January 3, 2025
My final year research project asks a question that sits at the intersection of two fields: Can we teach neural networks to solve physics problems by embedding physical laws directly into how they learn?
The approach is called Physics-Informed Neural Networks, or PINNs.
Here's the idea:
Traditional neural networks learn from data. You show them millions of examples, and they find patterns. But physics isn't just patterns in data. Physics is governed by equations. The Schrödinger equation tells us exactly how quantum systems behave. Newton's laws tell us exactly how objects move.
What if instead of just feeding a neural network data, we told it: "Whatever solution you find, it must satisfy these equations"?
That's a PINN. The physics is built into the loss function. The network can't cheat. It has to learn solutions that obey the laws of nature.
I'm applying this to quantum mechanics, specifically the Schrödinger equation. Three systems: - A particle trapped in a box (infinite square well) - A quantum harmonic oscillator - A double-well potential where quantum tunneling occurs
Why this matters:
Quantum mechanics governs how atoms and molecules behave. If you want to design new materials, new drugs, new quantum devices, you need to solve these equations. Traditional numerical methods work but have limitations. Machine learning offers a new computational paradigm.
The beautiful thing about PINNs is they're not replacing physics with AI. They're making AI respect physics. The neural network becomes a tool that already knows the rules of the universe.
There's something poetic about this.
We're teaching machines to think like physicists. Not by showing them textbooks, but by encoding the laws of nature into their learning process. The same equations that Schrödinger wrote down in 1926 are now embedded in silicon, guiding how artificial systems understand reality.
I don't know where this field goes. But I know the intersection of AI and physics is where some of the most interesting problems live.
And I like interesting problems.