Karel Crombecq

A Novel Hybrid Sequential Design Strategy for Global Surrogate Modeling of Computer Experiments

Many complex real-world systems can be accurately modeled by simulations. However, high-fidelity simulations may take hours or even days to compute. Because this can be impractical, a surrogate model is often used to approximate the dynamic behavior of the original simulator. This model can then be used as a cheap, drop-in replacement for the simulator. Because simulations can be very expensive, the data points, which are required to build the model, must be chosen as optimally as possible. Sequential design strategies offer a huge advantage over one-shot experimental designs because they can use information gathered from previous data points in order to determine the location of new data points. Each sequential design strategy must perform a trade-off between exploration and exploitation, where the former involves selecting data points in unexplored regions of the design space, while the latter suggests adding data points in regions which were previously identified to be interesting (for example, highly nonlinear regions). In this paper, a novel hybrid sequential design strategy is proposed which uses a Monte Carlo-based approximation of a Voronoi tessellation for exploration and local linear approximations of the simulator for exploitation. The advantage of this method over other sequential design methods is that it is independent of the model type, and can therefore be used in heterogeneous modeling environments, where multiple model types are used at the same time. The new method is demonstrated on a number of test problems, showing that it is a robust, competitive, and efficient sequential design strategy.

Efficient space-filling and non-collapsing sequential design strategies for simulation-based modeling

Simulated computer experiments have become a viable cost-effective alternative for controlled real-life experiments. However, the simulation of complex systems with multiple input and output parameters can be a very time-consuming process. Many of these high-fidelity simulators need minutes, hours or even days to perform one simulation. The goal of global surrogate modeling is to create an approximation model that mimics the original simulator, based on a limited number of expensive simulations, but can be evaluated much faster. The set of simulations performed to create this model is called the experimental design. Traditionally, one-shot designs such as the Latin hypercube and factorial design are used, and all simulations are performed before the first model is built. In order to reduce the number of simulations needed to achieve the desired accuracy, sequential design methods can be employed. These methods generate the samples for the experimental design one by one, without knowing the total number of samples in advance. In this paper, the authors perform an extensive study of new and state-of-the-art space-filling sequential design methods. It is shown that the new sequential methods proposed in this paper produce results comparable to the best one-shot experimental designs available right now.

A novel sequential design strategy for global surrogate modeling

In mathematical/statistical modeling of complex systems, the locations of the data points are essential to the success of the algorithm. Sequential design methods are iterative algorithms that use data acquired from previous iterations to guide future sample selection. They are often used to improve an initial design such as a Latin hypercube or a simple grid, in order to focus on highly dynamic parts of the design space. In this paper, a comparison is made between different sequential design methods for global surrogate modeling on a real-world electronics problem. Existing exploitation and exploration-based methods are compared against a novel hybrid technique which incorporates both an exploitation criterion, using local linear approximations of the objective function, and an exploration criterion, using a Monte Carlo Voronoi tessellation. The test results indicate that a considerable improvement of the average model accuracy can be achieved by using this new approach.

Sequential modeling of a low noise amplifier with neural networks and active learning

The use of global surrogate models has become commonplace as a cost effective alternative for performing complex high fidelity computer simulations. Due to their compact formulation and negligible evaluation time, global surrogate models are very useful tools for exploring the design space, what-if analysis, optimization, prototyping, visualization, and sensitivity analysis. Neural networks have been proven particularly useful in this respect due to their ability to model high dimensional, non-linear responses accurately. In this article, we present the results of an extensive study on the performance of neural networks as compared to other modeling techniques in the context of active learning. We investigate the scalability and accuracy in function of the number design variables and number of datapoints. The case study under consideration is a high dimensional, parametrized low noise amplifier RF circuit block.

Adaptive Sampling Algorithm for Macromodeling of Parameterized

This paper presents a new adaptive sampling strategy for the parametric macromodeling of -parameter-based frequency responses. It can be linked directly with the simulator to determine up front a sparse set of data samples that characterize the design space. This approach limits the overall simulation and macromodeling time. The resulting sample distribution can be fed into any kind of macromodeling technique, provided that it can deal with scattered data. The effectiveness of the approach is illustrated by a parameterized H-shaped microwave example.

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Simulating and optimizing complex physical systems is known to be a task of considerable time and computational complexity. As a result, metamodeling techniques for the efficient exploration of the design space have become standard practice since they reduce the number of simulations needed. However, conventionally such metamodels are constructed sequentially in a one-shot manner, without exploiting inherent parallelism. To tackle this inefficient use of resources we present an adaptive framework where modeler and simulator interact through a distributed environment, thus decreasing model generation and simulation turnaround time. This paper provides evidence that such a distributed approach for adaptive sampling and modeling is worthwhile investigating. Research in this new field can lead to even more innovative automated modeling tools for complex simulation systems.

-Parameter Responses

In this paper, the authors compare a Monte Carlo method and an optimization-based approach using genetic algorithms for sequentially generating space-filling experimental designs. It is shown that Monte Carlo methods perform better than genetic algorithms for this specific problem.

Adaptive distributed metamodeling

The use of computer simulations has become a viable alternative for real-life controlled experiments. Due to the computational cost of these high fidelity simulations, surrogate models are often employed as an approximation for the original simulator. Because of their compact formulation and negligible evaluation time, global surrogate models are very useful tools for exploring the design space, optimization, visualization and sensitivity analysis. Additionally, multiple surrogate models can be chained together to model large scale systems where the direct use of the original expensive simulators would be too cumbersome. Many surrogate model types, such as neural networks, support vector machines and rational models have been proposed, and many more techniques have been developed to minimize the number of expensive simulations required to train a sufficiently accurate surrogate model. In this chapter, we present a fully automated and integrated global surrogate modeling methodology for regression modeling and active learning that readily enables the adoption of advanced global surrogate modeling methods by application scientists. The work brings together insights from distributed systems, artificial intelligence, and modeling & simulation, and has applications in a very wide range of fields. The merits of this approach are illustrated with several examples, and several surrogate model types.

Generating sequential space-filling designs using genetic algorithms and Monte Carlo methods

In engineering design the use of approximation models (= surrogate models) has become standard practice for design space exploration, sensitivity analysis, visualization and optimization. Popular surrogate model types include neural networks, support vector machines, Kriging models, and splines. An engineering simulation typically involves multiple response variables that must be approximated. With many approximation methods available, the question of which method to use for which response consistently arises among engineers and domain experts. Traditionally, the different responses are modeled separately by independent models, possibly involving a comparison among model types. Instead, this paper proposes a multi-objective approach can benefit the domain expert since it enables automatic model type selection for each output on the fly without resorting to multiple runs. In effect the optimal model complexity and model type for each output is determined automatically. In addition a multi-objective approach gives information about output correlation and facilitates the generation of diverse ensembles. The merit of this approach is illustrated with a modeling problem from aerospace.

Automatic approximation of expensive functions with active learning

Simulation and optimization of complex mechanical and electronical systems is a very time consuming and computationally intensive task. Therefore, metamodeling techniques are often used for the efficient exploration of the design space, as they reduce the number of simulations needed. However, constructing such metamodels (or surrogate models) is typically done in a sequential fashion. In this paper we argue that this approach can still be improved. We propose a framework where modeler and simulator interact through a distributed environment, (using established grid computing techniques) thus decreasing model generation and simulation turnaround time.