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Détails bibliographiques
Auteurs principaux: Gopakumar, Vignesh, Gray, Ander, Giles, Dan, Zanisi, Lorenzo, Kusner, Matt J., Betcke, Timo, Pamela, Stanislas, Deisenroth, Marc Peter
Format: Preprint
Publié: 2026
Sujets:
Accès en ligne:https://arxiv.org/abs/2602.23113
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Table des matières:
  • Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work introduces a physics-informed training framework that addresses these limitations by decomposing PDEs using operator splitting methods, training separate neural operators to learn individual non-linear physical operators while approximating linear operators with fixed finite-difference convolutions. This modular mixture-of-experts architecture enables generalisation to novel physical regimes by explicitly encoding the underlying operator structure. We formulate the modelling task as a neural ordinary differential equation (ODE) where these learned operators constitute the right-hand side, enabling continuous-in-time predictions through standard ODE solvers and implicitly enforcing PDE constraints. Demonstrated on incompressible and compressible Navier--Stokes equations, our approach achieves better convergence and superior performance when generalising to unseen physics. The method remains parameter-efficient, enabling temporal extrapolation beyond training horizons, and provides interpretable components whose behaviour can be verified against known physics.