A neural network study of the nonlinear evolution dynamics in a planetary atmosphere: large-scale vortex and the governing equation

JAXA Supercomputer System Annual Report February 2025-January 2026

Report Number: R25EACA64

Subject Category: JSS Inter-University Research

Responsible Representative: Nobuyuki Sawado, Professor, Tokyo University of Science
Contact Information: Nobuyuki Sawado(sawadoph@rs.tus.ac.jp)
Members: Nobuyuki Sawado, Yuichiro Shimazaki, Yuta Suzuki

Abstract

Mathematical models that describe phenomena of planetary atmosphere and related subjects enjoying the chaotic property are closely related to nonlinear partial differential equation (PDE) in (quasi-)integrable systems. We try to give a formal mathematical characterization of the relationship between various (quasi-)integrable PDEs and these models of fluid mechanics. In terms of the Physics Informed Neural Networks (PINNs), we investigate several PDEs of the forward analysis and of the parameter discovery. Our aim in this study is to propose a unified scheme for analyzing nonlinear PDEs by means of PINNs sparse learning algorithms.

Reference URL

N/A

Reasons and benefits of using JAXA Supercomputer System

Since the research group with which we have collaborated have an account on the JAXA supercomputing system, we think it desirable to use this.

Achievements of the Year

We continuously preparations for implementing the PINNs analysis. Such as nvcr.io_nvidia_Tensorflow, Adam, L-BFGS were activated. We studied the forward analysis of the nonlinear Schroedinger equation and obtained several soliton solutions. Particularly, condition of emergence of the ｃhaos was extensively studied in this method. The quasi-integrable system such as the Zakharov-Kuznetsov equation was successfully analyzed by means of the PINNs. For the inverse analysis using PINNs, we primarily focused on parameter discovery between the ZK equation and the regularized version of long-wave equation.

Publications

- Peer-reviewed papers

1) A.Nakamula, K.Obuse, N.Sawado, K.Shimasaki, Y.Shimazaki, Y.Suzuki, K.Toda, "Discovery of Quasi-Integrable equations from traveling-wave data using the Physics-Informed Neural Networks", Phys.Scripta 100 (2025) 5, 056012.

2) N.Sawado, Y.Shimazaki, Y.Suzuki, "PINNs Study for the Bekki–Nozaki Chaos in the Nonlinear Schrödinger equation", J.Phys.Conf.Ser. 3152 (2025) 1, 012032

- Invited Presentations

N.Sawado, "A study of a quasi-integrable system and the dynamical vortex ― to be DIFC, or not to be ―", Nonperturbative methods in QFTs ― Kondo Condensation ― March 25, 2025

- Oral Presentations

1) Yuichiro Shimazaki, Nobuyuki Sawado, Yuta Suzuki, "PINNs Study for the Bekki-Nozaki Chaos", The XXIX International Conference on Integrable Systems and Quantum Symmetries, July 11, 2025.

2)Y.Shimazaki, N.Sawado, "A Modified Conserved Quantity of the Zakharov--Kuznetsov Equation", SBREW (Soliton BREakthrough Workshop)-EAST2026, March 16, 2026.

- Poster Presentations

Y.Shimazaki, N.Sawado, Y.Suzuki, "Deep learning analysis of chaos, instability and solitons in quasi-integrable systems via Physics-Informed Neural Networks", YITP Workshop: Field Theory and String Theory2025. July 20, 2025

Usage of JSS

Computational Information

Process Parallelization Methods: MPI
Thread Parallelization Methods: Automatic Parallelization
Number of Processes: 1 - 32
Elapsed Time per Case: 8 Hour(s)

JSS3 Resources Used

Fraction of Usage in Total Resources*1(%): 0.21

Details

Please refer to System Configuration of JSS3 for the system configuration and major specifications of JSS3.

Computational Resources
System Name	CPU Resources Used (Core x Hours)	Fraction of Usage*2(%)
TOKI-SORA	0.00	0.00
TOKI-ST	1731783.67	1.79
TOKI-GP	0.00	0.00
TOKI-XM	0.00	0.00
TOKI-LM	1753.31	0.13
TOKI-TST	0.00	0.00
TOKI-TGP	0.00	0.00
TOKI-TLM	0.00	0.00

File System Resources
File System Name	Storage Assigned (GiB)	Fraction of Usage*2(%)
/home	1024.00	1.64
/data and /data2	102400.00	0.67
/ssd	30720.00	1.87

Archiver Resources
Archiver Name	Storage Used (TiB)	Fraction of Usage*2(%)
J-SPACE	0.00	0.00

*1: Fraction of Usage in Total Resources: Weighted average of three resource types (Computing, File System, and Archiver).

*2: Fraction of Usage：Percentage of usage relative to each resource used in one year.

ISV Software Licenses Used

ISV Software Licenses Resources
	ISV Software Licenses Used (Hours)	Fraction of Usage*2(%)
ISV Software Licenses (Total)	0.00	0.00

*2: Fraction of Usage：Percentage of usage relative to each resource used in one year.