and land management. This research highlights machine learning's potential in wildfire prediction, offering a framework for integrating environmental data to mitigate fire risks and address global challenges.

Join us for Paul Guidas’ Undergraduate Honor's Project “A Demonstration of Supercomputer Use Using a Separation-Preserving Clustering Algorithm” on Friday November 22, 2024 from 12:30 pm – 1:30 pm in Student Commons Building 4113 or on Zoom. Email [email protected] for the link. Title: A Demonstration of Supercomputer Use Using a Separation-Preserving Clustering Algorithm Abstract: Supercomputing, also called High Performance Computing (HPC), is becoming increasingly important in mathematical and statistical research. Datasets are larger and more complex than they have ever been and understanding how to work on hardware which can handle this data is becoming a necessary skill in today's world. The Department of Mathematical and Statistical Sciences at the University of Colorado Denver understands this shift towards technology and thus, has a dedicated HPC cluster named Alderaan which students and faculty can request access to. We are interested in educating people on the use of this resource through the alteration of previously written code which was written to demonstrate a clustering algorithm published in 2022. We will show how to alter this code to run on Alderaan and also discuss what to consider when creating or modifying code to run on HPC systems. We will also demonstrate some basic bash scripting which is necessary for us to efficiently parallelize our workload and organize the output. Educating students and researchers on what resources are available, and how to use them, will allow for an increase in both the quantity and quality of mathematical and statistical research that can be done. By performing this research and documenting it in the style of a walk-through, we ease the burden for others who wish to use Alderaan and help to smooth out the steep learning curve often experienced by mathematicians and statisticians when learning how to use technology to improve their workflow.

?? New Paper Alert in Engineering Applications of Artificial Intelligence! Machine learning shows promise in predicting complex system behavior, but using these models for design optimization or inverse problems presents a greater challenge. Inverse problems often have multiple valid solutions, and traditional single-stage surrogate models may struggle to capture this complexity. To overcome this limitation, our new paper introduces a two-stage surrogate modeling framework. This approach enhances exploration of the solution space and safeguards against inaccurate or uncertain results. #AI #machinelearning #engineering #conformalprediction ?? Read the full paper for free until December 7th: https://lnkd.in/g7N4fBpz

Join us for a department seminar, Adam Spiegler on “Broadening Interest in Calculus with Data Science” on Monday January 27, 2025 from 1:00pm - 1:30pm in Student Commons Building 4017 or on Zoom. Email [email protected] for link. Title: Broadening Interest in Calculus with Data Science Abstract: The rapidly growing demand in data science presents an exciting opportunity for math and statistics departments to redesign courses to benefit both traditional math and statistics majors as well as welcome new students from other growing disciplines such as data science. In this talk I will demo a set of newly created Python labs for a first semester calculus course that integrate data and coding as tools to welcome more diversity into our mathematics community and provide students a virtual lab setting to experiment with mathematical concepts. Each lab is an interactive Jupyter notebook that students interact with using Google Colaboratory (Colab) which is free, cloud-based platform where students experiment with Python code to help deepen their understanding of calculus. The materials are open source and freely available to share. Speaker: Adam Spiegler, PhD Department of Mathematical and Statistical Sciences, CU Denver

Join us for a department seminar, Emily Speakman on “Volume Formulae for Mathematical Optimization” on Monday January 27, 2025 from 12:30pm - 1:00pm in Student Commons Building 4017 or Zoom. Email [email protected] for link Title: Volume Formulae for Mathematical Optimization Abstract: The spatial branch-and-bound algorithmic framework, used for solving non-convex mixed-integer nonlinear optimization problems, relies on obtaining quality convex approximations of non-convex substructures in a problem formulation. A common example is the monomial, y = x1x2, . . . , xn, dened over a box [a1, b1] × [a2, b2] × · · · × [an, bn] ? Rn. There are many choices of convex set that could be used to approximate this solution set, with the (polyhedral) convex hull giving the tightest or best possible outer approximation. By computing the volume of the convex hull, we obtain a measure that can be used to evaluate other approximations in comparison. In previous work, we obtained a formula for the volume of the convex hull of the graph of a trilinear monomial (i.e., n = 3) in terms of the 6 (= 2n) box parameters. Here, we seek to extend our work to the case of general n by making additional assumptions on the box domain. In particular, we assume that only k variables have a non-zero lower bound. In this work, we consider k = 1, 2, 3, and conjecture the volume of the convex hull in each case. Moreover, we provide a proof for k = 1. Speaker: Emily Speakman, PhD Department of Mathematical and Statistical Sciences, CU Denver

?? Publication Alert ?? Dr. Troy Butler and co-authors Kirana Bergstrom and Tim Wildey publish A Distributions-Based Approach for Data-Consistent Inversion Kirana O. Bergstrom,?Troy D. Butler, and?Timothy M. Wildey SIAM Journal on Scientific Computing?2024?46:5,?A3124-A3150 https://lnkd.in/gxFiKCAp Abstract: We formulate a novel approach to solve a class of stochastic problems, referred to as data-consistent inverse (DCI) problems, which involve the characterization of a probability measure on the parameters of a computational model whose subsequent push-forward matches an observed probability measure on specified quantities of interest (QoI) typically associated with the outputs from the computational model. Whereas prior DCI solution methodologies focused on either constructing nonparametric estimates of the densities or the probabilities of events associated with the preimage of the QoI map, we develop and analyze a constrained quadratic optimization approach based on estimating push-forward measures using weighted empirical distribution functions. The method proposed here is more suitable for low-data regimes or high-dimensional problems than the density-based method, as well as for problems where the probability measure does not admit a density. Numerical examples are included to demonstrate the performance of the method and to compare with the density-based approach where applicable. ? Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://lnkd.in/gTQdRV-e.

The CU Denver math & stats club invites the CU Denver undergraduate students for a session on "COMAP MCM/ICM competition experience sharing". This will happen on Tuesday November 12th from 5:00pm to 6:00pm in Student Commons Building room 4125. Three previous competitors will share their experience: Shunye Wang, Annie Ha (Annie Huppenthal) and Kyle Cunningham. During the session, (1) you will know more information about the contest! (2) if you haven't formed a team yet, don’t worry, find teammates here! (3) listen to the experience of previous participants to help you better win the competition! Professor Steffen Borgwardt, Julien Langou, and Adam Spiegler will also be present. Pizzas ?? will be served. Remember about the COMAP MCM/ICM competition. The competition lasts 99 straight hours from Thursday January the 23rd 2025 at 3:00pm to Monday January 27th 2025 at 6:00pm. Teams are up to three students. The department will (*) pay registration fees, (*) provide space on the floor of the Student Commons Building for you to work, (*) will provide some meals, and (*) moral support and encouragement and some coaching! More information at: https://lnkd.in/gMnkkw9Z

Join us for Rachel Drummond’s PhD in Applied Mathematics Research Proposal “Algorithmic Exploration of Coreset Creation and other uses of Conformal Prediction with a Focus on Regression Tasks“ on Monday November 4, 2024 from 3PM – 5PM in Student Commons Building 4018. Title: Algorithmic Exploration of Coreset Creation and other uses of Conformal Prediction with a Focus on Regression Tasks Abstract: The current explosion of machine learning combined with vast troves of data to learn from, brings with it unique challenges.?We propose to explore efficient, algorithmic ways to reduce, anonymize, and validate while avoiding specialization in models types, distributions, and applications. Specific avenues include new ways to use conformal prediction for coreset construction and time-series uncertainty quantification in regression tasks.??

Join us for a department Seminar, Yaning Liu on “Machine learning approaches for efficient global sensitivity analysis” on Monday November 18, 2024 from 1:00pm – 1:30pm in Student Commons Building 4017 or on Zoom. Email [email protected] for the Zoom link. Title: Machine learning approaches for efficient global sensitivity analysis Abstract: Global sensitivity analysis (GSA), an important topic in uncertainty quantification, studies how uncertainty in the model output can be attributed to each model input while all inputs vary simultaneously. GSA is known to be time-consuming, as it requires a large number of forward model evaluations to obtain accurate estimates of GSA indices. In this presentation, we discuss three recent projects that leverage machine learning techniques to enhance the efficiency of global sensitivity analysis. The first project focuses on Bayesian learning-based sparse arbitrary polynomial chaos expansion (PCE), employing a Bayesian approach to sparse polynomial chaos expansion. The method targets variance-based GSA to provide efficient and accurate sensitivity indices using a parsimonious set of features. The second project explores Dirichlet Process Mixture Modeling (DPMM) for moment-independent GSA. By leveraging DPMM, this approach captures complex input-output relationships and enables sensitivity analysis that is independent of output moments, broadening its applicability to models where variance alone may be insufficient for understanding sensitivity. The third project involves sparse high-dimensional model representation (HDMR) with Fourier Amplitude Sensitivity Testing (FAST), which combines sparse HDMR with FAST to efficiently manage high-dimensional inputs, making it well-suited for large-scale systems requiring detailed sensitivity insights. Through this presentation, we aim to demonstrate the potential of these machine learning-based approaches to improve the scalability and precision of GSA in diverse applications. Speaker: Yaning Liu, PhD Department of Mathematical and Statistical Sciences, CU Denver

Join for a department seminar, Florian Pfender on “Hypergraph Turán Densities" on Monday November 18, 2024 from 12:30pm - 1:00pm in Student Commons Building 4017. Email [email protected] for the Zoom link. ? Title: Hypergraph Turán Densities Abstract: How many edges can a graph have if it does not contain a triangle? Questions like this lead to the definition of extremal numbers. Extremal numbers are asymptotically known for all graphs. How about hypergraphs? The question is the same, but answers are almost non-existing. We explore this topic a bit, and show how we can find some answers using semidefinite programming methods. Speaker: Florian Pfender, PhD Department of Mathematical and Statistical Sciences, CU Denver