We intend the terms scientific computing and data science to be broadly defined and inclusive. Topics of interest include but are not limited to:

- High-performance computing, novel numerical methods, parallel algorithms, and application problems that involve numerical challenges.
- Machine learning algorithms, deep learning and neural networks, applied/predictive modeling with real-world data, data-enabled science, dimensionality reduction, Bayesian methods, natural language processing, and computational statistics.

Our group is led by Harish Bhat, Tommaso Buvoli and Mayya Tokman.

During Spring 2020 we will meet on **Tuesday** at **10:00am-11:am** in the Arts and Computational Sciences building **(ACS) room 362B**. If you are interested in giving a talk please select an empty time slot in our box note. To be added as an editor for the box file email or talk to Tommaso Buvoli.

This seminar is part of the RTG theme “Scientific Computing and Data Science.” Graduate students should register for Math 298 (2 units) using CRN 37113; the instructor of record for the course is Harish Bhat.

## Semiars are canceled for now until further notice due to COVID-19. Seminars might move toward remote delivery after Spring Break.

### Schedule Spring 2020

**Jan 28th:**Organizational Meeting

**Feb 11:**Yuanran Zhu*Title:*Introduction to Mori-Zwanzig theory*Abstract:*Modern mathematics often needs to address the dimension reduction problem for high dimension systems with complex dynamics. In practice, such dimension reduction problems can be formulated as the construction of effective models that describe the dynamics of low-dimensional quantities of interest. To this end, the Mori-Zwanzig formulation, which was first established in irreversible statistical mechanics provides us a general framework to derive the exact evolution equation of such quantities from the underlying high dimensional equation of motion. In this talk, we will provide an overview on the derivation, interpretation and approximation of the Mori-Zwanzig equation. Specific examples from physics and applied mathematics will be given to show how to use the Mori-Zwanzig equation in practice. In addition, we will discuss the extension of the Mori-Zwanzig theory and its possible connections with other research topics such the kinetic theory and combinatorics.

**March 3:**Harish Bhat*Title:**Abstract:*

**March 18:**Majerle Reeves*Title:**Abstract*

### Schedule Fall 2019

**Sept 3:**Organizational Meeting

**Sept 10:**Alex Nguyen*Title:*Simulating Charged Particle Dynamics with Exponential Integrators*Description:*A critical component of the computational simulation of plasma and accelerated beam physics is solving for charged particle trajectories in electromagnetic fields - the so called particle pushing problem. In this talk we discuss a novel approach to particle pushing using exponential integrators, and report our findings.

**Sept 24:**John Butcher (University of Auckland)*Time:***3:00pm***Location:*ACS 362C*Title:*Order of multivalue-multistage methods*Description:*A “general linear method” is an s-stage, r-value method charac- terised by a partitioned (s + r) × (s + r) matrix. This includes the classical linear multistep and Runge–Kutta methods and it has been natural to base error analysis and asymptotic order on these well- studied models. This talk will review the established approaches to defining and analysing the order of general linear methods, with emphasis on B-series analysis, based on an arbitrary starting method. It will be shown that this can be rewritten in terms of two simple algorithms in which the actual starting method is eliminated from the calculations.

**Oct 8:**Cosmin Safta (Sandia National Laboratories)*Time: 10:00am**Location:*ACS 362B*Title:*Uncertainty Quantification and Machine Learning Algorithms for Physical Models - Tackling Computational Expense and High-Dimensionality*Description:*This presentation will focus on analysis workflows for quantifying uncertainty in physical systems. In this context I will describe challenges posed by the computational cost and high-dimensionality associated with applications of interest to DOE (Earth System Model, Atmospheric Transport Models) and DoD (Scramjet Engine). I will outline algorithmic developments adapted to each application including both supervised and unsupervised sparse learning techniques.

**Oct 15:**David Strubbe (UC Merced)*Title:*Deep Learning and Density Functional Theory: Towards Quantum Calculations of Molecules and Solids*Description:*We show that deep neural networks can be integrated into, or fully replace, the Kohn-Sham density functional theory (DFT) scheme for multielectron systems in simple harmonic oscillator and random external potentials with no feature engineering. We show that self-consistent charge densities calculated with different exchange-correlation functionals can be used as input to an extensive deep neural network to make predictions for correlation, exchange, external, kinetic, and total energies simultaneously. We use a deep convolutional inverse graphics network to predict the charge density given an external potential for different exchange-correlation functionals and assess the viability of the predicted charge densities. This work shows that extensive deep neural networks are generalizable and transferable given the variability of the potentials (maximum total energy range ≈100 Ha) because they require no feature engineering and because they can scale to an arbitrary system size with an O(N) computational cost.

**Oct 22:**Omar DeGuchy (UC Merced)*Title:*Machine Learning For Applications in Synthetic Aperture Radar*Description:*In the world of remote sensing, machine learning algorithms have shown promise in solving a variety of problems associated with a variety of imaging modalities. In particular, the use of neural networks in conjunction with Synthetic Aperture Radar (SAR) images have been shown to be effective for automatic target recognition. This talk focuses on two different applications of neural networks with SAR data. In the first application, we address the lack of SAR data used for training target recognition models by augmenting the quality of synthetic SAR data using a modified generative adversarial network. In the second application, we propose a method to solve the forward and inverse scattering problems for SAR. The method takes advantage of a simplified neural network where the goal is to learn the sensing matrix that maps reflectivities to SAR measurements. We also propose a similar method to learn an approximate inverse used to recover reflectivites from SAR measurements.

**Nov 12:**Harish Bhat (UC Merced)*Title:*BCD-Prox Methods for Simultaneous Filtering & Parameter Estimation*Description:*Suppose we have a dynamical system with parameters whose values we'd like to estimate using noisy observations of the system's state. This is the simultaneous filtering and parameter estimation problem -- here filtering is in the sense of the classical Kalman filter, where one seeks to estimate the system's true states from noisy observations. We describe our recent work on block coordinate descent proximal methods (BCD-prox) to solve this problem. As compared to state-of-the-art methods, BCD-prox exhibits increased robustness (to noise, parameter initialization, and hyperparameters), decreased training times, and improved accuracy of both filtered states and estimated parameters. We show how BCD-prox can be used with multistep numerical discretizations, and we establish convergence of BCD-prox under hypotheses that include real systems of interest.

**Dec 3:**Maxime Theillard (UC Merced)*Title:*Volume-preserving reference maps*Description:*TBA

### Schedule Spring 2019

**March 13th:**Maxime Theliard (UC Merced)*Title:*The projection method for the incompressible Navier-Stokes equations*Description:*An introduction to the projection method for simulating incompressible newtonian fluids. We will both look at the standard method and how it can be implemented on adaptive grids to simulate single and two phase flows.

**April 3rd:**Tommaso Buvoli (UC Merced)*Title:*Time-Integration Techniques for Stiff Systems*Description:*An introduction to several types of time-integration techniques used to solve stiff systems arising from the discretization of partial differential equations.

**April 17th**: Changho Kim ( UC Merced)*Title:*Stochastic Differential Equations 101*Description:*An introductory lecture to SDEs and their numerical solutions will be presented. No prerequisite knowledge is assumed.

**April 24th**: Leonardo Zepeda-Núñez*Title:*Fast and Scalable Algorithms for the High-Frequency Helmholtz Equation in 3D*Description:*There is much truth to the conventional wisdom that computational wave propagation is harder when the frequency is higher. Ten years ago, it was unclear that scalable sequential algorithms could even exist for the Helmholtz equation. Today, linear complexity is not only available in many scenarios of interest, but it is becoming clear that parallelism can take us much further. I will show recent results that indicate that genuinely sublinear parallel runtimes are possible in the 3D case, both with respect to the total number of unknowns, and the number of right-hand sides. ** Joint work with Laurent Demanet (MIT), Matthias Taus (MIT), Russell Hewett (Total), and Adrien Scheuer (UCL).

**May 1st**: Camille Carvalho (UC Merced)*Title:*Ad Hoc Finite element method for sign-changing Laplacian*Description:*In this presentation we will discuss how to use the finite element method for solving Laplace's equation in a partitioned domain (two materials for example). We will discuss the method, the error estimate, and how to design ad hoc meshes to ensure optimal convergence.