https://github.com/dino65-dev/pinn-physics-informed-nn-
PINNs can successfully incorporate physical laws to predict system behavior even when training data contains noise.
https://github.com/dino65-dev/pinn-physics-informed-nn-
Last synced: 10 months ago
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PINNs can successfully incorporate physical laws to predict system behavior even when training data contains noise.
- Host: GitHub
- URL: https://github.com/dino65-dev/pinn-physics-informed-nn-
- Owner: dino65-dev
- License: mit
- Created: 2025-05-27T09:16:59.000Z (about 1 year ago)
- Default Branch: main
- Last Pushed: 2025-05-27T09:33:13.000Z (about 1 year ago)
- Last Synced: 2025-05-27T10:29:59.360Z (about 1 year ago)
- Language: Jupyter Notebook
- Size: 77.1 KB
- Stars: 0
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Physics-Informed Neural Network (PINN) for Ball Trajectory
A simple PyTorch implementation of Physics-Informed Neural Networks (PINNs) applied to a fundamental physics problem - the trajectory of a ball under gravity.
## Problem Description
This project models the height of a ball over time, governed by the equation:
$$h(t) = h_0 + v_0t - 0.5gt^2$$
where:
- $h_0$ = 1.0 (initial height)
- $v_0$ = 10.0 (initial velocity)
- $g$ = 9.8 (acceleration due to gravity)
## Implementation
The PINN uses a simple feedforward neural network to learn the solution while respecting:
1. **Physics constraints**: The ODE $\frac{dh}{dt} = v_0 - gt$
2. **Initial condition**: $h(0) = h_0$
3. **Data fitting**: Limited noisy measurements
The loss function combines these constraints with tunable weights:
L = λ_data * L_data + λ_ode * L_ode + λ_ic * L_ic
## Features
- Automatic differentiation for computing derivatives in the physics loss
- Synthetic data generation with adjustable noise
- Visualization of PINN predictions against exact solution
- Adjustable hyperparameters for loss weighting
## Results
**The PINN demonstrates excellent performance throughout the entire trajectory:**
- The blue PINN prediction line closely tracks the black exact solution
- Strong agreement across all time points from t=0 to t=6
- The model successfully learns the physics despite the presence of noisy data
- Even in regions with sparse or noisy data points, the PINN maintains accuracy
- The trained PINN successfully recovers the true physics-based trajectory even with limited and noisy data points, demonstrating how incorporating physics into neural networks enhances their predictive power and generalization capabilities.