pypinn 1.0.1

1 Introduction

Physical Information Neural Network implemented using pytorch, Mainly to facilitate the solution of ordinary differential equations.

2 External dependencies for pypinn

torch, numpy, and tqdm.

3 Usage

3.1 step 1

Define a class that inherits from pypinn.Pinn, such as Net. Write the equation to be solved in the get_f function of Net. Here is an example:

import pypinn

import torch

import torch.nn as nn



class Net(pypinn.Pinn):

    def __init__(self, input_size: int, hidden_sizes: list, output_size: int, seed=0):

        super().__init__(input_size, hidden_sizes, output_size, seed)



    def get_f(self,x):

        y, dy = self.get_y_and_dy(x)

        f1 = dy[0]-y[1]

        f2 = dy[1]-(-y[1]-(2+torch.sin(x))*y[0])

        f3 = self.forward(torch.tensor([[0.0]])) - torch.tensor([[0,1]])

        return f1,f2,f3

The above example is used to solve a system of equations:

$$

\begin{cases}

\frac{\mathrm{d}y_1}{\mathrm{d}x} = y_2,\\

\frac{\mathrm{d}y_2}{\mathrm{d}x} = -y_2-(2+\sin x)y_1,\\

y_1(0)=0,y_2(0)=1.

\end{cases}

$$

Tips: dy[0], dy[1] represent $\frac{dy_1}{dx}, \frac{dy_2}{dx}$, y[0], y[1] represent $y_1, y_2$. The number of equations can theoretically be arbitrarily large.

3.2 step 2

Instantiate the class we defined, for example, set the number of input neurons to 1, the hidden layer to 20*20, and the number of output neurons to 2: mdl = Net(1,[20,20],2).

3.3 step 3

Configure the training data, loss function, optimizer, learning rate, number of iterations, and then use mdl.train(**settings) to train.

settings={

    'x': torch.linspace(0,6,301,requires_grad=True).view(-1,1),

    'loss_fn': nn.MSELoss(),

    'optimizer': torch.optim.Adam,

    'lr': 1e-3,

    'epochs': 5000

}

mdl.train(**settings)

3.4 step 4

After the model is trained, it can be visualized. Here is a simple example:

import matplotlib.pyplot as plt

t = torch.linspace(0,6,500).view(-1,1)

plt.plot(t,mdl.predict(t))

plt.show()

Update log

1.0.1 More detailed instructions have been added

1.0.0 first updata