Difference between revisions of "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations"

From statwiki
Jump to: navigation, search
(Introduction)
(Introduction)
Line 4: Line 4:
 
== Introduction ==
 
== Introduction ==
  
In recent years, there has been an enormous growth in the amount of data and computing power available to researchers. Unfortunately, for many real-world scenarios, the cost of data acquisition is simply too high to collect an amount of data sufficient to guarantee robustness or convergence of training algorithms. In such situations, researchers are faced with the challenge of trying to generate results based on partial or incomplete datasets. The authors refer to these situations as \textit{small data regime}
+
In recent years, there has been an enormous growth in the amount of data and computing power available to researchers. Unfortunately, for many real-world scenarios, the cost of data acquisition is simply too high to collect an amount of data sufficient to guarantee robustness or convergence of training algorithms. In such situations, researchers are faced with the challenge of trying to generate results based on partial or incomplete datasets.
 +
 
 +
Luckily, for problems that we have data for, we also have a vast amount of prior-known information. this prior-known information often manifests in the form of mathematical models, specifically partial differential equations (PDEs). The authors provide a technique where a PDE model of a physical system can be used as a regularization agent that constrains the space of admissible solutions to a manageable size. This technique effectively artificially enhances the size of the dataset, allowing the optimization to converge more quickly and more accurately to the solution even when only a few training examples are available.
  
 
== Another Section ==
 
== Another Section ==
 
Weeee
 
Weeee

Revision as of 14:08, 13 November 2020

Presented by

Cameron Meaney

Introduction

In recent years, there has been an enormous growth in the amount of data and computing power available to researchers. Unfortunately, for many real-world scenarios, the cost of data acquisition is simply too high to collect an amount of data sufficient to guarantee robustness or convergence of training algorithms. In such situations, researchers are faced with the challenge of trying to generate results based on partial or incomplete datasets.

Luckily, for problems that we have data for, we also have a vast amount of prior-known information. this prior-known information often manifests in the form of mathematical models, specifically partial differential equations (PDEs). The authors provide a technique where a PDE model of a physical system can be used as a regularization agent that constrains the space of admissible solutions to a manageable size. This technique effectively artificially enhances the size of the dataset, allowing the optimization to converge more quickly and more accurately to the solution even when only a few training examples are available.

Another Section

Weeee