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This paper proposes a gradient descent based optimization method that relies on automatic differentiation for the computation of gradients. The method uses tools and techniques originally developed in the field of artificial neural networks…
This research concerns design optimization problems involving numerous design parameters and large computational models. These problems generally consist in non-convex constrained optimization problems in large and sometimes complex search…
A generic algorithm for the extraction of probabilistic (Bayesian) information about model parameters from data is presented. The algorithm propagates an ensemble of particles in the product space of model parameters and outputs. Each…
We propose an optimization algorithm to improve the design and performance of quantum communication networks. When physical architectures become too complex for analytical methods, numerical simulation becomes essential to study quantum…
The objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for…
In this paper we consider a continuous description based on stochastic differential equations of the popular particle swarm optimization (PSO) process for solving global optimization problems and derive in the large particle limit the…
We consider distributed optimization problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We develop unbiased parameter averaging methods for randomized second order optimization…
A new approach to the solution of Economic Dispatch using Particle Swarm Optimization is presented. It is the progression of allocating production amongst the dedicated units such that the restriction forced are fulfilled and the power…
A major obstacle to non-convex optimization is the problem of getting stuck in local minima. We introduce a novel metaheuristic to handle this issue, creating an alternate Hamiltonian that shares minima with the original Hamiltonian only…
Global optimization of black-box functions from noisy samples is a fundamental challenge in machine learning and scientific computing. Traditional methods such as Bayesian Optimization often converge to local minima on multi-modal…
We present an instance of the optimal sensor scheduling problem with the additional relaxation that our observer makes active choices whether or not to observe and how to observe. We mask the nodes in a directed acyclic graph of the model…
For a time-limited version of the H$_2$ norm defined over a fixed time interval, we obtain a closed form expression of the gradients. After that, we use the gradients to propose a time-limited model order reduction method. The method…
In this paper, we generalize existing frameworks for $\mathcal{H}_2\otimes\mathcal{L}_2$-optimal model order reduction to a broad class of parametric linear time-invariant systems. To this end, we derive first-order necessary ptimality…
Learning new representations of input observations in machine learning is often tackled using a factorization of the data. For many such problems, including sparse coding and matrix completion, learning these factorizations can be…
Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…
Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to…
Global optimization, particularly for non-convex functions with multiple local minima, poses significant challenges for traditional gradient-based methods. While metaheuristic approaches offer empirical effectiveness, they often lack…
Hyper-parameter optimization is one of the most tedious yet crucial steps in training machine learning models. There are numerous methods for this vital model-building stage, ranging from domain-specific manual tuning guidelines suggested…
This paper considers simulation-based optimization of the performance of a regime-switching stochastic system over a finite set of feasible configurations. Inspired by the stochastic fictitious play learning rules in game theory, we propose…
We present a unified dynamical mean-field theory for stochastic self-organized critical models. We use a single site approximation and we include the details of different models by using effective parameters and constraints. We identify the…