physai 4.0.0

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

PhysAI: Modular PyTorch Library with Built-In Residual PDEs, Automatic PINN Losses, and Visualization Tools for Complex ODE/PDE Solving

Major update! Now Supporting Gauss Law, Ampere Law, and many more equations in electromagnetism!!

THE POWER OF PHYSAI

This animation was generated only using PhysAI's built-in 2D Schrödinger Residual Function and trained on the pre-built PINN on just 500 Epochs!

Wavefunction |ψ(x,t)| evolution over time

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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

If you use PhysAI in your research, academic publication, or official work, citation is required.

Please cite the software as follows:

APA:

Singh, M. (2025). PhysAI: Physics-Informed Neural Networks in PyTorch (Version 2.5.7) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.17214725

BibTeX:

@software{singh_physai_2025,
  author       = {Mankrit Singh},
  title        = {PhysAI: Physics-Informed Neural Networks in PyTorch},
  month        = sep,
  year         = 2025,
  publisher    = {Zenodo},
  version      = {2.5.7},
  doi          = {10.5281/zenodo.17214725},
  url          = {https://doi.org/10.5281/zenodo.17214725}
}

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License

Apache License. See LICENSE file.

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Important Notice: Ethical Use Required
This software must not be used for malicious, illegal, or unethical purposes.
Misuse of the library voids your license under the Ethical Use Clause.

Solve physics problems with PINNs and visualize them interactively!