PINN_PDE_ERROR

Provide 5 examples of solving PDEs, as well as constructing the error bounds.

Prerequisites

The project is built on MacbookPro M2 chip. Make sure you have the following installed on your system:

• Python 3.12.2
• pip3 (python package manager)

Installation

Follow these steps to set up your environment:

1. create python virtual environment run: python3 -m venv venv
2. activate python virtual environment run: source venv/bin/activate
3. install required packages run: pip3 install -r requirements.txt

Run Examples

1D OU process

The models are stored in the folder: examples/1d_ou/output/

The plots are saved in the folder: examples/1d_ou/figs/

• cd examples/1d_ou
• python main.py --train=0 (this will generate plots using pretrained models)
• python main.py --train=1 (this will train the models and generate plots)

1D State-dependent Dynamics

The models are stored in the folder: examples/1d_statedepend/exp1/main/output/

The plots are saved in the folder: examples/1d_statedepend/exp1/main/figs/

• cd examples/1d_statedepend
• python main.py --train=0 (this will generate plots using pretrained models)
• python main.py --train=1 (this will train the models and generate plots)

1D Nonlinear Dynamics

The models are stored in the folder: examples/1d_nonlinear/exp1/main/output/

The plots are saved in the folder: examples/1d_nonlinear/exp1/main/figs/

The data (of the Monte-Carlo simulation for "true" solution) is in the folder: examples/1d_nonlinear/exp1/data/

• cd examples/1d_nonlinear
• python main.py --train=0 (this will generate plots using pretrained models)
• python main.py --train=1 (this will train the models and generate plots)

2D Nonlinear Inverted Pendulum

The models are stored in the folder: examples/2d_nonlinear/exp1/main/output/

The plots are saved in the folder: examples/2d_nonlinear/exp1/main/figs/

The data (of the Monte-Carlo simulation for "true" solution) is in the folder: examples/2d_nonlinear/exp1/data/

• cd examples/2d_nonlinear
• python main.py --train=0 (this will generate plots using pretrained models)
• python main.py --train=1 (this will train the models and generate plots)

1D Heat Equation

The models are stored in the folder: examples/1d_heat/output/

The plots are saved in the folder: examples/1d_heat/figs/

• cd examples/1d_heat
• python main.py (this will train the models and generate plots)