CABLE: Convex Affine Blends of Latent Experts for parametric reduced-order modeling
Abstract
Non-intrusive reduced-order models often learn low-dimensional dynamical systems in a latent space, but existing approaches face a tradeoff between explicit structure and global expressive power. Equation-based reduced-order models are efficient and analyzable but can lack expressivity, while neural dynamical models are expressive but sacrifice explicit structure and can be computationally expensive. To address this tradeoff, we introduce CABLE (Convex Affine Blends of Latent Experts), which uses a neural network to learn how explicit latent operators are combined rather than replacing the operators themselves. This provides explicit operator representation for our dynamics, and uses neural operator selection to combine the learned, structured operators. CABLE represents latent dynamics as a convex mixture of shared affine ODE experts, providing global expressivity while retaining explicit differential-equation structure and efficient integration. This structure enables architecture-specific error analysis, stability guarantees through a common Lyapunov parameterization, and dynamics-based adaptive sampling without access to the governing equations. Across nonlinear, nonautonomous, and parametric systems, CABLE achieves accurate and efficient predictions. On a two-parameter Vlasov-Fokker-Planck two-stream instability problem, adaptive CABLE reduces worst-case prediction error while providing faster inference than parameterized neural ODE, Latent Space Dynamics Identification, UNet, and Fourier Neural Operator baselines. These results show that learned global latent dynamics can retain explicit structure without giving up the flexibility needed for complex parametric systems.
Related
- Tracking a Small Set of Experts in Online Convex Optimization
- Higher-Order QMC Galerkin FEM for Singular Perturbation: Reaction-Diffusion with Affine-Parametric Reaction
- Minimax Alternating Regret for the Experts Problem and Online Convex Optimization
- Comparison of a Parametric Physics-Informed Neural Network and a Tensorial Reduced-Order Model for the Shallow-Water Dam-Break Problem
- Conformal risk control for model-form uncertainty in parametric non-intrusive reduced-order models
BibTeX
@misc{anderson2026cable,
title = {{CABLE: Convex Affine Blends of Latent Experts for parametric reduced-order modeling}},
author = {William Anderson and Jiyoung Yoo and Robert Stephany and Lee F. Ricketson and Jingwei Hu and Youngsoo Choi},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05736441v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - CABLE: Convex Affine Blends of Latent Experts for parametric reduced-order modeling
AU - William Anderson
AU - Jiyoung Yoo
AU - Robert Stephany
AU - Lee F. Ricketson
AU - Jingwei Hu
AU - Youngsoo Choi
PY - 2026
DA - 2026/09/02
PB - HAL
UR - https://hal.science/hal-05736441v1
AB - Non-intrusive reduced-order models often learn low-dimensional dynamical systems in a latent space, but existing approaches face a tradeoff between explicit structure and global expressive power. Equation-based reduced-order models are efficient and analyzable but can lack expressivity, while neural dynamical models are expressive but sacrifice explicit structure and can be computationally expensive. To address this tradeoff, we introduce CABLE (Convex Affine Blends of Latent Experts), which uses a neural network to learn how explicit latent operators are combined rather than replacing the operators themselves. This provides explicit operator representation for our dynamics, and uses neural operator selection to combine the learned, structured operators. CABLE represents latent dynamics as a convex mixture of shared affine ODE experts, providing global expressivity while retaining explicit differential-equation structure and efficient integration. This structure enables architecture-specific error analysis, stability guarantees through a common Lyapunov parameterization, and dynamics-based adaptive sampling without access to the governing equations. Across nonlinear, nonautonomous, and parametric systems, CABLE achieves accurate and efficient predictions. On a two-parameter Vlasov-Fokker-Planck two-stream instability problem, adaptive CABLE reduces worst-case prediction error while providing faster inference than parameterized neural ODE, Latent Space Dynamics Identification, UNet, and Fourier Neural Operator baselines. These results show that learned global latent dynamics can retain explicit structure without giving up the flexibility needed for complex parametric systems.
ER -