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Abstract

Transient soft elastohydrodynamic lubrication (EHL) couples the Reynolds equation to the elastic response of a compliant half-space. A numerical method requires a dense non-local solve at every time step, which makes parametric studies expensive. We use a validated finite-difference solver by Wu, Hui and Jagota \citep{wu2023} for a rigid sphere that is indented into, and then slides over, an elastic half-space across a thin liquid film, to generate several trajectories of a two-parameter loading family at $\beta=200$, a dimensionless elastic–viscous coupling parameter. Three different types pf neural-operator surrogates for the pressure field are compared under one protocol: a direct branch/trunk DeepONet, an autoregressive FiLM-conditioned time-stepper trained with a pushforward loss, and a DeepONet trained with a discrete-Reynolds-residual loss. The best model is a symmetry-gated direct DeepONet whose exact pre-sliding axisymmetry is structural instead of learned. It uses closed-form kinematic trunk features and a loss that targets the sub-ambient pressure trough formed behind the contact once sliding starts. It reaches a mean final-time relative $L_2$ error of 3.1\% on held-out trajectories and recovers 96.6\% of the trough depth. The surrogate is mesh-independent and 19--377 times faster per time-step than the dense numerical solver solver.