Learning Physical Operators using Neural Operators

• URL: http://arxiv.org/abs/2602.23113v1
• Date: Thu, 26 Feb 2026 15:27:14 GMT
• Title: Learning Physical Operators using Neural Operators
• Authors: Vignesh Gopakumar, Ander Gray, Dan Giles, Lorenzo Zanisi, Matt J. Kusner, Timo Betcke, Stanislas Pamela, Marc Peter Deisenroth,
• Abstract summary: We train neural operators to learn individual non-linear physical operators while approximating linear operators with fixed finite-difference convolutions.<n>We formulate the modelling task as a neural ordinary differential equation (ODE) where these learned operators constitute the right-hand side.<n>Our approach achieves better convergence and superior performance when generalising to unseen physics.
• Score: 10.57578521926415
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: 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.

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