A deep learning solution approach for high-dimensional random differential equations

• Published in: Probabilistic engineering mechanics Vol. 57; pp. 14 - 25
• Main Authors: Nabian, Mohammad Amin, Meidani, Hadi
• Format: Journal Article
• Language: English
• Published: Barking Elsevier Ltd 01.07.2019; Elsevier Science Ltd
• Subjects: Algorithms; Artificial neural networks; Conduction heating; Conductive heat transfer; Curse of dimensionality; Deep learning; Deep neural networks; Finite element analysis; Least squares; Meshless methods; Monte Carlo simulation; Neural networks; Partial differential equations; Random differential equations; Residual networks; Stochastic models; Deep learning; Residual networks; Curse of dimensionality; Deep neural networks; Least squares; Random differential equations

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution approach for these problems based on deep learning. This approach is intrus...