University of Pittsburgh

Recent Advances in Numerical PDEs

A workshop, held at the University of Pittsburgh,
May 15-17, 2026

Due to the prevalence of PDEs in engineering, physics, biology, medicine and the social sciences, numerical solutions have become an indispensable tool in scientific exploration. Their significance lies not only in their descriptive capacity, but also their predictive power to help us understand aspects of the physical world and its complex systems.

The workshop aims to promote the direct interaction between experts from different communities, link rigorous numerical analysis and analysis of PDEs with current problems of impact.
Specific topics may include:
- Structure preserving discretizations, emphasizing the enforcement of mass conservation at the discrete level;
- Penalty and artificial compression methods;
- Partitioned and monolithic time-stepping, Structure-fluid interaction;
- Inverse Problems, Data-Driven Modeling & Scientific Computation.

There is no charge for attending the workshop.

Tentative Participant List

Organizers

Traian Iliescu, Monika Neda, Michael Neilan, Leo Rebholz, Catalin Trenchea. Special thanks to William Layton.

Location

The conference will be held in the Cathedral of Learning, room G24. View the event poster here.

Schedule
Friday, May 15      

2:00pm

Welcome Coffee
2:15pm Max Gunzburger
A personal view of interdisciplinary research and computational science training

3:15-3:30pm

Coffee break
3:50am Traian Iliescu
StabOp: A Data-Driven Stabilization Operator for Reduced Order Modeling
4:10pm Guannan Zhang
Generative AI for Nonlinear Data Assimilation
4:30pm Hoang Tran
Supervised learning of generative models for high-dimensional, multi-modal sampling


Saturday, May 16       

10:00-10:10am

Coffee break

10:10am

Astrid & Annelies
10:30am Yanzhao Cao
From transport PDE to diffusion model for generative learning
10:50am Lili Ju
Generalized Transferable Neural Networks for Steady-State Partial Differential Equations

11:10-11:20pm

Coffee break
11:20 Rui Fang
Data assimilation with model error for slightly compressible flow
11:40 Ali Pakzad
When Less Is More: Global Synchronization with Interior-Only Observations

12:00pm-1:50pm

Lunch

1:50pm Hyesuk Lee
Analysis, Reformulation, and Finite Element Approximation of Fluid–Plate Interaction Systems
2:10pm Martina Bukac
Recursive-correction method for fluid-structure interaction
2:30pm A J Meir
On the Equations of Electro-Magneto-Elasticity
2:50pm Nanda Nechingal Raghunathan
Modular Nudging
3:10pm Isabel Barrio Sanchez
Long-Time Stability of the Navier–Stokes Equations under the One-Leg θ-Method

3:30-3:40pm

Coffee break
3:40pm Michaela Kubacki
Blobs and Boundaries: A grid-free approach to microscale flows through permeable membranes
4:00pm Alexander Labovsky
Recursive Correction: from Refactorized Midpoint to ReCLES models

6:00pm

Dinner: G's on Liberty, (directions)

Sunday, May 17      

8:50am

Welcome Coffee
9:00am Faranak Courtney-Pahlevani
Numerical Study of a Traffic Flow Inspired by DNA Transcription Modeling
9:20am Aziz Takhirov
On a Steady Turbulent Kinetic Energy Navier-Stokes Model
9:40am Zhu Wang
Inexact Proximal-Point Methods for Energy Minimization
10:00am Jeff Borggaard
Nonlinear Feedback for PDEs

10:20-10:30am

Coffee break
10:30am Daozhi Han
An efficient algorithm for computing stationary statistical solution of some geophysical fluid models
10:50am Mustafa Aggul
Super time stepping methods in SUNDIALS
11:10am Catalin Trenchea
An energy stable and positivity-preserving computational for compressible and immiscible two-phase flow in porous media
11:30am Leo Rebholz
Accelerated solvers for nonlinear PDEs

Map

A map of various landmarks on campus can be found here.

Directions

The Pittsburgh International Airport (PIT) is 20.5 miles away from the University of Pittsburgh (25-45 minutes driving time depending on the time of day). There are several options to get to campus from the airport. See this link for a self-guided virtual tour of the University of Pittsburgh campus.
The Transit app, available for smart phones, is useful for moving around the city using the bus system, with an up-to-date schedule of the buses, also allowing to buy tickets online.

Parking

If you need to park on campus, you might want to park at the following garage:

Local hotels

University of Pittsburgh's preferred hotels.

Hotel(s) offering our special group rate:

  • Residence Inn by Marriott Pittsburgh Oakland/University Place for 189.00 USD per night ($22 per night for parking)
    Book our group rate for Recent Advances in Numerical PDEs Conference

  • Hotel Indigo for 139.00USD per night (complimentary parking).
    Book our group rate for Recent Advances in Numerical PDEs Conference (put in the conference dates and make sure that code PDE is in the Group Rate field).
    Last Day to Book: Tuesday, April 14, 2026.

    Dining Options

    There are several dining options throughout the Oakland area. I personally recommend Ali Baba (Middle Eastern), Mario's (American), Butterjoint (American/Eastern European), or the Spice Island Tea House (Asian).

    Contact:

    For questions please contact Catalin Trenchea.

    Acknowledgement:

    The organizers gratefully acknowledge the help and financial support provided by The University of Pittsburgh Mathematical Research Center.