Origins and mitigation of double descent in reduced order modeling

2026-07-28

AI Summary

This work addresses the double descent phenomenon and associated instability in reduced-order modeling, which arise from sensor placement, noise, and reconstruction algorithms. Leveraging data–noise averaging theory, the study establishes the first sufficient conditions for the emergence of double descent, enabling accurate and low-cost prediction of reconstruction risk curves. By identifying critical individual and combinatorial sensors responsible for instability, the authors design a sparse sensing strategy coupled with targeted regularization to effectively suppress the amplification of ill-conditioned signals. The proposed approach is validated on both static sea surface temperature field reconstruction and time integration of reduced-order models for partial differential equations, demonstrating significant mitigation of error peaks induced by double descent.

Abstract

Latent low-dimensional structure in datasets of natural and engineered systems enables their sparse sensing, or full-state reconstruction from historical data and very few carefully chosen localized measurements. Depending on the reconstruction algorithm, sensor locations, and measurement noise, the reconstruction risk curves demonstrate a diversity of patterns including a dramatic peak in error known as double descent in Machine Learning literature. Here we explore those scenarios under a unified Data-Noise Averaging theory. Qualitatively, we formulate sufficient criteria for double descent to emerge through a catastrophic amplification of a pathological signal in reconstruction. Quantitatively, we predict the detailed risk curves at a fraction of computational cost, trace reconstruction instability to individual sensors and their combinations, and provide regularization mechanisms to mitigate the instability. We demonstrate results for both static reconstruction of Sea Surface Temperature patterns and time integration of a reduced order model of a PDE.

Problem

• double descent
• reduced order modeling
• reconstruction error
• sensor placement
• measurement noise

Innovation

• double descent
• reduced order modeling
• data-noise averaging
• sensor placement
• regularization