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Deep Learning-based Algebraic Reynolds Stress Closures for RANS simulations of Turbulent Flows

NeurIPS 2026 · Probabilistic and scientific modeling › Differential equations and PDEs · approach: Physics-informed operator learning · 0 citations (OpenAlex)

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Proposes DARSM, a physics-derived implicit algebraic Reynolds stress closure whose neural network perturbs ARSM constants, trained end-to-end through a stiff RANS solver using a hybrid discrete adjoint that reuses forward implicit solvers.

Problem

Data-driven RANS turbulence closures trained offline suffer distribution shift at deployment, and end-to-end training through stiff implicit RANS solvers fails with unrolled or standard implicit autodiff, especially at practical grid sizes.

Approach

Embed a small neural network to model the empirical constants (c1, c2) of an implicit explicit algebraic Reynolds stress model derived under weak equilibrium, so the tensor-basis coefficients are physics-derived rational functions; train it by a hybrid discrete adjoint that solves implicit adjoint sub-steps with the forward solver's own structured solvers and uses reverse-mode AD for explicit part

Key results

• On square duct Reynolds-number split, DARSM test error J=3.56e-3 vs 7.38e-3 for default EARSM (about 48% reduction; the paper describes this as a 2x reduction at extrapolation to Re_b=40000).
• On aspect-ratio split, DARSM test mean 1.70e-3 vs 5.90e-3 for default EARSM (about 3x).
• On periodic hills, DARSM out-of-sample test mean 1.50e-3 vs 5.76e-3 for default EARSM (about 4x); duct-trained DARSM transfers to hills with test mean 1.36e-3.

Surprising findings

• A-priori (offline-trained) NN-EARSM diverges when inserted into the solver, and a-priori TBNN is 50-120% wrong in Frobenius norm at deployment.
• A closure trained only on attached square-duct flow transfers without retraining to separated periodic-hill flow with accuracy matching a hill-trained closure.

Limitations

• All results are on 2D grids; 3D generalisation not tested.
• Requires steady-state converged RANS; unsteady flows not covered.
• Relies on the weak-equilibrium assumption of EARSM, which may fail with strong curvature or non-equilibrium flows.

Experimental setup

Datasets: square-duct DNS at Re_b 4410-40000 (six cases) periodic hills DNS at Re_b=5600 (alpha=1.0) parametric-hills database

Benchmarks: square duct velocity error (Reynolds-number and aspect-ratio splits) periodic hills velocity error across alpha

Metrics: component-normalised velocity error J relative Frobenius error

Baselines: Default EARSM a-priori NN-EARSM TBNN FIML DeepONet PINN Source Term Neural Closure

Builds on: explicit algebraic Reynolds stress model k-omega turbulence model tensor-basis neural network field inversion machine learning DPM adjoint

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