On Data-Driven Sparse Sensing and Linear Estimation of Fluid Flows.

Area of Science:

• Fluid dynamics
• Data assimilation
• Scientific computing

Background:

• Reconstructing fine-scale information from sparse, irregularly located data is crucial for applications like fluid dynamics and data assimilation.
• Traditional linear estimation struggles with sparse data, necessitating recovery on low-dimensional bases like Fourier or Proper Orthogonal Decomposition (POD) modes.
• Non-orthogonal bases, such as those from Extreme Learning Machine (ELM) autoencoders, pose challenges for sparse reconstruction due to inefficient data representation.

Purpose of the Study:

• To develop an efficient and robust framework for sparse data-driven sensor placement.
• To enable the recovery of higher-resolution fields from limited, sparse measurements.
• To address the challenges of sparse reconstruction using non-orthogonal bases.

Main Methods:

• Utilizing linear estimation techniques with non-orthogonal bases derived from shallow Extreme Learning Machine (ELM) autoencoder networks.
• Developing a framework for optimal sparse sensor placement.
• Implementing a method for recovering higher-resolution fields of basis vectors.
• Benchmarking against Proper Orthogonal Decomposition (POD)-based sparse recovery methods.

Main Results:

• Demonstrated an efficient and robust framework for sparse data-driven sensor placement and field recovery.
• Showcased performance improvements in fluid flow examples of varying complexity.
• Validated the framework's effectiveness compared to established POD-based sparse recovery techniques.

Conclusions:

• The proposed framework offers an effective solution for sparse data reconstruction, particularly with non-orthogonal bases.
• The method enhances the recovery of fine-scale information in fluid dynamics and related fields.
• This approach provides a valuable tool for data assimilation and model recovery from limited data.