Progressive Mixture-of-Experts with autoencoder routing for continual RANS turbulence modelling

Abstract: Developing Reynolds-averaged Navier-Stokes (RANS) turbulence models that remain accurate across diverse flow regimes remains a long-standing challenge. In this work, we propose a novel framework, termed the progressive mixture-of-experts (PMoE), designed to enable continual learning for RANS turbulence modelling. The framework employs a modular autoencoder-based router to associate each flow scenario with a specialised turbulence model, referred to as an expert. When an unseen flow regime cannot be adequately represented by the existing router and expert set, a new expert together with its routing component can be introduced at low cost, without modifying or degrading previously trained ones, thereby naturally avoiding catastrophic forgetting. The framework is applied to a range of flows with distinct physical characteristics, including baseline airfoil wakes, wall-attached flows, separated flows and corner-induced secondary flows. The resulting PMoE model effectively integrates multiple experts and achieves improved predictive accuracy across both seen and unseen test cases. Owing to sparse activation, model expansion does not incur additional computational cost during inference. The proposed framework therefore provides a scalable pathway towards lifelong-learning turbulence models for industrial computational fluid dynamics.