This Workshops is the fourth of a series started in Cachan, France in 2011, and continued in Blois (2013). Its aim is to present and exchange ideas on recent developments in Reduced Basis (RB) approaches, Proper Orthogonal Decomposition (POD) and Proper Generalized Decomposition (PGD) methods for the numerical resolution of models involving partial differential equations. Other model size reduction methods are welcome in order to foster cross-fertilization of ideas and their synergy.

Mechanics, like other domains, continues to supply numerous engineering problems which, despite the impressive progress of computational simulation techniques, remain intractable today. POD, RB, PGD and other model reduction methods are leading to a new generation of high-performance computational tools which provide solutions to engineering problems which are inaccessible to standard codes based on classical and well-established numerical techniques. This is a true breakthrough with a potential gain of several orders of magnitude.

The workshop is intended to be a meeting ground for the various contributors, including mechanical engineers, applied mathematicians and other researchers and engineers involved in testing and computation. The Workshop should provide answers to questions such as:

• What are the benefits, but also the drawbacks, of RB and POD/PGD methods?
   
• What engineering challenges, especially in engineering sciences and applied mathematics could be addressed in the near future?
   
• What are the key scientific issues?