mlsanityData to 7 Oct 2026

Origins and mitigation of double descent in reduced order modeling

arXiv 2607.26414 ↗First posted 29 Jul 2026stat.ML cs.LG math.DScited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 25 of its 66 references that are in the map. First posted on arXiv 29 Jul 2026.

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25 of 66 references.

References · 25

  1. 2018Reconciling modern machine learning practice and the bias-variance trade-offcited by 919
  2. 2019Deep Double Descent: Where Bigger Models and More Data Hurtcited by 667
  3. 2019Surprises in High-Dimensional Ridgeless Least Squares Interpolationcited by 508
  4. 2019The generalization error of random features regression: Precise asymptotics and double descent curvecited by 410
  5. 2019Two models of double descent for weak featurescited by 194
  6. 2023Modern Bayesian Experimental Designcited by 121
  7. 2020Optimal Regularization Can Mitigate Double Descentcited by 107
  8. 2020Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regimecited by 95
  9. 2021The Shape of Learning Curves: a Reviewcited by 67
  10. 2018A jamming transition from under- to over-parametrization affects loss landscape and generalizationcited by 65
  11. 2020Triple descent and the two kinds of overfitting: Where & why do they appear?cited by 64
  12. 2017Data-Driven Sparse Sensor Placement for Reconstructioncited by 57
13 more
  1. 2020A Brief Prehistory of Double Descentcited by 44
  2. 2020Memorizing without overfitting: Bias, variance, and interpolation in over-parameterized modelscited by 26
  3. 2025Reduced Order Modeling with Shallow Recurrent Decoder Networkscited by 24
  4. 2019Minimizers of the Empirical Risk and Risk Monotonicitycited by 11
  5. 2020Multi-fidelity sensor selection: Greedy algorithms to place cheap and expensive sensors with cost constraintscited by 10
  6. 2021PySensors: A Python Package for Sparse Sensor Placementcited by 8
  7. 2016The Peaking Phenomenon in Semi-supervised Learningcited by 5
  8. 2023Data-Induced Interactions of Sparse Sensors Using Statistical Physicscited by 3
  9. 2024Unveiling Multiple Descents in Unsupervised Autoencoderscited by 3
  10. 2025PySensors 2.0: A Python Package for Sparse Sensor Placementcited by 3
  11. 2022Exposure theory for learning complex networks with random walkscited by 2
  12. 2022Learning Dynamic Graphs, Too Slowcited by 1
  13. 2024State Estimation Using Sparse DEIM and Recurrent Neural Networkscited by 1

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