PINNs

Introduction

Around this time last year, I spent two months working on a simulation of a two-dimensional cylindrical wake using PINNs. I hadn’t finished working on this article. This time, since I built a new Python development environment, I decided to tackle this theme as an example project, with Claude as my companion.

Introduction

Two months ago in this post, laminar flow around a 2D circular cylinder (Laminar Flow), using the governing equations for each of the ST and VP forms, The simulation was performed using the governing equations for each of the ST form and VP form.

Since then, we have simulated the flow around a 2-D cylinder in the time range 0 to 60 seconds for various parameters, and the results are summarized here.

Motivation

Since the end of last year, I have been studying PINNs, learning models using the PINNs method for 2-dimensional fluids, and using those models to make inferences. It was not easy to show the results of the paper I referred to, and I had some difficulties. As I wrote in the “Summary” section of this post, I was thinking of trying to predict the Karman’s vortex street using the PINNs method.

In the course of my research, I learned from this paper that “data-free PINNs are unable to predict vortex shedding”. If that is the case, I decided to try simulating the Karman’s vortex in OpenFOAM first.

This post is a summary of my simulation of the Karman’s vortex in OpenFOAM.

Introduction

In my previous post, I summarized the learning and inference results from PINNs for Laminar Flow (laminar flow) in the unsteady state, using the governing equations of ST (Stress Tensor) form. The results were different from those in the referenced paper.

Introduction.

In previous post, I reproduced the Laminar Flow of the transition state in PINNs using the governing equations of the VP form with reference to the paper, but the results were very different from the values in the reference paper. This time, I also performed it with the governing equations of ST form, and I will summarize the results in this post.

Introduction

I recently posted what was obtained by PINNs for steady-state laminar flow. This time, I applied the PINNs method to unsteady laminar flows. The results of this time are not correct and different from the results of the referenced paper. I am investigating the cause, but I do not know.

Introduction

I have been trying to simulate steady state laminar flows with PINNs since the end of last year, but I was stumped by the derivation of the Navier Stokes (NS) equations of Cauchy stress tensor type. I coded PINNs with the governing equations based on the Velocity-pressure type NS equations. I got a result that looks like it, and I will summarize it in this post.

Introduction

Recently, I summarized the mass, spring, and damper problem with PINNs. This time, I’ve worked on the Burgers’ equation and summarized it.

Motivation

I tried PINNs (Physics-Informed Neural Networks) with NVIDIA Modulus over a year ago, After that, it was completely untouched. I have heard Riken/Matsuoka-san’s talk at a recent seminar (AI for Science; here and here), I decided to study it again and tried to implement PINNs using a physically understandable problem as an example.

Introduction

Over a month ago, I became interested in NVIDIA Modulus at the How to Speed Up Simulation with AI Surrogate Models? seminar I attended, I became interested in NVIDIA Modulus, so I bought the book and started studying it. As a prerequisite for future study of Modulus, I installed Modulus in my environment, so I summarized the installation process as “Introduction to PINNs”.