Neural operator discovery from heterogeneous trajectories

2026-07-25

AI Summary

This work addresses the challenge of learning neural operators applicable across a family of dynamical systems from heterogeneous trajectory data, without access to explicit physical parameters, geometric specifications, or boundary condition annotations. The authors propose a Neural Operator Discovery (NOD) framework that jointly learns a shared solution operator and system-specific variations through factorized latent-conditioned modeling, requiring neither known control factors nor explicit supervision. By integrating trajectory disentangled sampling with dimensionality selection, the method constructs a latent-conditioned neural operator architecture. Experiments across diverse dynamical systems demonstrate that the learned latent representations accurately capture the intrinsic low-dimensional structure underlying system variations, enabling zero-shot extrapolation to unseen systems, stable long-term predictions, and strong interpretability.

Abstract

Neural operators provide data-driven mappings for modeling dynamical systems. Extending them to families of systems typically requires explicit conditioning variables such as physical parameters, geometries, or boundary conditions. In many real-world settings, these quantities are unobserved. Here, we formulate neural operator discovery (NOD) as the problem of learning both shared solution operators and system-specific variation directly from heterogeneous trajectories without access to labeled governing factors. We introduce a factorized latent-conditioning formulation that jointly learns a neural operator and a low-dimensional latent representation through factorized prediction, trajectory-decoupled sampling, and dimension selection. Across diverse systems, the learned latent representation captures the intrinsic dimensionality of system variation and organizes system instances in a smooth and approximately invertible latent structure aligned with the underlying governing factors. This organization enables generalization to previously unseen system instances, including zero-shot extrapolation across regimes and stable long-horizon prediction. These results establish an interpretable paradigm for operator learning in the absence of explicit factor supervision.

Problem

• neural operator discovery
• heterogeneous trajectories
• latent representation
• system variation
• operator learning

Innovation

• neural operator discovery
• latent conditioning
• heterogeneous trajectories
• zero-shot extrapolation
• factorized representation