Noisy Expected Improvement under a Gaussian process prior converges at rate O(t^{-1/2} log^{(d+1)/2} t) for squared exponential kernels and O(t^{-nu/(2nu+d)} log^{nu/(2nu+d)} t) for Matérn kernels.
Optimization of process parameters in additive manufacturing based on the finite element method
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abstract
A design optimization framework for process parameters of additive manufacturing based on finite element simulation is proposed. The finite element method uses a coupled thermomechanical model developed for fused deposition modeling from the authors' previous work. Both gradient-based and gradient-free optimization methods are proposed. The gradient-based approach, which solves a PDE-constrained optimization problem, requires sensitivities computed from the fully discretized finite element model. We show the derivation of the sensitivities and apply them in a projected gradient descent algorithm. For the gradient-free approach, we propose two distinct algorithms: a local search algorithm called the method of local variations and a Bayesian optimization algorithm using Gaussian processes. To illustrate the effectiveness and differences of the methods, we provide two-dimensional design optimization examples using all three proposed algorithms.
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On the convergence rate of noisy Bayesian Optimization with Expected Improvement
Noisy Expected Improvement under a Gaussian process prior converges at rate O(t^{-1/2} log^{(d+1)/2} t) for squared exponential kernels and O(t^{-nu/(2nu+d)} log^{nu/(2nu+d)} t) for Matérn kernels.