Origins and mitigation of double descent in reduced order modeling

arXiv:2607.26414 · stat.ML, cs.LG, math.DS, physics.data-an · Submitted 2026-07-29 · Read on arXiv

Andrei A. Klishin, J. Nathan Kutz, Krithika Manohar

stat.ML, cs.LG, math.DS, physics.data-an

Submitted: 2026-07-29

Comments: 20 RevTeX pages, 11 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Regularization — 40× in this paper · explained in 3 episodes
• Reconstruction Error — 11× in this paper · explained in 2 episodes
• Sparsity — 7× in this paper · explained in 5 episodes
• Fidelity — 6× in this paper · explained in 2 episodes
• Trace — 6× in this paper · explained in 2 episodes
• Data-Noise Averaging — 4× in this paper
• Decoder — 3× in this paper · explained in 2 episodes
• Overfitting — 3× in this paper · explained in 2 episodes
• Proper Orthogonal Decomposition — 3× in this paper
• Benchmark — 2× in this paper · explained in 2 episodes
• Benchmarking — 2× in this paper · explained in 4 episodes
• Digital Twin — 2× in this paper · explained in 6 episodes
• Discrete Empirical Interpolation Method — 2× in this paper
• Generalization — 2× in this paper · explained in 14 episodes
• Inverse Problem — 2× in this paper · explained in 2 episodes
• Semi-supervised Learning — 2× in this paper · explained in 4 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Clarity — 1× in this paper · explained in 3 episodes
• Computational Efficiency — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Generalized Aliasing Decomposition — 1× in this paper
• Monotonicity — 1× in this paper · explained in 2 episodes
• Redundancy — 1× in this paper · explained in 2 episodes
• Uncertainty Quantification — 1× in this paper · explained in 9 episodes
• Unsupervised Learning — 1× in this paper · explained in 2 episodes

Sources

• Data-Induced Interactions of Sparse Sensors Using Statistical Physics
• PySensors: A Python Package for Sparse Sensor Placement
• Unveiling Multiple Descents in Unsupervised Autoencoders
• PySensors 2.0: A Python Package for Sparse Sensor Placement
• Learning Dynamic Graphs, Too Slow

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