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

Haoyu Ji, Yinhang Luo, Hanyu Zhou, Yaomin Zhao

TL;DR

This work tackles the challenge of generalizing Reynolds-averaged Navier-Stokes turbulence closures across diverse flow regimes by introducing Progressive Mixture-of-Experts (PMoE), a continual-learning framework with a modular autoencoder router that progressively expands with new flow regimes. PMoE decomposes the problem into specialized experts (including wall-bounded, separated, and corner-induced flows) and activates only a small subset of them at inference time, keeping computational cost in check. The approach demonstrates robust continual learning, avoiding catastrophic forgetting while achieving improved accuracy on both seen and unseen cases, validated through a curriculum of flows and extensive a priori and a posteriori tests. The framework offers a scalable, plug-and-play pathway for industrial CFD, enabling living turbulence-closure systems that evolve with advancing modelling strategies.

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.

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

TL;DR

This work tackles the challenge of generalizing Reynolds-averaged Navier-Stokes turbulence closures across diverse flow regimes by introducing Progressive Mixture-of-Experts (PMoE), a continual-learning framework with a modular autoencoder router that progressively expands with new flow regimes. PMoE decomposes the problem into specialized experts (including wall-bounded, separated, and corner-induced flows) and activates only a small subset of them at inference time, keeping computational cost in check. The approach demonstrates robust continual learning, avoiding catastrophic forgetting while achieving improved accuracy on both seen and unseen cases, validated through a curriculum of flows and extensive a priori and a posteriori tests. The framework offers a scalable, plug-and-play pathway for industrial CFD, enabling living turbulence-closure systems that evolve with advancing modelling strategies.

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.
Paper Structure (20 sections, 15 equations, 10 figures, 7 tables)

This paper contains 20 sections, 15 equations, 10 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Introduction to the generic mixture-of-experts framework
  4. Progressive mixture-of-experts framework for turbulence modelling
  5. Feature extraction and physics-informed sampling
  6. Modular autoencoder-based router for continual learning
  7. Sparsely activated expert group with heterogeneous formulation
  8. Continuously learning PMoE model with various cases introduced progressively
  9. Stage 0: Baseline initialization
  10. Stage 1: Adaptation to wall-bounded turbulence
  11. Stage 2: Capturing flow separation
  12. Stage 3: Modelling corner-induced anisotropy
  13. Model validation
  14. Validation for the PMoE router
  15. Prevention of catastrophic forgetting via in-distribution tests
  16. ...and 5 more sections

Figures (10)

  • Figure 1: Schematic of the generic MoE framework with a MLP softmax gating network. (a) The whole process of the MoE framework. (b) Zoom-in view of a gating network based on MLP.
  • Figure 2: Schematic of the proposed PMoE framework.
  • Figure 3: Structure of the router based on autoencoder. (a) Neural network architecture design for the autoencoder component. (b) The modular architecture of the router.
  • Figure 4: Schematic diagrams of typical examples of various flow regimes. (a) 2DANW. (b) Fully developed channel flow. (c) Periodic hill flow. (d) Square duct flow.
  • Figure 5: Velocity profiles and contours predicted by the baseline SA model, the expert model and high-fidelity data. (a) Expert for S0 trained by 2DANW. (b) Expert for S1 trained by C5200. (c) Expert for S2 trained by PH1p0. (d) Expert for S3 trained by SD2500 and SD5693.
  • ...and 5 more figures