Deep learning based numerical approximation algorithms for stochastic partial differential equations

arXiv:2012.01194 · math.NA, cs.LG, cs.NA, math.PR, stat.ML · Submitted 2020-12-02 · Read on arXiv

math.NA, cs.LG, cs.NA, math.PR, stat.ML

Submitted: 2020-12-02

Updated: 2026-09-01

Code: https://github.com/seb-becker/deep_spde

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Trace — 11× in this paper · explained in 2 episodes
• Adam — 5× in this paper · explained in 2 episodes
• Activation Function — 2× in this paper · explained in 1 episode
• Bayesian Inference — 1× in this paper · explained in 5 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Covariate Shift — 1× in this paper · explained in 2 episodes
• Diffusion Processes — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Loss Function — 1× in this paper · explained in 2 episodes
• Neural Network Approximation — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Robustness — 1× in this paper · explained in 5 episodes

Sources

• Solving Backward Doubly Stochastic Differential Equations through Splitting Schemes
• A modified semi--implict Euler-Maruyama Scheme for finite element discretization of SPDEs with additive noise

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