Modern industrial processes often resort to complex simulation models whose computational cost requires substitution by a surrogate of much lesser complexity. The surrogate quality depends on the set of simulation runs (the design) used for its construction. Quality increases with design size, which can often only be decided on-line, during the sequential integration of simulation results.

INDEX (INcremental Design of EXperiments) studies efficient incremental solutions to combinatorial optimisation problems occurring in design of computer experiments. The objective is to propose an ordered design (a sequence of simulation runs) which is nearly optimal (for the corresponding size) when stopped at any of its point, while satisfying a set of intrinsic user-defined constraints.

Many variants of this constrained subset-selection problem are NP-hard and algorithms with approximation guarantees have been proposed in the computer science community. We believe that more efficient approximation bounds and algorithms can be constructed by taking the specificity of the design problem into account. 

INDEX federates the research efforts of two academic partners (I3S and JKU) and one industrial company (EDF) with the goal of achieving a deeper understanding of the design problem, both for space-filling and information criteria and under several kinds of constraints, as well as of its incremental solutions. The academic and applicative teams of INDEX have a strong experience in the field of experimental design, and gather experts three different scientic communities: applied mathematicians, computer scientists, and applied statisticians working in industry with physicists on real life problems.

Additionally, the project will benefit from two on-going international collaborations of the proposing partners:
  • ​ between I3S, the School of Maths of Cardiff University (Prof. Anatoly Zhigljavsky) and the London School of Economics (Prof. Henry Wynn)
  • between JKU and the Comenius University of Bratislava (Prof. Radoslav Harman).

INDEX will apply its results to three test cases provided by EDF that cover a wide range of practical difficulties.
  • Case study 1 Simulation of the electrical production of photovoltaic installations. The objective is to minimise the cost a photovoltaic plant.
  • Case study 2 Simulation of welding processes by numerical simulations solving the unsteady magnetohydrodynamics equations. Goal is the optimisation of repair processes.
  • Case study 3 Simulation of non-destructive control experiments (by finite-element models of eddy current and ultrasonic waves) for controlling weld or flaw in materials of power plants. The objective is the qualification of non-destructive control processes.

INDEX is formally organized around 4 Tasks.

Task 1 (Linear constraints, privacy sets and matroids)  studies the expressive power and the relations between three distinct constraint types and their relevance  in the framework of experimental design.
Task 2 (Design algorithms as dynamical systems) studies the application of the theory of discrete dynamical systems to the study of design algorithms, with the goal of clarifying the relation between their ergodic properties and geometric features induced by usual design criteria.
Task 3 (Greedy algorithms for constrained incremental experimental design) is dedicated to the study of incremental design algorithms, under more generic conditions than matroids, both for space-filling and information criteria. 
Task 4 (Forward-type procedures for constrained experimental design) is dedicated exchange algorithms, that act upon finite sets of design points.