To develop and validate structural optimisation solvers considering uncertainties scalable at the exascale.

A general purpose numerical stochastic optimization methodology will be formulated, capable of achieving optimum designs, given the corresponding deterministic problems addressed in WP4 and WP5. This objective aims at implementing an integrated computational strategy in order to master the challenges associated with high fidelity simulation models with the treatment of large-scale simulation problems with uncertainties which, in the context of stochastic optimization with possibly nonlinear and/or dynamic system response, constitute an extremely computationally intensive task.

In order to integrate the deterministic problems into a stochastic analysis and optimization framework, a number of uncertain parameters must be identified with corresponding, design variables, influencing the response of the systems under consideration. In order to formulate the stochastic optimization problem, a preliminary sensitivity analysis for each case examined in this project (structural, fluid, etc.), will determine the variables that are important with respect to their influence on system response. These parameters will form the stochastic design space with respect to which a stochastic optimization problem will be formulated.

Emphasis will be put on the implementation of these formulations for solving real-world problems involving complex multiphysics phenomena, as described in WP4 and WP5, using cutting edge HPC technologies.

Representing uncertainty and error is an on-going research challenge at the exascale, because it can provide high fidelity representations of random quantities and probability distributions, which it is essential to work at different scales. Research within this workpackage will also work in how to combine different representations of uncertainty.

The solution of large-scale optimization problems considering uncertainties can only be achieved with a synergy of the following actions during the numerical simulation and design procedure:- Implementing efficient solution algorithms which exhibit numerical and parallel scalability for handling the resulting discretized equations
- Applying reliable and efficient metaheuristic optimization algorithms for improving the design procedure;
- Rational modelling of the system uncertainties and
- Fully exploitation of recent and future advances in HPC computing technology with hybrid CPU/GPU architectures. ?he combined implementation of all these actions will lead to the desired ten orders of magnitude reduction of the required computational effort, ensuring thus the feasibility of the proposed objective.

The combined implementation of all these actions will lead to the desired ten orders of magnitude reduction of the required computational effort, ensuring thus the feasibility of the proposed objective.

For performing this task, a large number of linear or nonlinear analyses are required for the solution of design optimization problems considering uncertainties, depending on the type of deterministic problem, as considered in WP4 and WP5. At the heart of these methods is the solution of a linearized problem which will be numerically treated following the advanced algorithms developed in WP4 and WP5.

The use of metaheuristic optimization algorithms (MOA) in structural optimization requires a number of analyses for evaluating the objective and constraint functions at each optimization step. An important characteristic of MOA, which makes them differ from mathematical programming algorithms, is that in place of a single design point MOA work simultaneously with a population of design points. This allows for a straightforward implementation of the optimization procedure in parallel computer environments (natural parallelization). In a massively distributed memory computing environment, however, this implementation cannot be realized for large-scale simulations since there is not enough memory at each processor to accommodate the full finite element model. A work by researchers at NTUA has proved that multi-level parallelism can be implemented for the exploitation of all available processors and for the feasibility check of design vectors. The DDM solvers will be specially tailored to address the specific demands of MOA methods and will be properly modified to exploit the capabilities of CPU/GPU computer platforms.

Furthermore, in RDO and RRDO, formulated in the framework of multi-objective problems, the computation of the complete Pareto front with feasible designs only, constitutes a very computationally challenging task. In an effort to achieve the desired feasible Pareto front, an efficient dynamic load-balancing algorithm for the optimum exploitation of the available computing resources will be proposed which will be adopted for improving the computational performance of the algorithms.

In all cases considered in the stochastic step of the probabilistic optimization problems, reliability analysis requires a cost-effective solution of repeated linear problems. This task will be formulated as a nearby problem combined with multiple right-hand sides and solved with customised solution methods exhibiting numerical and parallel scalability based on the P-DDM method. This approach drastically reduces the computational effort involved in the reliability analysis step, making the implementation of this type of stochastic analyses in computationally intensive optimization problems feasible.

WP/task leader: **NTUA**. Partners involved: **CIMNE, LUH-IKM, NTUA**

Starting date: month 7. Duration: 18 months

Lead beneficiary: **NTUA**

Lead beneficiary: **NTUA**

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