Organizing Committee
 Yanlai Chen
University of Massachusetts, Dartmouth  Serkan Gugercin
Virginia Tech  Misha Kilmer
Tufts University  Yvon Maday
Sorbonne Université  Shari Moskow
Drexel University  Akil Narayan
University of Utah  Daniele Venturi
University of California, Santa Cruz
Abstract
Mathematical models arising from scientific applications frequently have a large number of degrees of freedom, and modern observational or empirical datasets have highdimensional features. Such highdimensional realities from either simulation or experimental data makes direct computational analysis, compression, and/or probing tasks such as outerloop optimization, design, and/or uncertainty quantification computationally infeasible. One paradigm for addressing such a challenge is mathematicsbased model reduction, which aims to find and exploit lowdimensional structure in highdimensional models to generate a computationally efficient emulator, often with provable accuracy guarantees. A complementary class of approaches is found in lowrank approximation and statistics where data reduction techniques can efficiently explore and mine parsimonious summarizations of highdimensional datasets. One major goal of the Spring 2020 program, and the foundational theme for this proposed workshop, was the promotion of reciprocal and symbiotic interactions and advances that blend these data analysis and model reduction strategies spanning mathematical and statistical analysis, optimization, and data science. The proposed workshop will continue to fertilize such disciplinebridging advancements, tackling foundational challenges such as nonlinear reduction methods, datadriven reducedorder model identification, lowrank inference, and inverse problems, and efficient compression for highdimensional tensors.
Confirmed Speakers & Participants
Talks will be presented virtually or inperson as indicated in the schedule below.
 Speaker
 Poster Presenter
 Attendee
 Virtual Attendee

Christopher Beattie
Virginia Tech

Peter Benner
Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg

Yanlai Chen
University of Massachusetts, Dartmouth

Yingda Cheng
Michigan State University

Vladimir Druskin
Worcester Polytechnic Institute

Ion Victor Gosea
Max Planck Institute for Dynamics of Complex Technical Systems

Pawan Goyal
Max Planck Institute for Dynamics of Complex Technical Systems

Serkan Gugercin
Virginia Tech

Misha Kilmer
Tufts University

Boris Krämer
University of California San Diego

Peter Kramer
Rensselaer Polytechnic Institute

Sanda LEFTERIU
Continental Automotive Romania

Fengyan Li
Rensselaer Polytechinic Institute

Petar Mlinarić
Virginia Tech

Shari Moskow
Drexel University

Akil Narayan
University of Utah

Carmeliza Navasca
University of Alabama at Birmingham

Elizabeth Newman
Emory University

Davide Palitta
Alma Mater Studiorum, Universita' di Bologna

Benjamin Peherstorfer
Courant Institute, New York University

Zhichao Peng
Michigan State University

Igor Pontes Duff
Max Planck Institute for Dynamics of Complex Technical Systems

Elizabeth Qian
California Institute of Technology

Jemima Tabeart
University of Edinburgh

Daniele Venturi
University of California, Santa Cruz

Min Wang
Duke University

Zhu Wang
University of South Carolina

Steffen W. R. Werner
Courant Institute, New York University

Mikhail Zaslavskiy
Schlumberger
Workshop Schedule
Monday, May 23, 2022

3:50  4:00 pm EDTWelcome11th Floor Lecture Hall
 Brendan Hassett, ICERM/Brown University

4:00  5:30 pm EDTWelcome (Back!) ReceptionReception  11th Floor Collaborative Space
Tuesday, May 24, 2022

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, May 25, 2022

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, May 26, 2022

11:00  11:45 am EDTA casual talk on electromagnetic wave propagation and quantum computing11th Floor Lecture Hall
 Zhichao Peng, Michigan State University
Abstract
This talk will include two parts: (1) a scalable fast iterative solver for the frequencydomain Maxwell equations at high frequencies and (2) a practice of characterization and optimal control of a real quantum computer. The frequencydomain Maxwell equations at high frequencies has indefinite nature, and as a result, it is challenging for iterative linear solvers to invert it efficiently. It also has highresolution requirement, and the memory needed by standard multifrontal direct solvers may become prohibitive for practical highfrequency 3D problems. In the first part of the talk, we present an efficient scalable frequencydomain Maxwell solver built from scalable timedomain solvers called EMWaveHoltz. Due to its high potential, quantum computing recently draw a lot of attention from the scientific community. In the second part of the talk, we briefly introduce some main difference between a quantum computer and a classical computer. We also use deterministic and Bayesian methods to characterize a quantum computer based on experimental data. Control pulses are designed based on the characterization results, and their performance is demonstrated through experimental validations.

2:00  2:45 pm EDTDeep Learning for Highdimensional PDE11th Floor Lecture Hall
 Min Wang, Duke University
Abstract
Solving highdimensional PDEs is a longstanding challenge in scientific computing. Luckily, studies discovered that the neural networks can be used to approximate a certain class of functions without the curse of dimensionality. It is therefore natural to expect that the solutions to high dimensional PDEs can be accurately approximated with the neural networks under controllable numerical costs. Along this line, three questions have been widely considered: 1) How can a PDE problem be formulated into an optimization problem so that it fits into the frame of deep learning? 2) How accurate will a neural network approximation be? 3) How could the training be conducted in a systematic way so that we could be close to a global minimum? In this talk, I will briefly describe a few initial attempts I have made to answer the questions above.

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Friday, May 27, 2022

1:30  2:15 pm EDT$\mathcal{L}_2$Optimal ReducedOrder Modeling11th Floor Lecture Hall
 Petar Mlinarić, Virginia Tech
Abstract
Motivated by $\mathcal{H}_2$optimal model order reduction (MOR) for nonparametric linear timeinvariant (LTI) systems and $\mathcal{H}_2 \otimes \mathcal{L}_2$optimal parametric MOR for parametric LTI systems, we investigate $\mathcal{L}_2$optimal parametric MOR for parametric stationary problems arising from, e.g., discretizations of parametric stationary partial differential equations. We first develop gradients of the squared $\mathcal{L}_2$ error with respect to the reduced system operators, which then leads to a gradientbased optimization method for MOR of parametric stationary problems. We also illustrate that the optimization algorithm can be performed purely in a datadriven manner using only the samples of the quantities of interest without access to fullorder operators. Furthermore, we develop interpolatory conditions for optimal MOR of a class of parametric stationary problems. Finally, we discuss MOR methods based on (Petrov)Galerkin projection and whether $\mathcal{L}_2$optimal reducedorder models are necessarily of such type. We illustrate the theory via various numerical examples and compare our framework to standard projectionbased approaches.

2:15  3:00 pm EDTLearning Dynamical Models via Identifying Suitable QuadraticEmbeddings11th Floor Lecture Hall
 Pawan Goyal, Max Planck Institute for Dynamics of Complex Technical Systems
Abstract
Dynamical modeling of a process is essential to study its dynamical behavior and perform engineering studies such as control and optimization. With the ease of accessibility of data, learning models directly from the data have recently drawn much attention. It is also desirable to construct simple models describing complex nonlinear dynamics for efficient simulations and engineering studies. The simplest modelone can think ofis the linear model, but they are often not expressive enough to model complex dynamics. In this work, we propose \emph{McCormickenvelope} inspired modeling of nonlinear dynamics and discuss a common framework to model nonlinear dynamic processes. The preeminent idea, coming from the envelope, is smooth nonlinear systems can be written as quadratic systems in appropriate lifted coordinate systems without any approximation. We utilize deep learning capabilities and discuss suitable neural network architectures to find such a coordinate system using data. We also discuss an extension to highdimensional data, which exhibits a slow decay of singular values. We showcase the approach using data coming from applications in engineering and biology.

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Monday, May 30, 2022

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, May 31, 2022

2:00  2:45 pm EDTFrom frequency response data to (balanced) reducedorder models: systemtheoretical approaches11th Floor Lecture Hall
 Ion Victor Gosea, Max Planck Institute for Dynamics of Complex Technical Systems
Abstract
In many applied sciences applications, the underlying dynamics of the process under study may be inaccessible to direct modeling, or it may be only partially known. However, with the increasing prevalence of available data from practical experiments, it is of high relevance to include such measurements in the modeling process. Data corresponding to the underlying dynamical systems are available in various formats. For example, among others, in the form of the frequency response. In such cases, one could construct a simplified empirical model of lower dimension that fits the measured data, and hence accurately approximates the original system. This reducedorder system may then be used as a surrogate to predict behavior or derive control strategies. The main motivation of the methods discussed here is that measured system response data can be used in a beneficial way without the need of accessing any prescribed realization of the original model. The balanced truncation (BT) method (introduced by Moore '81) and Loewnermatrix (LM) methodologies (introduced by Mayo/Antoulas '07) are common model reduction approaches. However, only the latter approach (LM) is purely datadriven, while the first is not. We show how to implement a datadriven counterpart of the classical BT approach by using only frequency response data, without explicitly using the model (system's matrices). This recent method (G./Gugercin/Beattie '22) is based on implicitly imposing quadrature approximations on the infinite Gramians, and on constructing the reducedorder model by accessing the transfer function values only.

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, June 1, 2022

11:00  11:45 am EDTStabilizing Dynamical Systems in the Scarce Data Regime11th Floor Lecture Hall
 Steffen Werner, Courant Institute, New York University
Abstract
Stabilizing dynamical systems in science and engineering is challenging, especially in edge cases and limit states where typically little data are available. In this work, we propose a datadriven approach that guarantees finding stabilizing controllers from as few data samples as the dimension of the unstable dynamics, which typically is orders of magnitude lower than the state dimension of the system. The key is learning stabilizing controllers directly from data without learning models of the systems, which would require larger numbers of data points. Numerical experiments with chemical reactors and fluid dynamics behind obstacles demonstrate that the proposed approach stabilizes systems after observing fewer than five data samples even though the dimension of states is orders of magnitude higher.

2:00  3:00 pm EDTTensortensor Algebra for Optimal Representation and Compression of Multiway Data11th Floor Lecture Hall
 Elizabeth Newman, Emory University
Abstract
With evergrowing data resources and modern advancements of datadriven methods, it is imperative that we represent large datasets efficiently while preserving intrinsic features necessary for subsequent analysis. Traditionally, the primary workhorse for data dimensionality reduction and feature extraction has been the matrix singular value decomposition (SVD), which presupposes that data have been arranged in matrix format. However, many data are natively multidimensional and can be more compressible when treated as tensors (i.e., multiway arrays). In this talk, we will provide a brief overview of a particular compressed tensor representation, the tSVDM, which is formed under an algebraic tensortensor product. We will demonstrate that compressed representations obtained from the tSVDM satisfy EckartYounglike optimality results. Moreover, we will show that an optimal tSVDM representation is provably better than its matrix counterpart and two tensorbased analogs. We will support these theoretical findings with some empirical studies.

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, June 2, 2022

11:00 am  12:00 pm EDTReducedorder modeling and inversion for largescale problems of geophysical exploration11th Floor Lecture Hall
 Mikhail Zaslavsky, Schlumberger
Abstract
Geophysical exploration using electromagnetic and seismic method involves largescale forward and nonlinear inverse problems that often have to be solved in realtime. We address this challenge by employing reducedorder models (ROMs) that represent lowdimensional surrogate of fullscale problem. In this talk I will provide an overview of modeldriven ROMs we developed for forward modeling as well as structurepreserving datadriven ROMs that are crucial for inverse problems. The latter enable constructing physicspreserved loworder models with direct access to unknowns of inverse problem and, consequently, optimizationfree inversion algorithm. I will show numerical examples confirming the advantage of our approaches compared to stateofthe art algorithms.
Contributors: Liliana Borcea, Vladimir Druskin, Alexander Mamonov, Shari Moskow, Jorn Zimmerling
SchlumbergerPrivate 
2:00  3:00 pm EDTSteinbased Preconditioners for Weakconstraint 4Dvar11th Floor Lecture Hall
 Davide Palitta, Alma Mater Studiorum, Universita' di Bologna
 Jemima Tabeart, University of Edinburgh
Abstract
Algorithms for data assimilation try to predict the most likely state of a dynamical system by combining information from observations and prior models. One of the most successful data assimilation frameworks is the linearized weakconstraint fourdimensional variational assimilation problem (4DVar), that can be ultimately seen as a minimization problem. One of the main challenges of such approach is the solution of large saddle point linear systems arising as inner linear step within the adopted nonlinear solver. The linear algebraic problem can be solved by means of a Krylov method, like MINRES or GMRES, that needs to be preconditioned to ensure fast convergence in terms of number of iterations. In this talk we will illustrate novel, efficient preconditioning operators which involve the solution of certain Stein matrix equations. In addition to achieving better computational performance, the latter machinery allows us to derive tighter bounds for the eigenvalue distribution of the preconditioned saddle point linear system. A panel of diverse numerical examples displays the effectiveness of the proposed methodology compared to current stateoftheart approaches.#

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Friday, June 3, 2022

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Monday, June 6, 2022

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, June 7, 2022

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, June 8, 2022

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, June 9, 2022

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
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