Bilevel optimization for data-driven learning of Koopman embeddings using kernel-based autoencoders

arXiv:2610.12370 · cs.LG, math.DS, stat.ML · Submitted 2026-10-08 · Read on arXiv

cs.LG, math.DS, stat.ML

Submitted: 2026-10-08

Updated: 2026-10-08

Code: https://github.com/erichson/koopmanAE

Terminology

• Embeddings — 9× in this paper · explained in 2 episodes
• Hilbert Space — 7× in this paper · explained in 2 episodes
• Regularization — 6× in this paper · explained in 3 episodes
• Objective Function — 3× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Benchmark — 2× in this paper · explained in 2 episodes
• Conference on Decision and Control — 2× in this paper
• Consistency — 2× in this paper · explained in 3 episodes
• Loss Function — 2× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Interpretability — 1× in this paper · explained in 15 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• System Identification — 1× in this paper · explained in 3 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• How deep is your network? Deep vs. shallow learning of transfer operators
• Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction

Related papers

• Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
• AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
• Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
• Convergence issues in Relational Concept Analysis based on AOC-posets
• Beliefs Beyond Posteriors: Local-Consistency Optimisation for Bayesian Neural Networks
• Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks