Related papers: Koopman analysis of combinatorial optimization pro…
We consider optimization problems with uncertain constraints that need to be satisfied probabilistically. When data are available, a common method to obtain feasible solutions for such problems is to impose sampled constraints, following…
In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…
This paper presents a framework to tackle constrained combinatorial optimization problems using deep Reinforcement Learning (RL). To this end, we extend the Neural Combinatorial Optimization (NCO) theory in order to deal with constraints in…
While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. As an extension of the naive Monte Carlo method, the…
Diagrammatic expansions are a paradigmatic and powerful tool of quantum many-body theory. Their evaluation to high order, e.g., by the Diagrammatic Monte Carlo technique, can provide unbiased results in strongly correlated and challenging…
The recently introduced backward Monte-Carlo method [Johan Carlsson, arXiv:math.NA/0010118] is validated, benchmarked, and compared to the conventional, forward Monte-Carlo method by analyzing the error in the Monte-Carlo solutions to a…
We propose an efficient Monte Carlo algorithm for simulating a ``hardly-relaxing" system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replica is…
We develop a Monte Carlo scheme for sampling series of Feynman diagrams for the proper self-energy which are self-consistently expressed in terms of renormalized particle propagators. This approach is used to solve the problem of a single…
This paper addresses optimization problems constrained by partial differential equations with uncertain coefficients. In particular, the robust control problem and the average control problem are considered for a tracking type cost…
In order to find the equilibrium geometries of molecules and solids and to perform ab initio molecular dynamics, it is necessary to calculate the forces on the nuclei. We present a correlated sampling method to efficiently calculate…
We are interested in ensemble methods to solve multi-objective optimization problems. An ensemble Kalman method is proposed to solve a formulation of the nonlinear problem using a weighted function approach. An analysis of the mean field…
A large number and diversity of techniques have been offered in the literature in recent years for solving multi-label classification tasks, including classifier chains where predictions are cascaded to other models as additional features.…
We present a technique that enables the evaluation of perturbative expansions based on one-loop-renormalized vertices up to large expansion orders. Specifically, we show how to compute large-order corrections to the random phase…
This paper presents a Markov chain Monte Carlo method to generate approximate posterior samples in retrospective multiple changepoint problems where the number of changes is not known in advance. The method uses conjugate models whereby the…
Quantum Monte Carlo simulations, while being efficient for bosons, suffer from the "negative sign problem'' when applied to fermions - causing an exponential increase of the computing time with the number of particles. A polynomial time…
In this thesis I discuss combinatorial optimization problems, from the statistical physics perspective. The starting point are the motivations which brought physicists together with computer scientists and mathematicians to work on this…
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…
Indirect imaging problems in biomedical optics generally require repeated evaluation of forward models of radiative transport, for which Monte Carlo is accurate yet computationally costly. We develop a novel approach to reduce this…
The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…
The theory of stochastic resetting asserts that restarting a search process at certain times may accelerate the finding of a target. In the case of a classical diffusing particle trapped in a potential well, stochastic resetting may…