Surrogate-based optimisation using adaptively scaled radial basis functions

Urquhart, Magnus; Ljungskog, Emil; Sebben, Simone

doi:10.1016/j.asoc.2019.106050

Cited by 55 publications

(23 citation statements)

References 23 publications

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“…Here we briefly return to the question of simulation and inference of a cell proliferation assay reported previously in Figures 4–7 where we sampled θ using a uniform distribution. We now repeat the simulations in Figure 4 by sampling θ using a Latin hypercube design [52], as illustrated in Figure 15(a). Results in Figure 15(b)–(d) confirm that sampling θ in this way allows us to perform accurate simulations with the continuum limit model for the same parameter combinations explored in Figure 4…”

Section: Figure 12mentioning

confidence: 99%

Reliable and efficient parameter estimation using approximate continuum limit descriptions of stochastic models

Simpson

Baker

Buenzli

et al. 2022

Preprint

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Stochastic mathematical models are attractive for modelling biological phenomena because they naturally capture stochasticity and variability that is often evident in biological data. Stochastic models also often allow us to track the motion of individuals within the population of interest. Unfortunately, capturing this microscopic detail means that simulation and parameter inference can become computationally expensive. One approach for overcoming this computational limitation is to coarse-grain the stochastic model to provide an approximate continuum model that can be solved using far less computational effort. However, coarse-grained continuum models can be biased or inaccurate, particularly for certain parameter regimes. In this work, we aim to combine stochastic and continuum mathematical models in the context of lattice-based models of two-dimensional cell biology experiments. In particular we focus on models of cell proliferation assays and barrier assays. Our approach involves building a simple statistical model of the discrepancy between a fine-scale stochastic model and its associated coarse-grained continuum model. We form this statistical model based on a limited number of expensive model evaluations at design points sampled from a user-chosen distribution, corresponding to a computer experiment design problem. With straightforward design point selection schemes, we show that using a statistical model of the discrepancy allows us to use the computationally inexpensive continuum model to carry out prediction and inference while correcting for biases and inaccuracies due to the continuum approximation. We demonstrate this approach by simulating a proliferation assay, where the continuum limit model is the well-known logistic equation, as well as a barrier assay where the continuum limit model is closely related to the well-known Fisher-KPP partial differential equation. We construct an approximate likelihood function for parameter inference, both with and without discrepancy correction terms. Using maximum likelihood estimation, we provide point estimates of the unknown parameters and profile likelihood to characterise the uncertainty in these estimates and form approximate confidence intervals. For the range of inference problems considered, working with the continuum limit model alone leads to biased parameter estimation and confidence intervals with poor coverage. In contrast, incorporating correction terms allows us to recover the parameters accurately with minimal computational overhead. The main tradeoff is that the associated confidence intervals are typically broader, reflecting the additional uncertainty introduced by the approximation process. All algorithms required to replicate the results in this work are written in the open source Julia language and are available on GitHub.

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Section: Figure 12mentioning

confidence: 99%

Reliable and efficient parameter estimation using approximate continuum limit descriptions of stochastic models

Simpson

Baker

Buenzli

et al. 2022

Preprint

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“…and thin plate spline with ϕ(r) = r 2 log r. Note that we keep the shape/width parameter for every individual RBF constant such as proposed by Urquhart et al [27]. Moreover, all shape parameters are fixed to = 1.…”

Section: Radial Basis Function Fitting and Interpolationmentioning

confidence: 99%

SAMO-COBRA: A Fast Surrogate Assisted Constrained Multi-objective Optimization Algorithm

Winter

Stein

Bäck

2021

Lecture Notes in Computer Science

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This paper proposes a novel Self-Adaptive algorithm for Multi-Objective Constrained Optimization by using Radial Basis Function Approximations, SAMO-COBRA. The algorithm automatically determines the best Radial Basis Function-fit as surrogates for the objectives as well as the constraints, to find new feasible Pareto-optimal solutions. The algorithm also uses hyper-parameter tuning on the fly to improve its local search strategy. In every iteration one solution is added and evaluated, resulting in a strategy requiring only a small number of function evaluations for finding a set of feasible solutions on the Pareto frontier. The proposed algorithm is compared to a wide set of other state-of-the-art algorithms (NSGA-II, NSGA-III, CEGO, SMES-RBF) on 18 constrained multi-objective problems. In the experiments we show that our algorithm outperforms the other algorithms in terms of achieved Hypervolume after given a fixed small evaluation budget. These results suggest that SAMO-COBRA is a good choice for optimizing constrained multi-objective optimization problems with expensive function evaluations.

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“…the 2-norm. The hyperparameter is usually chosen and imposed by the user and the same for all the functions but multiple hyperparameters are possible and their computation can be done by cross-validation [17]. The function r can classically be [16] •…”

Section: Nonlinear Terms Interpolationmentioning

confidence: 99%

Nonlinear Data-Driven Model Order Reduction Applied to Circuit-Field Magnetic Problem

Pierquin¹,

Henneron

2021

IEEE Trans. Magn.

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As in most of the domains in physics, finite element formulation is a very common method for electromagnetic fields computation. Since many years both proper orthogonal decomposition and empirical interpolation method are also often used in a model order reduction context. If these methods are efficients, their application is intrusive because it requires an access to the matrices and the assembly step. To avoid such an aspect, a data-driven model order reduction based on proper orthogonal decomposition with an approximation of the nonlinear terms by radial basis functions interpolation is applied to a magnetostatic problem coupled with circuit equations. The nonlinear reduced order model only needs solutions of a finite element analysis to be generated.

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Surrogate-based optimisation using adaptively scaled radial basis functions

Cited by 55 publications

References 23 publications

Reliable and efficient parameter estimation using approximate continuum limit descriptions of stochastic models

Reliable and efficient parameter estimation using approximate continuum limit descriptions of stochastic models

SAMO-COBRA: A Fast Surrogate Assisted Constrained Multi-objective Optimization Algorithm

Nonlinear Data-Driven Model Order Reduction Applied to Circuit-Field Magnetic Problem

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