# Brown Bag Seminar

Machine Learning Stochastic Differential Equations: Applications in Reduced Order Models of Turbulence

The ubiquity of turbulence, as well as the importance and difficulty of its simulation are well-known. To combat the computational complexity, physically motivated "phenomenological" theories of reduced-order models have been hypothesized. While very interpretable, these theories struggle to match DNS results. We look to extend these phenomenological models, via neural networks. In this talk, I will focus mainly on our general training methodology to learn extensions to stochastic differential equations, and then touch on our applications to turbulence at the end.

Zoom: https://arizona.zoom.us/j/98593835992 Password: 021573

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*Online*

Summer Research Experience at the Nevada National Security Site: An MLE Approach to Metrology of Laser Propagation Axes

I will give a brief overview of my experience as a graduate associate in science at the Nevada National Security Site (NNSS) last summer. The NNSS (formerly known as the Nevada Test Site) is a 1360 square mile facility owned by the National Nuclear Security Administration, located north of Las Vegas, NV.

During the 10-week program, my research advisor Dr. Daniel Champion (a UA Mathematics alum) guided me on a project to recover the spatial parameters of multiple laser beams emitted from an optical diagnostics probe. Determining the direction of each beam is critical in collecting accurate measurements of target objects.

We applied a maximum likelihood estimator (MLE) method to recover beam axis orientations for the probe. The MLE resulted in a beam orientation having angular separation from ground truth of less than 1.7 degrees on average.

To determine the variance of the estimators, we used Monte-Carlo simulation to populate a sample distribution of recovered parameters. This resulted in a 0.07 degree standard deviation of angular separation from ground truth, averaged over the beams.

This work was done by Mission Support and Test Services, LLC, under Contract No. DE-NA0003624 with the U.S. Department of Energy. DOE/NV/03624--1042.

Zoom: https://arizona.zoom.us/j/98593835992 Password: 021573

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*Online*

Analyzing Multifaceted Scalar fields through Topological Similarity

Reeb graphs have been used in a number of applications including analyzing the topological properties of unifaceted scalar fields. It is natural to consider the situation of analyzing multiple scalar fields arising from multifaceted data via Reeb graphs. Several distances have been defined on Reeb graphs, three of which we will focus on here: The interleaving distance, the functional distortion distance, and the Reeb graph edit distance. Each distance pulls insipiration from different mathematical fields such as category theory, metric and Banach spaces, and sequence and string matching. Here, we provide an abridged construction for each distance as well as an analysis of the distance properties that each exhibit. We then discuss future directions for analysis of scalar fields using Reeb graph metrics either through these aforementioned distances or by taking a machine learning approach for graph similarity learning.

Zoom: https://arizona.zoom.us/j/98593835992 Password: 021573

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*Online*

Transitioning into the Role of a Machine Learning Engineer

In this talk, we will survey the experience of transitioning from an Applied Mathematician to a Machine Learning Engineer (using a sample size of one). In the first part, I will briefly share my experience of the job application process, preparing for interviews, and lessons learned along the way. In the second part, we will cover a high level view of two real world use cases -- Demand Forecasting for Retail and Production Cost Modeling for the Power Grid -- and touch on the pragmatic side of deploying a solution on the cloud (as time allows).

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*Online*

Are Neural Networks Cheating?

Neural networks produce state-of-the-art performance in several tasks these days. But how are they doing it? Or are they actually cheating their way through? In this talk I will present research that is being done at the Computational Language Understanding Lab of the Computer Science department of University of Arizona. Here, I will first introduce how neural networks work, from a math perspective, and then we will look deep into the workings of neural networks using natural language processing as a tool. I will then present how neural networks, many-a-times, rely on several subtle statistical patterns in the data to produce these state-of-the-art results. Further, I will also present a solution we have developed in our lab to counter this 'memorizing' habit of neural networks. The proposed solution, called Confluence Learning, uses data distillation and model distillation approaches over fact verification datasets. By using different delexicalized views of the data and encouraging the models to learn from each other through pairwise consistency losses, we prevent the neural networks from relying on such dataset artifacts, but instead learn the true underlying semantics of a given dataset.

Details about the presenter: Mitch is a final year PhD candidate at University of Arizona’s Department of Computer Science, where he is advised by Professor Mihai Surdeanu. He is broadly interested in the implementation of neural networks for natural language processing. His current research focuses on fact verification with an emphasis on domain transfer and has published in many prestigious conferences in the field including EMNLP. Mitch earned his bachelor's degree in Physics and Engineering, along with a Masters degree in Physics, from Birla Institute of Technology and Science(BITS), Pilani, India. He did his second masters in Computer Science at the University of Arizona. His other interests include network security and penetration testing.

Place: Zoom: https://arizona.zoom.us/j/98593835992 Password: 021573

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*Online*

Breaking into Data Science

Have you ever considered data science as a career? Are you curious to learn what skills companies are looking for in data scientists? Join us for a webinar to learn what it takes to be a top data scientist in industry. This webinar is presented by the team from Propheto, a data science talent startup! We’ll cover what data science really means in industry, the skills you need to make the transition, and why academics are suited to be data scientists. With our extensive backgrounds in analytics and data science at tech companies and in academia, the Propheto team has learned the ins and outs of what companies are looking for in data science hires. We have also seen first-hand the skills that MS students, PhDs, and postdocs need to successfully make the transition into industry as high-caliber data scientists. We look forward to sharing these lessons with you and more during the webinar.

About the Speakers: Dan McDade - CTO & Co-Founder of Propheto, Data scientist and product manager at two growth-stage software companies, Current MBA student at Carnegie Mellon University, B.S. in Mechanical and Environmental Engineering from Boston University

Sajeev Popat - CEO & Co-Founder of Propheto: Analytics leader at two growth-stage software startups, MBA from The Tuck School of Business at Dartmouth College and MPA from The Harvard Kennedy School of Government, B.S. in Quantitative Economics from Tufts University

About Propheto: Propheto is a talent marketplace platform that helps academics find short-term data science and analytics consulting engagements with companies. Go to www.propheto.io to learn more.

Zoom: https://arizona.zoom.us/j/98593835992 Password: 021573

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*Online*

Data-driven discovery of reduced Lagrangian models of turbulence

Turbulence in fluids is a rich and ubiquitous physical phenomena and reducing its computational complexity remains an active research topic due to its many potential scientific and engineering impacts. The main objective of this work is to automatically discover the best fit Lagrangian model from turbulence data using a parameterized family of models (SPH and MD) along with modern machine learning tools (such as differentiable programming combined with deep learning). In this talk I will share my ongoing research (and some progress) on developing physics informed machine learning tools to solve this problem. I will discuss the necessary background in Lagrangian models such as Smooth Particle Hydrodynamics (SPH) and Molecular Dynamics (MD) for the description of fluid dynamics and turbulence. Next, I will discuss how we use differentiable programming to create an entire simulator that is consistent with automatic differentiation to achieve parameter estimation and the discovery of unknown functions (like a pairwise potential function). Essentially our methodology involves embedding neural networks within differentiable simulators (or integrators) which allows for the flexibility to encode as much or as little physical structure as we want. I will show some preliminary results that suggest that we can "learn" or discover certain physical parameters of our models from data, as well as unknown functions (such as a potential function or smoothing kernel by using neural networks as function approximators).

Place: Zoom: https://arizona.zoom.us/j/98593835992 Password: 021573

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*Online*

Stochastic to Continuous Epidemiology: How Network Structure Effects Spreading Phenomena

In this talk I will introduce 3 main tools: network epidemic simulations, SINDy (a model discovery tool), and the ICC curve. With these tools for simulating and analyzing epidemics, I will explore the impact of network structure on the stochastic simulations, the associated discovered models and theoretical explanations for these results. Finally, we will see what impact the structure has on the associated ICC curves and the statistical analysis.

Zoom: https://arizona.zoom.us/j/98593835992 Password: 021573

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*Online*

Extracting the Additive Phase Shifts from the 2-soliton solution of the MKDV

This oral comprehensive exam talk in the field of integrable systems accomplishes the following: 1) deriving the focusing MKDV equation from a Lax Pair, 2) applying the Dressing Method to solve the Lax Pair, 3) solving the focusing MKDV equation for 1- and 2-soliton solutions, and 4) extracting the additive phase shifts from the 2-soliton solution. The talk concludes on future work for the topic of my dissertation: A Kinetic Theory of MKDV Solitons. Instead of describing a many-soliton solution (e.g. 10^8 solitons) analytically, physicists are interested in looking at a statistical description of "soliton gases", effectively describing an "integrable turbulence". It all depends on the additive phase shift. Zoom: https://arizona.zoom.us/j/98593835992 Password: 021573

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*Online*

Organizational Meeting

Come sign up to give a Brown Bag talk! Priority goes to students in the department. We are also actively looking for out of department speakers with mathematical content in their work. Brown bag talks are a great opportunity to present your research and gain public feedback! If you would like to give a talk, or recommend someone else to give a talk, please join this organizational meeting. We will also discuss SIAM's plans for this upcoming year.

Place: Zoom: https://arizona.zoom.us/j/98593835992 Password: 021573

## When

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*Online*