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DGM: A deep learning algorithm for solving partial differential equations
High-dimensional PDEs have been a longstanding computational challenge. We propose a deep learning algorithm similar in spirit to Galerkin methods, using a deep neural network instead of linearExpand
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An investigation of earthquake induced pounding between adjacent buildings
The response of adjacent buildings in city blocks to several strong earthquakes is analysed, taking into account the mutual collisions, or pounding, resulting from insufficient or non-existingExpand
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Stochastic Gradient Descent in Continuous Time
TLDR
Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models. Expand
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Mean Field Analysis of Neural Networks: A Central Limit Theorem
We rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) large numbers ofExpand
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Mean Field Analysis of Neural Networks
Machine learning, and in particular neural network models, have revolutionized fields such as image, text, and speech recognition. Today, many important real-world applications in these areas areExpand
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An efficient ant colony optimization system for the manufacturing cells formation problem
An ant colony optimization (ACO) scheme for the manufacturing cells design problem is proposed, which uses a tight eigenvalue-based bound to guide and accelerate the search. This feature is combinedExpand
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Importance Sampling for Multiscale Diffusions
TLDR
We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Expand
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Default clustering in large portfolios: Typical events.
We develop a dynamic point process model of correlated default timing in a portfolio of firms, and analyze typical default profiles in the limit as the size of the pool grows. In our model, a firmExpand
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An optimal tree search method for the manufacturing systems cell formation problem
TLDR
A solution methodology producting exact solutions to the manufacturing systems cell formation problem is presented. Expand
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Performance Criteria for Liquid Storage Tanks and Piping Systems Subjected to Seismic Loading
In this paper, performance criteria for the seismic design of industrial liquid storage tanks and piping systems are proposed, aimed at defining a performance-based design framework towards reliableExpand
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