Unraveling the Design Pattern of Physics-Informed Neural Networks: Series 01
In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a remarkable approach that combines the power of neural networks with insights from fundamental physical laws. As I immersed myself in this field, I often feel overwhelmed by the vast number of research papers and various techniques they proposed. Navigating through this sea of information became a challenging task, especially when I wanted to find the most effective solutions for my specific problems.
My personal journey and experiences have sparked the idea of starting this blog series: my idea is that, in each blog post, I will focus on one or several research papers and distill their contributions into easily understandable insights. My hope is that this blog series could serve as a structured map that PINN practitioners can rely on, to identify the most suitable techniques for specific challenges at hand, stay updated with the latest advancements, and navigate the world of PINNs more confidently.
So, how should this distillation process look like? Personally, I find the concept of Design Patterns to be a very nice framework:
Design pattern refers to reusable solutions to commonly occuring problems that have been tested and proven to be effective. Design patterns provide a template for solving these problems, which can be adapted to different situations as needed. They serve as best practices, capturing the collective knowledge and experience of experts in the field.
Therefore, this blog series will go beyond traditional paper reviews. It will serve as an organized catalog, encompassing:
- the problem, the specific problem the proposed strategy is trying to address;
- the solution, the key components of the proposed strategy, how it is implemented, and why it might work;
- the benchmark, what physical problems are evaluated, and what's the associated performance;
- the strengths & weaknesses, under which conditions the proposed strategy can be effective, while also highlighting its potential limitations;
- the alternatives, other approaches proposed to address a similar problem, thus providing a broader perspective on potential solutions.
I hope this approach resonates with you, as it truly reflects my passion for organizing knowledge and making it accessible. Without further ado, let's embark on this exciting journey together by exploring the first PINN paper, where we will focus on creating better residual points for PINN training.
As this series continues to expand, the collection of PINN design patterns grows even richer
