akenji's lab

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

Continuing from yesterday, I tried the book example (Chapter 4 of the book). It was quite interesting.

Introduction

Yesterday, I installed OpenFOAM and ParaView and tried to simulate and visualize a Poiseuille flow (Hagen-poiseuille flow). This time, I followed the book and ran “cavity” from the OpenFOAM built-in tutorial.

Motivation

I have been working on PINNs since the end of last year and have attempted two problems. I am planning to select and work on problems in the field of fluid dynamics. In fact, I am working on incompressible flow around a cylinder, but I have been stuck for a week because I can’t figure out how to relate the output of the model to the differential equations (the key part of PINNs).

I decided to learn a bit of OpenFOAM if I am going to work on the fluid dynamics area, so I installed OpenFOAM, ParaView, and tried the examples.

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

It has already been a week since I created the knowledge graph in my local environment and started building the GraphRAG environment. It is finally in a decent working condition. This post is a summary of GraphRAC using Ollama and neo4j that I built in my local environment.