Related papers: Efficient Approximation of Expected Hypervolume Im…
This paper presents a novel learning-based approach to construct a surrogate problem that approximates a given parametric nonconvex optimization problem. The surrogate function is designed to be the minimum of a finite set of functions,…
We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput.,…
Numerical simulations are crucial for modeling complex systems, but calibrating them becomes challenging when data are noisy or incomplete and likelihood evaluations are computationally expensive. Bayesian calibration offers an interesting…
The surrogate-assisted optimization algorithm is a promising approach for solving expensive multi-objective optimization problems. However, most existing surrogate-assisted multi-objective optimization algorithms have three main drawbacks:…
Bayesian optimization is a sample-efficient approach to solving global optimization problems. Along with a surrogate model, this approach relies on theoretically motivated value heuristics (acquisition functions) to guide the search…
Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a…
The celebrated Monte Carlo method estimates an expensive-to-compute quantity by random sampling. Bandit-based Monte Carlo optimization is a general technique for computing the minimum of many such expensive-to-compute quantities by adaptive…
This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…
Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…
In this work, we present a trust-region optimization framework that employs Hermite kernel surrogate models. The method targets optimization problems with computationally demanding objective functions, for which direct optimization is often…
In this paper, an efficient solver for the Helmholtz equation using a noval approximation space is developed. The ingradients of the method include the approximation space recently proposed, a discontinuous Galerkin scheme extensively used,…
Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel…
Numerical methods for the optimal feedback control of high-dimensional dynamical systems typically suffer from the curse of dimensionality. In the current presentation, we devise a mesh-free data-based approximation method for the value…
Estimating the number of eigenvalues located in a given interval of a large sparse Hermitian matrix is an important problem in certain applications and it is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often an…
Electric machine design optimization is a computationally expensive multi-objective optimization problem. While the objectives require time-consuming finite element analysis, optimization constraints can often be based on mathematical…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
This paper presents a particle swarm optimization algorithm that leverages surrogate modeling to replace the conventional global best solution with the minimum of an n-dimensional quadratic form, providing a better-conditioned dynamic…
We present an algorithmic solution to the problem of incremental belief updating in the context of Monte Carlo inference in Bayesian statistical models represented by probabilistic programs. Given a model and a sample-approximated…
We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational…
Multi-objective Bayesian optimization (MOBO) provides a principled framework for optimizing expensive black-box functions with multiple objectives. However, existing MOBO methods often struggle with coverage, scalability with respect to the…