A Deep Dive into Physics-Informed Neural Networks: Modelling Quantum Wavefunctions

Introduction

In recent years, the fusion of deep learning and scientific computing has led to significant advancements in solving complex physical problems. One such breakthrough is the development of Physics-Informed Neural Networks (PINNs), a technique that leverages the power of neural networks while embedding physical laws directly into the learning process. This approach has proven particularly useful in solving partial differential equations (PDEs), which are ubiquitous in physics, engineering, and other scientific disciplines.

In this comprehensive guide, I will explore the method I’ve created that shows how PINNs can be applied to model the quantum wavefunction of a particle, a fundamental concept in quantum mechanics. We’ll begin with an in-depth discussion of the Schrödinger equation, the cornerstone of quantum theory. From there, we’ll dive into the mathematics behind the equation and how it governs the behavior of quantum systems. Finally, we’ll walk through the implementation of a PINN using TensorFlow, breaking down the code step by step to ensure a thorough understanding.

Whether you’re a physicist looking to integrate machine learning into your work or a data scientist eager to explore new frontiers, this guide will provide you…