1. WORKSHOP AND MC MEETING TARTU, FEBRUARY 8-9, 2018

2. A “warm” welcome to Tartu!
Name seems to mean “historic” (in German: Dorpat)
2nd city of Estonia with > inhabitants
Capital of the province of Tartumaa
The university is the largest and oldest in Estonia
Approximately 8000 students
Famous Nobel laureate: Wilhelm Ostwald (chemistry)
Famous mathematician: Anders Lindstedt, known by the Lindstedt-Poincare method for uniformly approximating periodic solutions to ordinary differential equations

3. What is “Model order reduction”?
Nowadays, there is a high demand for ever more accurate and realistic simulations
Coupled problems, combining several aspects of a problem (temperature, mechanical, electromagnetic, fluid)
Complex structures with enormous numbers of nodes/degrees of freedom
Observation: often, there is a lot of superfluous detail generated in the computations
Generating only the dominant features is much more efficient; how to do this?
Model order reduction
11 October 2011

4. Model Order Reduction is about capturing dominant features
Automatically produce a low-order model that still provides an accurate description of the behavior

5. MOR by Picasso?
Thanks to Vincenzo Capasso!
January 2010

6. Example
Integrated circuits need 3-D structure for wiring
10 years ago
1-2 layers of metal, no influence on circuit performance
Present situation:
8-10 layers of metal
Delay of signals, parasitic effects due to high frequencies
3-D solution of Maxwell equations leads to millions of extra unknowns
Gradual
Can we construct a compact model for the interconnect in an automated way?
circuit

7. Example: MOR for transmission line (RC)
Original
Reduced
Netlist size (Mb)
0.53
0.003
# ports 22
# internal nodes
3231 12
# resistors
5892 28
# capacitors
3065 97

8. Model Reduction and related areas
Scientific computing, numerical MOR,
Krylov methods, linear algebra, tensors
Pade-via-Lanczos and PRIMA
Passivity preserving
Structure preserving
Linear and nonlinear problems
Parameterized methods
Tensor analysis
Systems and control, Lyapunov, Truncated Balanced Realization
Large-scale Lyapunov systems
Balanced realizations
Observability and controllability Gramians
Port-Hamiltonian systems
Hankel singular values
Projection methods
Mathematical modeling, behavioral modeling, models via data
Reduced basis methods
MOR at operator level
Karhunen-Loeve expansions
Neural networks
Vector fitting
Behavioral models

9. Why these topics together?
Scientific computing, numerical MOR,
Krylov methods, linear algebra, tensors
Systems and control, Lyapunov, Truncated Balanced Realization
Remarkably, they share the same common phenomenology!
Mathematical modeling, behavioral modeling, models via data

10. Many urgent and challenging problems need a unified approach!
Why COST? Why now?
Scientific computing, numerical MOR,
Krylov methods, linear algebra, tensors
Many urgent and challenging problems need a unified approach!
Systems and control, Lyapunov, Truncated Balanced Realization
Mathematical modeling, behavioral modeling, models via data

11. Objectives of EU-MORNET
Main Action objective: “significantly bringing down computation times for realistic simulations and co-simulations of industrial, scientific, economic and societal models by developing appropriate model reduction methods”
Secondary objectives:
A unified framework of model reduction techniques
Support fundamental research in MOR in all areas
Stimulate development of novel methods and models
Disseminate the results towards other communities
Foster the multidisciplinary/multisectorial training of ESRs
Promote ESRs commitment towards outreach activities

12. Long term impact The Action will
Publish a handbook on “Model Order Reduction” covering from the fundamental didactical aspects to the most recent interdisciplinary research. The preparation of the volumes will start during year 1 (plan discussed during KO) and will proceed till the end of the Action. These volumes will constitute the final Action publication.
Foster the training of a new class of ESR with interdisciplinary background. These ESR will be the warranty that “Model Order Reduction” will continue as a supra- disciplinary field in the longer period, well after the end of the Action.
Set up a series of conferences. These will be of a highly interdisciplinary nature.

13. The Working Groups
WG1: Model reduction methods (Gianluigi Rozza) coordination of research in the broad area of model reduction, with techniques from the fields of numerical analysis, systems-control theory, behavioural modelling and related fields
WG2: Design optimization techniques (Miguel Silveira) Applying model reduction techniques to coupled and multiphysics problems in order to significantly speed up simulations, in a setting with parameters and optimization requirements. Bridge the gap between researchers working in academia and industry, using model reduction techniques to obtain improved and optimized designs of products, coordinate these efforts on a European scale. Joint supervision of ESRs and monitoring the entire process of STSMs.
/ department of mathematics and computer science

14. The Working Groups
WG3: Applications (Andreas Zilian) using model reduction and design optimisation methods to solve challenging industrial and societal problems. WG 3 explores the current application-driven state of industrial requirements for reduced order modelling at the European level and communicates these to WG 1 (theoretical and methodological development) and WG 2 (design optimisation techniques). WG 3 supports critical performance assessment of MOR approaches developed through a wide catalogue of benchmarking industrial problems and fosters application-oriented knowledge transfer between academia and industry.
WG4: Dissemination and outreach (Karen Veroy) This WG is responsible for the (i) dissemination of results obtained; and (ii) outreach to the broad community of model reduction researchers and stake holders.

15. This meeting Workshop today and resuming tomorrow at 11 AM
Tomorrow from there will be a management committee meeting, accessible only to MC members and MC substitutes
Lunch today from on the first floor of this building
There will be an excursion today from
/ department of mathematics and computer science

16. Finally……..
For any questions or requests, please contact the local organiser (Peep Miidla) or me
We all wish you a very nice and interesting, fruitful meeting
/ department of mathematics and computer science