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Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…
We propose a multi-fidelity neural network surrogate sampling method for the uncertainty quantification of physical/biological systems described by ordinary or partial differential equations. We first generate a set of low/high-fidelity…
Modern safety-critical systems are heterogeneous, complex, and highly dynamic. They require reliability evaluation methods that go beyond the classical static methods such as fault trees, event trees, or reliability block diagrams.…
In this contribution, we develop an efficient surrogate modeling framework for simulation-based optimization of enhanced oil recovery, where we particularly focus on polymer flooding. The computational approach is based on an adaptive…
In this note, we present a derivative-free trust-region (TR) algorithm for reliability based optimization (RBO) problems. The proposed algorithm consists of solving a set of subproblems, in which simple surrogate models of the reliability…
Reliable, risk-averse design of complex engineering systems with optimized performance requires dealing with uncertainties. A conventional approach is to add safety margins to a design that was obtained from deterministic optimization.…
Ensuring safety in industrial control systems usually involves imposing constraints at the design stage of the control algorithm. Enforcing constraints is challenging if the underlying functional form is unknown. The challenge can be…
The optimization of large-scale multibody systems is a numerically challenging task, in particular when considering multiple conflicting criteria at the same time. In this situation, we need to approximate the Pareto set of optimal…
Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven…
This paper aims to motivate stochastic optimization problems from a statistical perspective and a statistical learning perspective, where the goal is to maximize the log-likelihood or minimize the population risk. We briefly describe the…
Random microstructures of heterogeneous materials play a crucial role in the material macroscopic behavior and in predictions of its effective properties. A common approach to modeling random multiphase materials is to develop so-called…
We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical…
Evaluating failure probability for complex engineering systems is a computationally intensive task. While the Monte Carlo method is easy to implement, it converges slowly and, hence, requires numerous repeated simulations of a complex…
Recent developments of advanced driver-assistance systems necessitate an increasing number of tests to validate new technologies. These tests cannot be carried out on track in a reasonable amount of time and automotive groups rely on…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…
Variational quantum algorithms are a leading candidate for early applications on noisy intermediate-scale quantum computers. These algorithms depend on a classical optimization outer-loop that minimizes some function of a parameterized…
Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…
We show that deliberately introducing a nested simulation stage can lead to significant variance reductions when comparing two stopping times by Monte Carlo. We derive the optimal number of nested simulations and prove that the algorithm is…
We consider the problem of forecasting debt recovery from large portfolios of non-performing unsecured consumer loans under management. The state of the art in industry is to use stochastic processes to approximately model payment behaviour…
We propose a variant of the Simulated Annealing method for optimization in the multivariate analysis of differentiable functions. The method uses global actualizations via the Hybrid Monte Carlo algorithm in their generalized version for…