Organizing Committee
Abstract

The goal of this two-week research and professional development workshop is to support the retention and success of junior and mid-career computational mathematicians who are from groups that are underrepresented in the field. Participants will forge strong collaborations in mentored research groups and engage in professional development via no-lead learning communities. The larger goal of the workshop is to form a positive, diverse community of researchers who are committed to supporting each other’s professional and scholarly growth.

In research teams led by experienced mentors, participants will be introduced to cutting-edge opportunities in numerical analysis and scientific computing, and will actively work on and contribute to a research project with their team. The supportive formal and informal mentoring will help participants grow their scientific and collaborative skills. In addition, the collaborative learning communities will provide the participants with a forum for personal and professional growth in their self-identified areas of need and will deliver professional and leadership development in a small group setting. The workshop will also include panels and discussions on a range of issues including addressing intersectional issues involving gender, race, and LGBTQ+ status in the profession.

This research collaborative effort is run in collaboration with SIAM which will provide support for sustained interaction and collaboration even beyond the two-week workshop.

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Application Information

ICERM welcomes applications from faculty, postdocs, graduate students, industry scientists, and other researchers who wish to participate. Some funding may be available for travel and lodging. Graduate students who apply must have their advisor submit a statement of support in order to be considered.

Via the application process, rank the top 3 preferred research projects you would like to join and participate at this workshop. It is intended that the collaborated projects initiated during this workshop will continue beyond the two-week workshop period.

Application Deadline: March 12, 2024

Your Visit to ICERM

ICERM Facilities
ICERM is located on the 10th & 11th floors of 121 South Main Street in Providence, Rhode Island. ICERM's business hours are 8:30am - 5:00pm during this event. See our facilities page for more info about ICERM and Brown's available facilities.
Traveling to ICERM
ICERM is located at Brown University in Providence, Rhode Island. Providence's T.F. Green Airport (15 minutes south) and Boston's Logan Airport (1 hour north) are the closest airports. Providence is also on Amtrak's Northeast Corridor. In-depth directions and transportation information are available on our travel page.
Lodging
ICERM's special rate will soon be made available via this page for our preferred hotel, the Hampton Inn & Suites Providence Downtown. ICERM also regularly works with the Graduate Hotel and Hilton Garden Inn who both have discounted rates available. Contact housing@icerm.brown.edu before booking anything.
The only way ICERM participants should book a room is through the hotel reservation links located on this page or through links emailed to them from an ICERM email address (first_last@icerm.brown.edu). ICERM never works with any conference booking vendors and never collects credit card information.
Childcare/Schools
Those traveling with family who are interested in information about childcare and/or schools should contact housing@icerm.brown.edu.
Technology Resources
Wireless internet access ("Brown-Guest") and wireless printing is available for all ICERM visitors. Eduroam is available for members of participating institutions. Thin clients in all offices and common areas provide open access to a web browser, SSH terminal, and printing capability. See our Technology Resources page for setup instructions and to learn about all available technology.
Accessibility
To request special services, accommodations, or assistance for this event, please contact accessibility@icerm.brown.edu as far in advance of the event as possible. Thank you.
Discrimination and Harassment Policy
ICERM is committed to creating a safe, professional, and welcoming environment that benefits from the diversity and experiences of all its participants. Brown University's "Code of Conduct", "Discrimination and Workplace Harassment Policy", "Sexual and Gender-based Misconduct Policy", and "Title IX Policy" apply to all ICERM participants and staff. Participants with concerns or requests for assistance on a discrimination or harassment issue should contact the ICERM Director or Assistant Directors Kathryn Boots or Jenna Sousa; they are the responsible employees at ICERM under this policy.
Fundamental Research
ICERM research programs aim to promote Fundamental Research and mathematical sciences education. If you are engaged in sensitive or proprietary work, please be aware that ICERM programs often have participants from countries and entities subject to United States export control restrictions. Any discoveries of economically significant intellectual property supported by ICERM funding should be disclosed.
Exploring Providence
Providence's world-renowned culinary scene provides ample options for lunch and dinner. Neighborhoods near campus, including College Hill Historic District, have many local attractions. Check out the map on our Explore Providence page to see what's near ICERM.

Visa Information

Contact visa@icerm.brown.edu for assistance.

Eligible to be reimbursed
B-1 or Visa Waiver Business (WB)
Ineligible to be reimbursed
B-2 or Visa Waiver Tourist (WT)
Already in the US?

F-1 and J-1 not sponsored by ICERM: need to obtain a letter approving reimbursement from the International Office of your home institution PRIOR to travel.

H-1B holders do not need letter of approval.

All other visas: alert ICERM staff immediately about your situation.

ICERM does not reimburse visa fees. This chart is to inform visitors whether the visa they enter the US on allows them to receive reimbursement for the items outlined in their invitation letter.

Financial Support

This section is for general purposes only and does not indicate that all attendees receive funding. Please refer to your personalized invitation to review your offer.

ORCID iD
As this program is funded by the National Science Foundation (NSF), ICERM is required to collect your ORCID iD if you are receiving funding to attend this program. Be sure to add your ORCID iD to your Cube profile as soon as possible to avoid delaying your reimbursement.
Acceptable Costs
  • 1 roundtrip between your home institute and ICERM
  • Flights on U.S. or E.U. airlines – economy class to either Providence airport (PVD) or Boston airport (BOS)
  • Ground Transportation to and from airports and ICERM.
Unacceptable Costs
  • Flights on non-U.S. or non-E.U. airlines
  • Flights on U.K. airlines
  • Seats in economy plus, business class, or first class
  • Change ticket fees of any kind
  • Multi-use bus passes
  • Meals or incidentals
Advance Approval Required
  • Personal car travel to ICERM from outside New England
  • Multiple-destination plane ticket; does not include layovers to reach ICERM
  • Arriving or departing from ICERM more than a day before or day after the program
  • Multiple trips to ICERM
  • Rental car to/from ICERM
  • Flights on a Swiss, Japanese, or Australian airlines
  • Arriving or departing from airport other than PVD/BOS or home institution's local airport
  • 2 one-way plane tickets to create a roundtrip (often purchased from Expedia, Orbitz, etc.)
Travel Maximum Contributions
  • New England: $350
  • Other contiguous US: $850
  • Asia & Oceania: $2,000
  • All other locations: $1,500
  • Note these rates were updated in Spring 2023 and superseded any prior invitation rates. Any invitations without travel support will still not receive travel support.
Reimbursement Requests

Request Reimbursement with Cube

Refer to the back of your ID badge for more information. Checklists are available at the front desk and in the Reimbursement section of Cube.

Reimbursement Tips
  • Scanned original receipts are required for all expenses
  • Airfare receipt must show full itinerary and payment
  • ICERM does not offer per diem or meal reimbursement
  • Allowable mileage is reimbursed at prevailing IRS Business Rate and trip documented via pdf of Google Maps result
  • Keep all documentation until you receive your reimbursement!
Reimbursement Timing

6 - 8 weeks after all documentation is sent to ICERM. All reimbursement requests are reviewed by numerous central offices at Brown who may request additional documentation.

Reimbursement Deadline

Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. Submissions after thirty days will incur applicable taxes. No submissions are accepted more than six months after the program end.

Projects

Inverse Problems and Uncertainty Quantification in Imaging Applications

Andrea Arnold (Worcester Polytechnic Institute), Misha Kilmer (Tufts University)

Inverse problems have a rich history in imaging, addressing challenging problems such as the reconstruction of images from sparse, corrupted observations in a variety of complex applications (e.g., computed tomography). When analyzing results, uncertainty quantification (UQ) plays a key role in understanding the reliability of predicted outcomes due to changes in the input variables. This project will address inverse problems and UQ in the context of imaging applications, including recent approaches to tackle ill-posedness and assess the reliability of results under model uncertainties.

Compatible Discretizations for Nonlinear Optical Phenomenon

Vrushali Bokil (Oregon State University), Claire Scheid (University of Nice), Camille Carvalho (University of California, Merced)

The proposed research collaboration will focus on numerical modeling of nonlinear optical phenomena, with particular interest on developing efficient numerical methods that naturally capture the inherent physical aspects of the problem under consideration. Nonlinear optics is the area of optics that studies the interaction of light with matter in the regime where the response of the material system depends in a nonlinear manner on the amplitude of the applied optical excitation. As a consequence, when light of one or more frequencies impinges on a sample, light at a different or several different frequencies emerges (a phenomenon called frequency mixing). A simple example is the second-harmonic generation that is obtained when the wavelength of the light that emerges is exactly half that of the incident beam. Such phenomena, although essentially known since the beginning of optics, became particularly important as lasers came into widespread use. Indeed, these modifications of the optical properties of a given material are only obtained with sufficiently intense (and coherent) light. Nonlinear optical phenomena are nowadays at the heart of optical communications systems, optical sensing, optical imaging, the design of new laser sources etc. As a support to experiments, numerical modelling of nonlinear optical phenomena is essential. Numerous challenges need to be overcome to find appropriate and relevant models and provide efficient numerical computing environments for a given realistic scenario.

Modeling and Numerical Simulations of Microswimmers in Confined Domains

Ricardo Cortez (Tulane University), Shilpa Khatri (UC Merced)

Microswimmers are ubiquitous in nature and understanding their behavior is essential in biological fields and industrial applications. Due to their size and speeds, the fluid motion generated by these swimmers can be modeled using the Stokes equations, a linear PDE. The method of regularized Stokeslets and several variants and improvements have been developed over the last two decades for microscopic viscous flows. Recent developments related to these methods include regularized Stokeslet segments, a method of images for regularized Stokeslets near an infinite solid plane or outside a solid sphere, and evaluation techniques for the boundary integrals that arise in applications. In this project, the participants will have opportunities to (1) extend some of these methods to address novel applications and to (2) model applications and implement the methods. We expect the directions of the project will develop naturally based on the interests of the participants. Potential projects include comparisons of different numerical methods applied to test problems that provide insight into particular applications, modeling flows in confined domains, and improving on current numerical methods. The project will begin with a tutorial and hands-on activities on regularized Stokeslets, including discussions about their applications and limitations. Participants can expect some early reading assignments on background material.

Agnostic Numerical Filters Based on Convolution

Ayaboe Edoh (Jacobs Engineering, Inc. (AFRL Edwards)), Jennifer Ryan (KTH Royal Institute of Technology)

Convolutional filters are powerful tools that have proven useful in multiple areas, such as data compression, shock filtering, post-processing, and machine learning. The popularity of this approach has given rise to the need for effective and efficient design of convolution kernels that are both scheme and grid agnostic. In this project, the goal is to increase efficiency, effectiveness and flexibility of robust convolutional filters. This project will focus on identifying the essential properties in convolutional filter design in the mesh-free context. This will entail: (1) An investigation of grid dependence of the data; (2) Optimising the underlying evaluation of the convolutional kernel; (3) Exploring the affect on stability and conservation of the resulting filter operator.

Stability Analysis of Mixed Model Additive Runge–Kutta Methods

Sigal Gottlieb (University of Massachusetts Dartmouth), Zachary J Grant (Oak Ridge National Lab)

The development of mixed-precision algorithms for solving ordinary differential equations (ODEs) using Runge--Kutta methods [1,2] was proposed in [3]. The approach builds on the work in [6,5,4] which studies additive Runge--Kutta methods and perturbations of such methods. Using this rigorous approach, he developed novel mixed precision and mixed model Runge--Kutta additive (MP-ARK) methods that reduce the cost of the computationally expensive implicit stages in the Runge--Kutta methods by employing a cheaper low-precision or low-order model computation. The explicit stages are then performed using a high-precision or high- order model computation, providing a correction to the implicit stages. The structure of the MP-ARK is designed to further suppress the errors coming from either the low precision or low order model by introducing inexpensive explicit high-precision correction terms, or by designing novel methods that internally suppress the low- precision perturbations.

In this research project we will learn about additive Runge--Kutta methods and their perturbations, and about ODE linear and nonlinear stability theory. Our research will focus on several questions for mixed model computations, including: 1) What stability properties do the low- and high-order models have to satisfy so that the mixed model is stable? 2) How do the correction terms impact the stability of the mixed model? 3) Can we devise a different type of correction that will improve the stability of the corrected mixed model method?

No specialized prior background is required: we will assume that the participants have used some numerical methods for ordinary differential equations (possibly even Runge-Kutta methods), can identify the difference between implicit and explicit methods, and are familiar with the concept of a fixed point iteration. However, these can be quickly picked up before or as the project begins.

Reduced Order Modeling for Kinetic Models and Applications

Yunan Yang (Cornell University), Jingwei Hu (University of Washington), Fengyan Li (Rensselaer Polytechnic Institute)

An ingredient in many science and engineering applications, such as solving optimal design and control problems, is to efficiently and accurately simulate many realizations of underlying mathematical models, especially differential equations depending on a set of model parameters. For example, in control, one seeks an optimal strategy to drive a system to a prescribed configuration, and this will be sought via optimizing suitably chosen objective functions of the state variables (i.e., the solutions of the parametric equations) and hence of the model parameters. Many queries of high-fidelity solutions of the underlying models can be computationally prohibitive. Reduced order modeling (ROM) techniques have been developed to provide efficient and reliable surrogate solvers to address such challenges.

We will consider systems governed by kinetic models (e.g., Fokker-Planck, Vlasov-type, Boltzmann equation) and investigate ROMs with applications in control and design problem using such kinetic models which are characterized by high dimensions, multi-scale, and possible nonlinearity. We will address the following aspects or questions. (1) ROMs will be designed by leveraging specific model structures (e.g., bilinear, quadratic, asymptotic preservation). (2) Despite their high computational cost, high-fidelity full-order models (FOMs) often provide training data for building efficient ROM surrogate solvers, and we will examine the interplay between the choice of FOMs and the properties of ROMs. (3) In the optimization step of control and design problems, it is crucial to work with a quality initial guess for a given objective function or to design objective functions with “good” landscapes. When ROMs are used as a fast surrogate solver, what challenges and opportunities will be brought to these components?

The tasks above will provide a starting point. The team's various skill sets and perspectives will work together to refine, shape, and advance this collaborative pro

Low Rank Tensor Methods for High Dimensional Multi-scale Multi-physics PDE Models

Jingmei Qiu (University of Delaware), William Taitano (Los Alamos National Laboratory), Joseph Nakao (Swarthmore College)

Recently, low rank tensor methods experienced progress in handling high-dimensional multi-scale partial differential equation (PDE) models. Leveraging the inherent low rank structure of solutions in various multi-scale scenarios, these methods have demonstrated computational savings in storage and CPU/GPU time. Despite this, several open challenges persist in the field.

- Establishing Rigorous Analysis: The accuracy, stability, and convergence of algorithms necessitate investigation. Addressing these aspects will bolster the reliability and applicability of low rank tensor methods in diverse multi-scale PDE contexts. - Preserving Intrinsic Physics Structures: Ensuring the preservation of the underlying physical structures and model asymptotics is crucial. By doing so, low rank methods can effectively capture the essential features of the system and enhance the predictive power of the models. - Multi-scale Multi-Physics Applications: A challenge lies in extending low rank algorithms to accommodate challenging applications that couple multiple physics across disparate scales, such as those encountered in high energy density, fusion, and space plasmas. Such systems often support stiff parasitic scales, which may be dynamically irrelevant but require short lengths and time scales for numerical stability. Developing efficient, low-rank compatible implicit solvers and specialized models is vital for broadening the applicability of low rank tensor methods. - High-Performance Computing (HPC) Considerations: Efficient utilization of HPC resources is critical for reaching the full potential of low rank methods. Integrating these algorithms with HPC architectures will enable large-scale simulations and widen the scope of their applicability.

We'll explore these directions, identify common areas of interest, and share insights leading to a deeper understanding of low rank tensor methods and their applications in high-dimensional multi-scale PDE models.