physai 2.1.0

Physics-Informed Neural Network (PINN) library for solving ODEs/PDEs with visualization and training tools

PhysAI - Physics-Informed Neural Networks (PINNs)

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Overview

PhysAI is a Python package for solving ordinary differential equations (ODEs) and partial differential equations (PDEs) using Physics-Informed Neural Networks (PINNs). It integrates physics directly into neural network training, allowing the solution of classic physics problems without relying on traditional numerical solvers.

PhysAI supports a wide range of physics problems including:

• ODEs: Logistic growth, Newton’s law of cooling, damped/simple harmonic oscillators, Markov processes.
• PDEs: Heat equation, wave equation, Burgers' equation, KdV equation, convection-diffusion.
• Quantum Mechanics: Schrödinger equation.
• Electromagnetism & Quantum Phenomena: Planck’s law, photoelectric effect.
• Fluid Dynamics: 2D incompressible Navier-Stokes.
• Static Problems: Laplace and Poisson equations (2D/3D).

Key features:

• Flexible PDE/ODE residual computation for various physics laws.
• Mixed-precision training for faster computation on GPUs.
• Gradient clipping and learning rate schedulers supported.
• Visualization and animations of solutions using matplotlib.
• Weighted loss functions combining residual and boundary conditions.

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Installation

Clone the repository and install dependencies:

git clone https://github.com/yourusername/physai.git
cd physai
pip install -r requirements.txt

Python >= 3.10 recommended.

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Repository Structure

physai/
├── __init__.py
├── models.py          # PINN neural network class
├── trainer.py         # trainer cls for PINNs
├── visualization.py
├── pde_residual.py    # residuals for ODEs/PDEs
├── losses.py
├── utils.py 
examples/              
├── example_schrodinger.py
├── example_newton_cooling.py
├── example_markov.py
├── example_photoelectric.py
├── example_planck.py
README.md             
requirements.txt      
.gitignore             

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Quick Start Example

import torch
from physai.models import PINN
from physai.pde_residual import pde_residual
from physai.losses import pinn_loss
from physai.visualization import plot_1d_solution

# Define a 1D logistic growth ODE
def logistic(x, y):
    r, K = 1.0, 1.0
    return torch.autograd.grad(y, x, grad_outputs=torch.ones_like(y), create_graph=True)[0] - r*y*(1 - y/K)

# Create a PINN model
model = PINN(layers=[1, 20, 20, 1], activation='tanh')

# Training points
x_train = torch.linspace(0, 5, 100).reshape(-1,1)

# Train the model
from physai.trainer import Trainer
trainer = Trainer(model, collocation_points=x_train, pde_type='logistic')
history = trainer.train(epochs=500, lr=1e-3)

# Plot solution
plot_1d_solution(model, x_train, title='Logistic Growth')

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Training a PDE Example: 1D Heat Equation

import torch
from physai.models import PINN
from physai.trainer import Trainer
from physai.visualization import animate_2d

# PINN model
model = PINN(layers=[2, 50, 50, 1], activation='tanh')

# Collocation points
x = torch.linspace(0, 1, 50).reshape(-1,1)
t = torch.linspace(0, 2, 50).reshape(-1,1)
inputs = torch.cartesian_prod(x.squeeze(), t.squeeze())
inputs = inputs.float()

# Trainer
trainer = Trainer(model, collocation_points=inputs, pde_type='heat')
history = trainer.train(epochs=1000, lr=1e-3)

# Animate solution
animate_2d(model, x, t, title='Heat Equation Evolution')

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Physics Problems Supported

Type	Equations / Laws
ODE	Logistic Growth, Simple/Damped Harmonic Oscillator, Newton's Law of Cooling, Markov Chains
PDE	Heat Equation, Wave Equation, Burgers', KdV, Convection-Diffusion, Laplace, Poisson
Quantum	Schrödinger Equation, Planck's Law
Quantum/Electromag	Photoelectric Effect
Fluid Dynamics	2D Incompressible Navier-Stokes
3D PDEs	Laplace 3D, Poisson 3D

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Visualization

• 1D plots: plot_1d_solution(model, x)
• 2D surface plots: plot_2d_surface(model, X, Y)
• Animation over time: animate_2d(model, x, t)
• Training loss plots: plot_loss(trainer.history)

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Advanced Features

• Mixed precision training for faster GPU computation
• Gradient clipping
• Flexible learning rate scheduling
• Weighted PINN loss for custom PDE/BC importance
• Supports custom potentials (V(x,t)) for Schrödinger equation

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Citation / Usage in Papers

If you use PhysAI in your research, please cite it as:

@misc{PhysAI2025,
  author = {Mankrit Singh},
  title = {PhysAI: Physics-Informed Neural Networks in PyTorch},
  year = {2025},
  howpublished = {\url{https://github.com/MS-AGI/PhysAI}
}

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License

MIT License. See LICENSE file.

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Solve physics problems with PINNs and visualize them interactively!