# Modeling and Comp Seminar

Spatio-Temporal Additive Regression Model Selection for Urban Water Demand

Understanding the factors influencing urban water use is critical for meeting demand and conserving resources. To analyze the relationships between urban household-level water demand and potential drivers, we develop a method for Bayesian variable selection in partially linear additive regression models, particularly suited for high-dimensional spatio-temporally dependent data. Our approach combines a spike-and-slab prior distribution with a modified version of the Bayesian group lasso to simultaneously perform selection of null, linear, and nonlinear models and to penalize regression splines to prevent overfitting. We investigate the effectiveness of the proposed method through a simulation study and provide comparisons with existing methods. We illustrate the methodology on a case study to estimate and quantify uncertainty of the associations between several environmental and demographic predictors and spatio-temporally varying household-level urban water demand in Tampa, FL. Zoom: https://arizona.zoom.us/j/95834019930

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*Zoom Session: TBA*

Deep Learning for Efficient Modeling of High Dimensional Spatiotemporal Physics

Turbulence is an exceptionally complex and high-dimensional phenomena, exhibiting spatio-temporal dynamics, non-linearity and chaos. In an era where vast quantities of such DNS data are generated; building practical, physics-driven reduced order models (ROM) of such phenomena are crucial. While Deep neural networks for spatio-temporal data have shown considerable promise, they face severe computational bottlenecks in learning extremely high dimensional datasets, often with > 10^9 degrees of freedom. These application-agnostic networks may also lack physical constraints and interpretability that is desired in scientific ROMs. In this work, we present our efforts in integrating the strong mathematical and physical foundations underlying numerical methods and wavelet theory with deep neural networks. In this talk, we demonstrate computationally efficient learning of 3D turbulence with embedded physics constraints for improved interpretability and physics guarantees, and outline ongoing efforts. Zoom: : https://arizona.zoom.us/j/97722828578

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*Zoom Session*

Universal Differential Equations for Scientific Machine Learning

In the context of science, the well-known adage "a picture is worth a thousand words" might well be "a model is worth a thousand datasets." Scientific models, such as Newtonian physics or biological gene regulatory networks, are human-driven simplifications of complex phenomena that serve as surrogates for the countless experiments that validated the models. Recently, machine learning has been able to overcome the inaccuracies of approximate modeling by directly learning the entire set of nonlinear interactions from data. However, without any predetermined structure from the scientific basis behind the problem, machine learning approaches are flexible but data-expensive, requiring large databases of homogeneous labeled training data. A central challenge is reconciling data that is at odds with simplified models without requiring "big data". In this work we develop a new methodology, universal differential equations (UDEs), which augments scientific models with machine-learnable structures for scientifically-based learning. We show how UDEs can be utilized to discover previously unknown governing equations, accurately extrapolate beyond the original data, and accelerate model simulation, all in a time and data-efficient manner. This advance is coupled with open-source software that allows for training UDEs which incorporate physical constraints, delayed interactions, implicitly-defined events, and intrinsic stochasticity in the model. Our examples show how a diverse set of computationally-difficult modeling issues across scientific disciplines, from automatically discovering biological mechanisms to accelerating climate simulations by 15,000x, can be handled by training UDEs. Zoom link: https://arizona.zoom.us/j/9437861265

Bio: Christopher Rackauckas is an Applied Mathematics Instructor at the Massachusetts Institute of Technology and a Senior Research Analyst at University of Maryland, Baltimore, School of Pharmacy in the Center for Translational Medicine. Chris's research is focused on numerical differential equations and scientific machine learning with applications from climate to biological modeling. He is the developer of many core numerical packages for the Julia programming language, including DifferentialEquations.jl for which he won the inaugural Julia community prize, and the Pumas.jl for pharmaceutical modeling and simulation. Zoom link: https://arizona.zoom.us/j/94378612659

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*Zoom Session*

Convex Relaxations for Severe Damage Analysis in AC Power Networks

The analysis of severe multi-component damage on AC power networks is central to understanding the infrastructure's vulnerability to large-scale natural disasters and coordinated multi-agent attacks. However, solving the non-convex nonlinear AC power flow equations, after severe network damage, is a challenging task and presents a notable obstacle in vulnerability analysis. In this work we explore how recent power system analysis methods, based on convex optimization, can be leveraged for severe damage analysis of real-world AC power network datasets. A rigorous empirical evaluation across seven networks and thousands of damage scenarios demonstrates that convex relaxations of the AC power flow equations can provide a reliable and scalable method for bounding the amount of load shedding required in severe damage scenarios. Furthermore, this preliminary study suggests that the resilience of different power networks to severe damage scenarios may vary more than previously thought.

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*Math, 402*

New analytic chain soliton and self-similar solutions to the Kadomtsev-Petviashvili equation

The KP (Kadomtsev-Petviashvili) equation is probably the most studied (2+1)-dimensional integrable wave equation of the known (2+1)-dimensional integrable models. The KP equation has application to the modeling of weakly nonlinear fluid waves in the presence of gravity and depending on the sign of dispersion, can also describe a one parameter group of time dependent potentials of the Schrodinger equation.

In this work, the exact nonlinear instability of the KP-1 equation is described where an unstable soliton decays into a slow soliton and fast ‘chain’ soliton. Certain aspects of the behaviour of the solutions are explored, such as, branching of the periodic chain solitons. And finally, the self-similar solution to the KP equation is constructed and the resulting ODE is related to the cylindrical KDV equation as well as the Painlevé integrability criteria.

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*Math, 402*

Information-Theoretic Sequential Decision Making: Stochastic and Deterministic Approaches

A natural goal in many sequential decision making processes is to identify a sequence of decisions that reduce uncertainty about some quantity of interest. In the Bayesian setting this problem can be formalized as sequentially maximizing the mutual information (MI) between observations and unknowns. Unfortunately, MI is challenging to estimate or bound in all but the simplest models. This talk will present recent work on algorithms for sequential MI maximization using, both, sample-based estimators and variational approximations. After characterizing the problem, I will present sample-based methods based on sequential M-estimation. Using techniques from the literature on robust statistics I will show that this approach achieves superior accuracy compared to standard Monte carlo methods in the finite sample regime. For larger problem instances I will present a variational approach, which sequentially optimizes lower bounds on MI to yield high-quality decisions with minimal computation. I will demonstrate the strengths and weaknesses of each method on interesting problems, such as gene regulatory network inference, active learning for semi-supervised topic models, and target tracking in a sensor field.

BIO: Jason Pacheco is an assistant professor in the department of Computer Science. Jason’s research interests are in statistical machine learning, probabilistic graphical models, approximate inference algorithms, and information-theoretic decision making. Prior to joining the University of Arizona Jason was a postdoctoral associate at MIT in the Computer Science and Artificial Intelligence Laboratory (CSAIL) with John Fisher III. Jason completed his PhD work at Brown University with Erik Sudderth.

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*Math, 402*

Time delays in gene expression and evolutionary games

It is usually observed, and expected, that small time delays do not change behavior of dynamical systems and large time delays may cause oscillations. We will show that effects of time delays depend of their microscopic origins. A simple stochastic model of gene expression with delayed degradation will be presented. We will show that contrary to what was claimed, delayed degradation does not cause oscillations. We will also discuss models with self-repressed genes. We will show that microscopic models of evolutionary games with strategy-dependent time delays, in which payoffs appear some time after interactions of individuals, lead to a new type of replicator dynamics. Unlike in all previous models, stationary states of such dynamics, and in fact their number, depend on time delays.

References:

J. Miękisz and M. Bodnar, Evolution of populations with strategy-dependent time delays, preprint (2019).

M. Bodnar, J. Miękisz, and R. Vardanyan, Three-player games with strategy-dependent time delays,

Dynamic Games and Applications, on-line 4 December (2019).

J. Miękisz, J. Poleszczuk, M. Bodnar, and U. Foryś, Stochastic model of gene expression with delayed degradation,

Bull. Math. Biol. 73: 2231-2247 (2011).

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*Math, 402*

Applied differential geometry and harmonic analysis in deep learning regularization

With the explosive production of digital data and information, data-driven methods, deep neural networks (DNNs) in particular, have revolutionized machine learning and scientific computing by gradually outperforming traditional hand-craft model-based algorithms. While DNNs have proved very successful when large training sets are available, they typically have two shortcomings: First, when the training data are scarce, DNNs tend to suffer from overfitting. Second, the generalization ability of overparameterized DNNs still remains a mystery despite many recent efforts.

In this talk, I will discuss two recent works to “inject” the “modeling” flavor back into deep learning to improve the generalization performance and interpretability of DNNs. This is accomplished by deep learning regularization through applied differential geometry and harmonic analysis. In the first part of the talk, I will explain how to improve the regularity of the DNN representation by imposing a “smoothness” inductive bias over the DNN model. This is achieved by solving a variational problem with a low-dimensionality constraint on the data-feature concatenation manifold. In the second part, I will discuss how to impose scale-equivariance in network representation by conducting joint convolutions across the space and the scaling group. The stability of the equivariant representation to nuisance input deformation is also proved under mild assumptions on the Fourier-Bessel norm of filter expansion coefficients.

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*Math, 402*

Organizational Meeting

The Modeling, Computation, Nonlinearity, Randomness and Waves Seminar will have an organizational meeting on Thursday, January 23, at 12:30 pm in Math 402. If you would like to speak this semester or nominate someone to speak this semester, please attend this meeting or write to the organizer Misha Stepanov. If you would like to subscribe to seminar announcements, please send an email to appliedmath@math.arizona.edu

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*Math, 402*

Adaptive Capacity Planning for Ambulatory Surgery Centers: A Bottom-up Strategy based on Optimization Combined with Data Analytics

The explosion of patient data is changing the way and the extent to which healthcare organizations capture data, analyze information, and make decisions. In this study, we develop an adaptive capacity planning model for ambulatory surgery centers (ASCs) that coordinate many activities connected closely, posing a significant challenge for delivering a smooth patient flow. When scheduling surgeries, ASCs face a trade-off between the need to be responsive to patients' demand and the need to efficiently schedule surgeries to maximize capacity utilization. Based on actual patient flow data, we first propose an approach to classify patients into a smaller number of groups using descriptive analytics, which significantly reduces the complexity of the capacity planning problem and improves the model’s practicality. Next, we develop several new mathematical formulations as prescriptive analytics models that derive capacity decisions. An extensive computational study demonstrates the effectiveness of our approach and provides implications under the uncertain nature of several business parameters. Considering more than 5,000 ASCs in the U.S. performing 23 million surgeries annually, we hope this study guides practitioners to make appropriate investments that will improve ASC operations via capacity adjustment and patient scheduling.

Bio: Seokjun Youn joined the Eller MIS Department this Fall 2019 as an assistant professor after earning his PhD in Operations and Supply Chain Management from Texas A&M University. His research to date focuses on healthcare operations and supply chain management. Specifically, he studies healthcare payment models, capacity planning and scheduling in healthcare, and logistics optimization for food safety. He holds a master’s degree from Texas A&M University and a bachelor’s degree from Seoul National University, both in Industrial Engineering. Prior to living in the U.S., Seokjun worked as an Air Force officer from South Korea.

## When

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*Math, 402*