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DGM: A deep learning algorithm for solving partial differential equations

- Justin A. Sirignano, K. Spiliopoulos
- Mathematics, Economics
- 24 August 2017

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 linear… Expand

492 66- PDF

An investigation of earthquake induced pounding between adjacent buildings

- S. Anagnostopoulos, K. Spiliopoulos
- Geology
- 1992

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-existing… Expand

220 7

Stochastic Gradient Descent in Continuous Time

- Justin A. Sirignano, K. Spiliopoulos
- Mathematics, Computer Science
- SIAM J. Financial Math.
- 17 November 2016

TLDR

29 4- PDF

Mean Field Analysis of Neural Networks: A Central Limit Theorem

- Justin A. Sirignano, K. Spiliopoulos
- Mathematics
- 28 August 2018

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 of… Expand

63 3- PDF

Mean Field Analysis of Neural Networks

- Justin A. Sirignano, K. Spiliopoulos
- Mathematics
- 2 May 2018

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 are… Expand

50 3- PDF

An efficient ant colony optimization system for the manufacturing cells formation problem

- K. Spiliopoulos, S. Sofianopoulou
- Engineering
- 1 March 2008

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 combined… Expand

42 3

Importance Sampling for Multiscale Diffusions

- P. Dupuis, K. Spiliopoulos, H. Wang
- Mathematics, Computer Science
- Multiscale Model. Simul.
- 27 July 2011

TLDR

60 3- PDF

Default clustering in large portfolios: Typical events.

- K. Giesecke, K. Spiliopoulos, R. Sowers
- Mathematics, Economics
- 10 April 2011

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 firm… Expand

69 3- PDF

An optimal tree search method for the manufacturing systems cell formation problem

- K. Spiliopoulos, S. Sofianopoulou
- Mathematics, Computer Science
- Eur. J. Oper. Res.
- 16 March 1998

TLDR

29 3- PDF

Performance Criteria for Liquid Storage Tanks and Piping Systems Subjected to Seismic Loading

- Maria Vathi, S. Karamanos, Ioannis A. Kapogiannis, K. Spiliopoulos
- Engineering
- 19 July 2015

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 reliable… Expand

21 3- PDF

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