El‐Ghazali Talbi

El-ghazali Talbi

Neuromorphic computing (NC) introduces a novel algorithmic paradigm representing a major shift from traditional digital computing of Von Neumann architectures. NC emulates or simulates the neural dynamics of brains in the form of Spiking Neural Networks (SNNs). Much of the research in NC has concentrated on machine learning applications and neuroscience simulations. This paper investigates the modelling and implementation of optimization algorithms and particularly metaheuristics using the NC paradigm as an alternative to Von Neumann architectures, leading to breakthroughs in solving optimization problems. Neuromorphic-based metaheuristics (Nheuristics) are supposed to be characterized by low power, low latency and small footprint. Since NC systems are fundamentally different from conventional Von Neumann computers, several challenges are posed to the design and implementation of Nheuristics. A guideline based on a classification and critical analysis is conducted on the different families of metaheuristics and optimization problems they address. We also discuss future directions that need to be addressed to expand both the development and application of Nheuristics.

Ali Hebbal, Loic Brevault, Mathieu Balesdent et al.

Multi-fidelity approaches combine different models built on a scarce but accurate data-set (high-fidelity data-set), and a large but approximate one (low-fidelity data-set) in order to improve the prediction accuracy. Gaussian Processes (GPs) are one of the popular approaches to exhibit the correlations between these different fidelity levels. Deep Gaussian Processes (DGPs) that are functional compositions of GPs have also been adapted to multi-fidelity using the Multi-Fidelity Deep Gaussian process model (MF-DGP). This model increases the expressive power compared to GPs by considering non-linear correlations between fidelities within a Bayesian framework. However, these multi-fidelity methods consider only the case where the inputs of the different fidelity models are defined over the same domain of definition (e.g., same variables, same dimensions). However, due to simplification in the modeling of the low-fidelity, some variables may be omitted or a different parametrization may be used compared to the high-fidelity model. In this paper, Deep Gaussian Processes for multi-fidelity (MF-DGP) are extended to the case where a different parametrization is used for each fidelity. The performance of the proposed multifidelity modeling technique is assessed on analytical test cases and on structural and aerodynamic real physical problems.

Ali Hebbal, Loic Brevault, Mathieu Balesdent et al.

Bayesian Optimization using Gaussian Processes is a popular approach to deal with the optimization of expensive black-box functions. However, because of the a priori on the stationarity of the covariance matrix of classic Gaussian Processes, this method may not be adapted for non-stationary functions involved in the optimization problem. To overcome this issue, a new Bayesian Optimization approach is proposed. It is based on Deep Gaussian Processes as surrogate models instead of classic Gaussian Processes. This modeling technique increases the power of representation to capture the non-stationarity by simply considering a functional composition of stationary Gaussian Processes, providing a multiple layer structure. This paper proposes a new algorithm for Global Optimization by coupling Deep Gaussian Processes and Bayesian Optimization. The specificities of this optimization method are discussed and highlighted with academic test cases. The performance of the proposed algorithm is assessed on analytical test cases and an aerospace design optimization problem and compared to the state-of-the-art stationary and non-stationary Bayesian Optimization approaches.