CABLE: Convex Affine Blends of Latent Experts for parametric reduced-order modeling

Non-intrusive reduced-order models often learn low-dimensional latent dynamics. However, existing approaches typically trade explicit structure for the flexibility needed to capture parametric and temporal variation. Equation-based models are efficient and analyzable, but can be too rigid for strongly varying dynamics. Neural dynamical models are more expressive but hide the learned vector field inside a network and can be costly to integrate. We introduce CABLE (Convex Affine Blends of Latent Experts), which represents the latent dynamics as a convex mixture of shared affine ordinary differential equation (ODE) experts. A neural gate varies the mixture weights with the parameters, latent state, or time, allowing a single model to adapt across dynamical regimes while retaining explicit operators. These operators enable rollout-error bounds, sufficient conditions for contraction imposed directly on the experts, and a dynamics-based adaptive sampling criterion. Across several parametric systems, CABLE produces accurate and efficient predictions. On a two-parameter Vlasov–Fokker–Planck two-stream instability, uniformly sampled CABLE matches or improves upon parameterized neural ODE, Latent Space Dynamics Identification, U-Net, and Fourier neural operator baselines in typical-case accuracy while providing lower upper-tail errors and the fastest inference. Adaptive sampling further improves upper-tail accuracy, approximately halving the maximum error relative to the best uniformly sampled baseline.