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Stochastic optimization is a popular modeling paradigm for decision-making under uncertainty and has a wide spectrum of applications in management science, economics and engineering. However, the stochastic optimization models one faces in practice are int ...
We propose a simulation-based decision strategy for the proactive maintenance of complex structures with a particular application to structural health monitoring (SHM). The strategy is based on a data-driven approach which exploits an offline-online decomp ...
We consider a general discrete state-space system with both unidirectional and bidirectional links. In contrast to bidirectional links, there is no reverse transition along the unidirectional links Herein, we first compute the statistical length and the th ...
Many decision problems in science, engineering, and economics are affected by uncertainty, which is typically modeled by a random variable governed by an unknown probability distribution. For many practical applications, the probability distribution is onl ...
This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm’s convergence properties in non-convex problems. We first show that the sequence of iterates generated by SGD remains bounded and converges with prob ...
Fiber reinforced polymers are massively used as an alternative to metals in structural applications. The brittle nature of their matrix, however, makes them more susceptible to crack formation and propagation resulting in costly repair operations and incre ...
Combinatorial optimization (CO) problems are notoriously challenging for neural networks, especially in the absence of labeled instances. This work proposes an unsupervised learning framework for CO problems on graphs that can provide integral solutions of ...
Consider the surface quasi-geostrophic equation with random diffusion, white in time. We show global existence and uniqueness in high probability for the associated Cauchy problem satisfying a Gevrey type bound. This article is inspired by a recent work of ...
Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In this work, we show ...
In the last few years, the critical temperature (Tc) of several ITER cable-in-conduit conductors (CICC) was determined by magnetization measurements at zero current. The distribution of the critical temperatures (Tc), caused by variation of strain in the N ...