Add Differentiable Physics: Mass-Spring System example

[AbhiLegend]

Summary

This PR adds a simple Differentiable Physics example implementing a Mass-Spring System using PyTorch.

• Particles are connected by springs and evolve under the influence of spring forces and gravity.
• The system is fully differentiable, allowing optimization of particle positions via gradient descent.
• Semi-implicit Euler integration is used for better numerical stability.
• The example does not require any external dependencies beyond PyTorch.

Files Added

• examples/differentiable_physics/mass_spring.py
• examples/differentiable_physics/README.md
• examples/differentiable_physics/requirements.txt

Features

• Training mode: Optimize particle positions to match a target configuration.
• Evaluation mode: Forward simulate without optimization.
• Particle 0 is pinned at (0,0) to prevent system drift.
• Gravity strength is customizable.
• Fully differentiable simulation with simple, clean code structure.

Testing

• Verified mass_spring.py runs successfully in both train and eval modes.
• Added a bash function to run_python_examples.sh for CI testing (5 epochs, 3 steps for quick test).
• Local testing was performed with Git Bash on Windows (python -m uv is used for compatibility).
• Confirmed loss convergence and expected particle behavior.

Notes

• Minor residual errors are expected due to the elasticity of springs and gravitational force.
• Example is designed to prioritize educational clarity and maintain a low dependency footprint.

Thank you for reviewing!

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[AbhiLegend]

@msaroufim I have just updated the example with PR, request you to check if it fits in the "differentiable physics" section