Scaling up Deep Learning for PDE-based Models

10/22/2018
by   Philipp Haehnel, et al.
0

In numerous applications, forecasting relies on numerical solvers for partial differential equations (PDEs). Although the use of deep-learning techniques has been proposed, the uses have been restricted by the fact the training data are obtained using PDE solvers. Thereby, the uses were limited to domains, where the PDE solver was applicable, but no further. We present methods for training on small domains, while applying the trained models on larger domains, with consistency constraints ensuring the solutions are physically meaningful even at the boundary of the small domains. We demonstrate the results on an air-pollution forecasting model for Dublin, Ireland.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/07/2022

A deep branching solver for fully nonlinear partial differential equations

We present a multidimensional deep learning implementation of a stochast...
research
04/27/2023

Learning Neural PDE Solvers with Parameter-Guided Channel Attention

Scientific Machine Learning (SciML) is concerned with the development of...
research
12/09/2022

PDE-LEARN: Using Deep Learning to Discover Partial Differential Equations from Noisy, Limited Data

In this paper, we introduce PDE-LEARN, a novel PDE discovery algorithm t...
research
07/01/2019

Lossy Compression for Large Scale PDE Problems

Solvers for partial differential equations (PDE) are one of the cornerst...
research
03/01/1999

An Algebraic Programming Style for Numerical Software and its Optimization

The abstract mathematical theory of partial differential equations (PDEs...
research
11/07/2022

Neural PDE Solvers for Irregular Domains

Neural network-based approaches for solving partial differential equatio...
research
02/15/2022

Lie Point Symmetry Data Augmentation for Neural PDE Solvers

Neural networks are increasingly being used to solve partial differentia...

Please sign up or login with your details

Forgot password? Click here to reset