Introduction to the Physics-based Deep Learning (PBDL) Book
The "Physics-based Deep Learning" book, commonly referred to as PBDL, serves as a comprehensive guide to integrating deep learning techniques with physical simulations. For those eager to dive into its content, the full version is accessible online at Physics-based Deep Learning and a single-PDF version is hosted on arXiv here.
Overview of the Book
PBDL is crafted to bridge the gap between the world of physical simulations and the powerful techniques of deep learning. The book provides a hands-on approach, offering Jupyter notebooks for practical understanding. By doing so, it emphasizes the application of deep learning in solving Partial Differential Equations (PDEs) while incorporating our foundational knowledge of physics and numerical methods.
The book delves into various approaches, including:
- Utilizing deep learning to tackle PDE problems.
- Merging deep learning with existing physics knowledge.
- Maintaining our understanding of numerical methods without replacing it entirely.
Focus Areas
The book primarily targets the following areas:
- Field-based Simulations: It concentrates on field-based methods over Lagrangian ones.
- Integration with Deep Learning: While there are numerous compelling machine learning (ML) techniques, this book specifically emphasizes the symbiosis with deep learning.
- Experimental Outlook: The book anticipates experiments that involve substituting synthetic data with real-world observations.
PBDL, as its name suggests, is about combining physical modeling and numeric simulations with neural networks. This hybrid approach is an emerging and exciting frontier in research, offering immense potential for transforming how simulations are conducted.
Objectives and Potential
A central aim of the book is to harness existing numeric techniques, blending them with deep learning to improve simulations. This fusion is especially beneficial when dealing with domain-specific problems, where leveraging pre-trained neural networks can significantly enhance performance over conventional solvers.
Recent Additions
For those familiar with earlier versions, PBDL v0.2 introduces:
- An expanded section on differentiable physics training.
- A new chapter dedicated to advanced learning methods for physics-related problems.
Featured Highlights
Some notable examples within the book include:
- Fluid Flow Solvers: A Jupyter notebook that demonstrates training hybrid fluid flow (Navier-Stokes) solvers via differentiable physics, which helps in reducing numerical errors. This can be explored here.
- Improved Learning Schemes: A notebook featuring a novel learning strategy that calculates update directions for both neural networks and physics, using half-inverse gradients. Try it here.
- Bayesian Neural Networks: Example code is provided for training Bayesian Neural Networks for RANS flow predictions around airfoils to estimate uncertainties, available here.
- Reinforcement Learning vs. Physics-based Learning: A comparative study on controlling PDEs using proximal policy-based reinforcement learning against physics-based learning indicates the latter's superior performance. Explore this through the notebook provided here.
This book is a treasure trove for anyone interested in pushing the boundaries of what's possible with simulation techniques, offering both theoretical insights and practical tools for innovation in this rapidly evolving field.