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Machine Learning and Computational Mathematics
Weinan E
Neural network-based machine learning is capable of approximating functions in very high dimension with unprecedented efficiency and accuracy. This has opened up many exciting new…
Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning
Weinan E, Jiequn Han, Arnulf Jentzen
In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonli…
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
Christian Beck, Weinan E, Arnulf Jentzen
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (C…
On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations
Weinan E, Martin Hutzenthaler, Arnulf Jentzen +1
Parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) are key ingredients in a number of models in physics and financial engineerin…
Solving high-dimensional partial differential equations using deep learning
Jiequn Han, Arnulf Jentzen, Weinan E
Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult pr…
Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
Weinan E, Jiequn Han, Arnulf Jentzen
We propose a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, by making an analog…