Interval and fuzzy physics-informed neural networks for uncertain fields

• Author: Jan N Fuhg
• Organization: Cornell University

Here, we propose a physics-informed neural network approach to solve interval and fuzzy partial differential equations[1]. We call these solvers fuzzy physics-informed neural network (fPINN) and interval physics-informed neural network (iPINN). In contrast to finite element approaches, no correlation length specification of the input fields as well as no Monte-Carlo simulations are necessary. In fact, information about the input interval fields is obtained directly as a byproduct of the presented solution scheme. Furthermore, all major advantages of PINNs are retained, i.e. meshfree nature of the scheme, and ease of inverse problem set-up

Fig.1 - Fuzzy PINN process where each α-cut level requires one iPINN solution.

Fig.1 - Schematic overview of iPINN process.

Installation

This code requires an Anaconda or Miniconda environment with a recent Python version. The complete repository can be cloned and installed locally. It is recommended to create a conda environment before installation. This can be done by the following the command line instructions

$ git clone https://github.com/FuhgJan/intervalAndFuzzyPINN.git ./intervalAndFuzzyPINN
$ cd intervalAndFuzzyPINN
$ conda env create -f environment.yml
$ conda activate intervalAndFuzzyPINN
$ cd interval_PDE

The time-dependent PDE example can then be run with

$ python3 interval_PDE.py

Outputs will be written to mixedDEM/outputs/vtk_files/ and can be opened with paraview.

The conda environment can be closed with

$ conda deactivate

The conda environment can be deleted with

$ conda env remove --name intervalAndFuzzyPINN

Dependencies

The code requires the following packages as imports:

• NumPy for array handling
• torch for the neural network and automatic differentiation libraries
• MatPlotLib for graphical output

References

If you use part of this code consider citing:

[1] Jan N. Fuhg and Ioannis Kalogeris and Amélie Fau and Nikolaos Bouklas. "Interval and fuzzy physics-informed neural networks for uncertain fields". Probabilistic Engineering Mechanics (2022): 103240

License

This package comes with ABSOLUTELY NO WARRANTY. This is free software, and you are welcome to redistribute it under the conditions of the GNU General Public License (GPLv3)

The contents are published under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0)