Reduced order modeling with shallow recurrent decoder networks.

Area of Science:

• Computational fluid dynamics
• Dynamical systems theory
• Machine learning for scientific modeling

Background:

• Reduced-order modeling (ROM) is crucial for analyzing high-dimensional spatio-temporal data.
• Existing ROM methods struggle with nonlinear dynamics, unknown parameters, and system behavior.
• There is a need for efficient and robust dimensionality reduction techniques.

Purpose of the Study:

• To develop a novel ROM technique, SHRED-ROM, for reconstructing complex dynamics from limited sensor measurements.
• To enhance computational efficiency and memory usage in dimensionality reduction.
• To create a versatile ROM strategy applicable to diverse scenarios and data types.

Main Methods:

• SHRED-ROM utilizes a shallow recurrent decoder architecture.
• Dimensionality reduction is achieved via data- or physics-driven basis expansions.
• The method employs compressive training of lightweight neural networks.

Main Results:

• SHRED-ROM successfully reconstructs high-dimensional dynamics from limited sensor data.
• The technique demonstrates robustness in chaotic and nonlinear fluid dynamics applications.
• SHRED-ROM handles fixed or mobile sensors, time-dependent parameters, and various data sources (simulations, videos).

Conclusions:

• SHRED-ROM offers a powerful decoding-only strategy for advanced reduced-order modeling.
• The method is agnostic to sensor placement and parameter values, enhancing its applicability.
• SHRED-ROM provides an efficient and versatile solution for inferring complex system behaviors.