- Optimization Methods and Software
- Inverse Problems (parameter estimation, imaging and sensing, etc.)
- Optimal Control
- Optimal Experimental Design (OED)
- Bayesian Inference/Inversion
- Machine Learning
- etc.,

and to provide opportunities to share new findings, and to potentially contribute with research ideas/projects.

## Spring 2023

For the Spring 2023 semester, seminars will take place on Thursdays from 3:00pm-4.00pm in person in ACS 362C.

- April 24, 2023

**Kyle Wright**(Graduate Student, Applied Mathematics, University of California, Merced)

*Structured Inverse Eigenvalue Problems with applications in quantum systems*

**Title Talk:****Structured inverse eigenvalue problems (SIEPs) have applications in quantum systems. We will explore SIEPs for symmetric matrices with parameterized diagonal components. This includes methods for solving the general 2x2 case and other special cases. We then discuss the applications of these methods in quantum systems.**

*Abstract:*- April 17, 2023

**Toby Isaac**(Argonne National Laboratory)

*Variable Metric Three Operator Splitting for Convex Optimization*

**Title Talk:****We explore the convergence properties of a variable metric formulation of the three operator splitting iteration of Davis & Yin, trying to balance convergence rates with robust adaptability.**

*Abstract:*- April 10, 2023

**Shashwat Sharan**(Graduate Student, Applied Mathematics, University of California, Merced)

*Quantum Mechanical Fluid Flow in a Channel (Dam Break Problem)*

**Title Talk:****The presentation involves quantum mechanical fluid flow in a channel. It discusses the classical dam break problem, an experiment conducted with Bose-Einstein condensates (BECs), and the Gross-Pitaevskii equation, which is used to model BECs. We also discuss how to numerically get its ground state and numerically evolve it in time.**

*Abstract:*- March 13, 2023

**Jacqueline Alvarez**(Graduate Student, Applied Mathematics, University of California, Merced)

*Machine Learning for Classifying Images with Motion Blur*

**Title Talk:****Motion blur in an image results from movements of objects within a scene or from the imaging system itself. In applications such as high-speed license plate recognition, motion blur introduces image artifacts leading to challenges in image classification. In this work, we investigate machine learning techniques for classifying images with motion blur using convolutional neural networks. In particular, we explore how different motion directions and lengths affect the predictive performance of our classification model. We used the MNIST dataset, which contains 70,000 images of handwritten digits, to generate training and testing datasets of images with motion blur using MATLAB. Specifically, we considered motion blurs at various angles and lengths to analyze the effects of different motion blurs on the classification accuracy of images of digits. We found that our model shows very high accuracy when training and testing on datasets with the same type of motion blur. In contrast, training and testing on datasets with different motion blurs result in lower accuracy. We describe how we can improve overall classification performance and offer insights on what additional information can be inferred from the MNIST dataset with motion blur.**

*Abstract:*## Fall 2022

For the Fall 2022 semester, seminars will take place on Thursdays from 3:00pm-4.00pm in person in ACS 362B.

- November 29, 2022

**Ruanui Nicholson**(Lecturer, Department of Engineering Science Te Herenga Mātai Pūkaha | Faculty of Engineering Waipapa Taumata Rau | University of Auckland)

*A Bayesian approach to optimal experimental design of large scale inverse problems in the presence of model uncertainties*

**Title Talk:**

- November 15, 2022

**Stephanie Chaillat**(Laboratoire POems, École Nationale Supérieure de Techniques Avancées Paris)

**Title Talk:**Fast Boundary Element Methods to simulate underwater explosions and their interactions with submarines**Assessing the impact of underwater explosions on submerged structures (submarines) is an important naval engineering problem. An underwater explosion mainly induces two distinct phenomena: a "shock wave" followed by an oscillating bubble of gas. Our goal is to create an efficient numerical method that accounts for the effects of both phenomena on submerged structures. Due to the unbounded nature of the ocean and the complex mechanical behavior of the submarine we want to take into account, it is natural to consider a Boundary Element Method/Finite Element Method (BEM/FEM) coupling. I will present how we can take advantage of fast BEMs in the frequency domain to model this time-domain problem, all the necessary improvements to be able to consider realistic configurations and the consequences on the convergence of the FEM/BEM coupling.**

*Abstract:*

- November 1, 2022

**Irabiel Romero**(Graduate Student, Applied Mathematics, University of California, Merced)

*Paper presentation: “Embedding Power Flow into Machine Learning for Parameter and State Estimation”, by Laurent Pagnier and Michael Chertkov*

**Title Talk:****Modern state and parameter estimations in power systems consist of two stages: the outer problem of minimizing the mismatch between network observation and prediction over the network parameters, and the inner problem of predicting the system state for given values of the parameters. The standard solution of the combined problem is iterative: (a) set the parameters, e.g. to priors on the power line characteristics, (b) map input observation to the prediction of the output, (c) compute the mismatch between predicted and observed output, (d) make a gradient descent step in the space of parameters to minimize the mismatch, and loop back to (a). We show how modern Machine Learning (ML), and specifically training guided by automatic differentiation allows to resolve the iterative loop more efficiently. Moreover, we extend the scheme to the case of incomplete observations, where Phasor Measurement Units (reporting real and reactive powers, voltage, and phase) are available only at the generators (PV buses), while loads (PQ buses) report (via SCADA controls) only active and reactive powers. Considering it from the implementation perspective, our methodology of resolving the parameter and state estimation problem can be viewed as embedding of the Power Flow (PF) solver into the training loop of the Machine Learning framework (PyTorch, in this study). We argue that this embedding can help to resolve high-level optimization problems in power system operations and planning.**

*Abstract:*

- October 18, 2022

**Roummel Marcia**(Professor, Applied Mathematics, University of California, Merced)

*Interpretability of ReLU for Inversion*

**Title Talk:****In this talk, we focus on the mathematical interpretability of fully-connected neural networks, especially those that use a rectified linear unit (ReLU) activation function. Our analysis elucidates the difficulty of approximating the reciprocal function. Notwithstanding, using the ReLU activation function halves the error compared with a linear model. In addition, one might have expected the errors to increase only towards a singular point, but both the linear and ReLU errors are fairly oscillatory and increase near both edge points.**

*Abstract:*- October 4, 2022

**Jacqueline Alvarez**(Graduate Student, Applied Mathematics, University of California, Merced)

*Synthetic aperture radar inverse scattering reconstruction using convolutional neural networks*

**Title Talk:****We address the reconstruction of synthetic aperture radar (SAR) images using machine learning. From previous work, we utilize a single, fully-connected layer to learn the sensing matrix of the forward scattering problem. We estimate the reflectivity of the SAR measurements by applying the conjugate transpose of the learned sensing matrix to the SAR measurements. We further improve the reconstructions of the reflectivity using convolutional layers. The model is trained to reconstruct images containing a single target but can be applied to data containing multiple targets without additional training. Resulting reconstructions are sharper images, where the background noise is significantly decreased.**

*Abstract:*- September 20, 2022

**Symeon Papadimitropoulos**(Postdoctoral Researcher, Applied Mathematics, University of California, Merced)

*Imaging in waveguides using physically-informed data-driven techniques*

**Title Talk:****Inverse source problems are central to many applications in acoustics, geophysics, non-destructive testing, and more. Traditional imaging methods suffer from the resolution limit, preventing distinction of sources separated by less than the emitted wavelength. In this work we propose a method based on physically-informed neural-networks for solving the source refocusing problem, constructing a novel loss term which promotes super-resolving capabilities of the network and is based on the physics of wave propagation. We demonstrate the approach in the setup of imaging an a-priori unknown number of point sources in a two-dimensional rectangular waveguide from measurements of wavefield recordings along a vertical cross-section. The results show the ability of the method to approximate the locations of sources with high accuracy, even when placed close to each other.**

*Abstract:*- September 6, 2022

**Chrysoula Tsogka**(Professor, Applied Mathematics, University of California, Merced)

*Phase and absorption contrast imaging using intensity measurements*

**Title Talk:****We consider imaging absorbing as well as non-absorbing objects using intensity only measurements. Objects with high absorption contrast can be imaged effectively using multiple illuminations and/or masks as in ghost imaging. On the other hand, transparent objects with low absorption contrast are more challenging to be imaged when only intensities are measured, even when they significantly change the phase of the waves as they go through them. We present a computational imaging approach that allows quantitative imaging of both absorbing and transparent objects. This problem arises in various fields such as X-ray crystallography, electron microscopy, coherent diffractive imaging and astronomy. The proposed algorithm guarantees exact recovery if the image is sparse with respect to a given basis, and it can be used, without any modification, when the illumination is partially coherent. This is important for, for example, phase-contrast X-ray imaging because fully coherent sources of X-rays are very hard to be obtained.**

*Abstract:*

## Spring 2022

For the Spring 2022 semester, seminars will take place on Thursdays from 2:00pm-3.00pm in person in ACS 362B (if you'd like to join via zoom, please send an email to Noemi Petra at npetra at ucmerced dot edu).

- February 03, 2022

**Ruanui Nicholson**(Lecturer, The University of Auckland)

**Title Talk:**On the use of (Linear) Surrogates in Bayesian Inverse Problems**In this talk we consider the use of surrogate (forward) models to efficiently solve Bayesian inverse problems. The problems considered are from a range of applications but are all high dimensional problems resulting from the discretisation of partial differential equations. We adopt the Bayesian approximation error approach to account for the model discrepancy, which is treated as an additional stochastic error term. We also prove a somewhat surprising result: under the assumption of a Gaussian prior and additive noise model the approximate posterior found by using a linear(-ised) surrogate is invariant to the choice of linear surrogate, so long as the model discrepancy is taken into account via the Bayesian approximation error approach. This is ongoing joint work with Noemi Petra, Umberto Villa, and Jari P. Kaipio.**

*Abstract:*- February 17, 2022

**Jacqueline Alvarez**(Graduate Student, Applied Mathematics, University of California, Merced)

**Title Talk:***Deep Learning for Signal and Image Processing with Limited Data*

- March 03, 2022

**Jingyi Wang**(Postdoctoral Researcher, LLNL)

**Title Talk:**A distributed-memory optimization solver for two-stage stochastic programming problems- March 17, 2022

**Kyle Wright**(Graduate Student, Applied Mathematics, University of California, Merced)

**Title Talk:**Numerical Methods for a Schrodinger Equation Inverse Eigenvalue Problem**Jocelyn Ornelas Munoz**(Graduate Student, Applied Mathematics, University of California, Merced)

**Title Talk:**Detecting Inherited and Novel Structural Variants in Low-Coverage Parent-Child Sequencing Data Using Negative Binomial Optimization- April 07, 2022

**Ki-Tae Kim**(Postdoctoral Researcher, Applied Mathematics, University of California, Merced)

**Title Talk:**Joint parameter and model dimension reduction for Bayesian*inverse problems with application to a nonlinear Stokes ice sheet*

*flow*

- April 21, 2022

**Tucker Hartland**(Graduate Student, Applied Mathematics, University of California, Merced)

**Title Talk:**Hierarchical Hessian approximation for large-scale inverse problems governed by PDE ice sheet models- May 05, 2022

**Radoslav Vuchkov**(Graduate Student, Applied Mathematics, University of California, Merced)

**Title Talk:**Inversion for the basal sliding coefficient for the Stokes ice sheet model under uncertain thermal distribution## Fall 2021

For the Fall 2021 semester, seminars will take place on Thursdays from 2:00pm-3.00pm in person in ACS 362B (if you'd like to join via zoom, please send an email to Noemi Petra at npetra at ucmerced dot edu).

- September 09, 2021

**Chrysoula Tsogka**(Professor, Applied Mathematics, University of California, Merced)

**Title Talk:**Inverse problems for waves- September 23, 2021

**Radoslav Vuchkov**(Graduate Student, Applied Mathematics, University of California, Merced)

**Title Talk:**Tensor Train Network and its Applications to Numerical Integration and Partial Differential Equations**Boaz Ilan**(Professor, Applied Mathematics, University of California, Merced)

**Title Talk:**Optimizing solar concentrators- October 7, 2021

**Tucker Hartland**(Graduate Student, Applied Mathematics, University of California, Merced)

**Title Talk:**Inversion of the Humboldt Glacier Basal Friction Coefficient in an Uncertain Ice Sheet Model**Kyle Wright**(Graduate Student, Applied Mathematics, University of California, Merced)

**Title Talk:**Discretizing Inverse Eigenvalue Problems- October 21, 2021

**Ki-Tae Kim**(Postdoc, Applied Mathematics, University of California, Merced)

**Title Talk:***Joint parameter and model dimension reduction for Bayesian*

*inverse problems with application to a nonlinear Stokes ice sheet*

*flow*

- November 04, 2021

**Sarah Downs**(Graduate Student, Applied Mathematics, University of California, Merced)

**Title Talk:**Explore the Effects of Taxonomic Structures for Multi-Sensor Fusion**Tucker Hartland**(Graduate Student, Applied Mathematics, University of California, Merced)

**Title Talk:**A Multigrid Interior-Point Approach for PDE- and Bound-Constrained Optimization## Spring 2021

For the Spring 2021 semester, seminars will take place on Thursdays from 3:00pm, via Zoom. If you are interested to join the seminar, please contact Noemi Petra at npetra at ucmerced dot edu.

- January 28, 2021

**Journal papers discussion**(Graduate Students, Applied Mathematics, University of California, Merced)

- February 11, 2021

**Radoslav Vuchkov**(Graduate Student, Applied Mathematics, University of California, Merced)

**Title Talk:**Exploring the potential of Firedrake as PDE solver when solving inverse problems governed by PDEs**Tucker Hartland**(Graduate Student, Applied Mathematics, University of California, Merced)

**Title Talk:**The Semi-Smooth Newton Method for Optimization with PDE and Bound Constraints- February 25, 2021 -
**Canceled**

- March 11, 2021

**Jacqueline Alvarez**(Graduate Student, Applied Mathematics, University of California, Merced)

**Title Talk:**Projection onto Affine Constraints**Alex Ho**(Graduate Student, Applied Mathematics, University of California, Merced)

**Title Talk:**A Deep Learning Approach for Computing Curvature in Level-Set Methods (recording)- April 15, 2021

**Ki-Tae Kim**(Postdoc, Applied Mathematics, University of California, Merced)

**Title Talk:**TBA- April 29, 2021

**Journal papers discussion**(Graduate Students, Applied Mathematics, University of California, Merced)

**Title Talk:**TBA## Fall 2020

For the Fall 2020 semester, seminars will take place on Thursdays from 10:30am to 11:30am, via Zoom. If you are interested to join the seminar, please contact Noemi Petra at npetra at ucmerced dot edu.

- September 10, 2020

**Roummel Marcia**(Professor, Applied Mathematics, University of California, Merced)

**Title Talk:**Optimization Methods for Machine Learning**Aditya Ranganath**(Grad Student, Electrical Engineering and Computer Science, University of California, Merced)

**Title Talk:**TBD- September 24, 2020

**Ki-Tae Kim**(Postdoc, Applied Mathematics, University of California, Merced)

**Title Talk:**MUQ-hIPPYlib: A Bayesian Inference Software Framework Integrating Data with Complex Predictive Models under Uncertainty- October 08, 2020

**Noemi Petra**(Professor, Applied Mathematics, University of California, Merced)

**Title Talk:**Optimal experimental design of large-scale Bayesian linear inverse problems under model uncertainty- October 22, 2020

**Tucker Hartland**(Grad Student, Applied Mathematics, University of California, Merced)

**Title Talk:**Hierarchical off-diagonal low-rank (HODLR) approximation for Hessians in Bayesian inference with application to ice sheet models**Radoslav Vuchkov**(Grad Student, Applied Mathematics, University of California, Merced)

**Title Talk:**Inexact Newton method with relaxed Krylov subspace approximation for inverse problems governed by PDEs- November 05, 2020

**Jacqueline Alvarez**(Grad student, Applied Mathematics, University of California, Merced)

**Title Talk:**Image Denoising With Limited Data Using Recurrent Neural Network (recording)**Alex Ho**(Grad student, Applied Mathematics, University of California, Merced)

**Title Talk:**Fundamentals of Recurrent Neural Networks (recording)- November 19, 2020

**Sarah Downs**(Grad Student, Applied Mathematics, University of California, Merced)

**Title Talk:**Classification of Forest Disturbance in California (recording)**Spring 2020 **

- January 30th:

**Jacqueline Alvarez**(grad student, Applied Mathematics, University of California, Merced)

**Title Talk:**Image Classification in Synthetic Aperture Radar using Reconstruction From Learned Inverse Scattering**Roummel Marcia**(Professor, Applied Mathematics, University of California, Merced)

**Title Talk:**Efficient Factorizations of Large-Scale Oblique Projection Matrices- February 27th:

**Toshiyuki Bandai**(grad student, Environmental Systems, University of California, Merced)

**Title Talk:**Inverse solution of Richards' equation using physics informed neural networks**Melissa Spence**(grad student, Applied Mathematics, University of California, Merced)

**Title Talk:**Predicting Novel and Inherited Structural Variants in Parent-Child Trios- March 12th: CANCELED - this talk is rescheduled to the end of April

**Yanting Zhao**(Ph.D. candidate, Univ Sci Tech of China (USTC), visiting Ph.D. at MESA Lab of UC Merced)

**Title Talk:**Fractional Order Gradient Descent (FOGD): An overview and future opportunities- April 2nd: CANCELED - this talk will be rescheduled for later in the Fall

**Tucker Hartland**(grad student, Applied Mathematics, University of California, Merced)

**Title Talk:**Hierarchical Off-diagonal Low-rank (HODLR) Approximation of Hessians for Inverse Problems with Application to Ice Sheet Flow**Ki-Tae Kim**(postdoc, Applied Mathematics, University of California, Merced)

**Title Talk:**MUQ-hIPPYlib: A Bayesian Inference So ware Framework Integrating Data with Complex Predictive Models under Uncertainty- April 16th: CANCELED

**Omar DeGuchy**(grad student, Applied Mathematics, University of California, Merced)

**Title Talk:**TBA- April 30th:

**Yanting Zhao**(Ph.D. candidate, Univ Sci Tech of China (USTC), visiting Ph.D. at MESA Lab of UC Merced)

**Title Talk:**Fractional Order Gradient Descent (FOGD): An overview and future opportunities**Fall 2019 **

- September 19th:

**Alex Ho**(grad student, Applied Mathematics, University of California, Merced)

**Title Talk:**Image Disambiguation with Deep Neural Networks**Ki-Tae Kim**(postdoc, Applied Mathematics, University of California, Merced)

**Title Talk:**Some advances in computational methods for fracture*mechanics, linear wave propagations and eigenvalue*

*problems*

- October 3rd:

**Noemi Petra**(Assistant Professor, Applied Mathematics, University of California, Merced)

**Title Talk**: Introduction to hIPPYlib- October 17th:

**Omar DeGuchy**(grad student, Applied Mathematics, University of California, Merced)

**Title Talk:**Deep Learning with Pytorch (Part I)- October 31st:

**Amalia Kokkinaki**(PhD, Assistant Professor, Environmental Science, Environmental Engineering, University of San Francisco)

**Title Talk:**Large-scale inverse problems and data assimilation in hydrogeology: developments and challenges**Abstract:**In hydrogeology, inverse problems and data assimilation are used to estimate the properties of the subsurface using noisy, indirect measurements, as well as to track fluid movement through the soil or rock matrix. Applications include characterization for improved site cleanup, water resources management, and identification of contaminant sources. The corresponding inverse problems range from weakly nonlinear, such as pressure dissipation in mildly heterogeneous formations, to strongly nonlinear, such as multiphase flow in heterogeneous formations. A variety of techniques have been used over the last two decades to tackle such inverse problems, including deterministic/regularization based techniques to stochastic Bayesian estimation techniques. In this talk, a review of these methods will be presented, focusing on methods that are applicable for large scale systems with thousands to millions of unknowns, and specifically addressing the tradeoff between computational efficiency and estimation accuracy. The challenges associated with strongly non-linear problems, and Kalman Filtering variants that can address such problems will be discussed. The talk will close with an overview of current research needs for inverse modeling methods in the field of hydrogeology.

- November 14th:

**Omar DeGuchy**(grad student, Applied Mathematics, University of California, Merced)

**Title Talk:**Deep Learning with Pytorch (Part II)- December 5th:

**Tucker Hartland**, (grad student, Applied Mathematics, University of California, Merced)

*Title Talk: Hierarchical Off-Diagonal Low-Rank Approximation forHessians in Inverse Problems*

**Radoslav****Vuchkov**(grad student, Applied Mathematics, University of California, Merced)

*Title Talk: Quasi-Newton Methods for Infinite-Dimensional Inverse Problems Governed by PDEs*

**Spring 2019 **

- February 14th:

*Title Talk: The Fundamentals of Deep Learning*

- February 21st:

*Title Talk:*

*Hierarchical Off-diagonal Low-rank Approximation for Hessians in Inverse Problems*

- March 7th:

*Title Talk: Quasi-Newton Methods for Off-the-Shelf Machine Learning*

- March 21st:

*Title Talk: Second-order adjoints in optimization with application*

*to machine*

*learning for the training of neural networks*

- April 4th:

*Title Talk: On mesh-independent secant quasi-Newton formulas*

- April 18th:

*Title Talk: Bayesian inversion for the basal sliding parameter field in a nonlinear Stokes ice sheet model with a nuisance rheology parameter in hIPPYlib*

- May 2nd:

*Title Talk: Odor Plume Problems and Introduction to POSIM*