TurTLES

A Large-Scale Benchmark for Turbulent 3D Neural PDE Surrogates

Anonymous Authors

Submission to NeurIPS 2026 · Datasets and Benchmarks Track

Streamwise velocity u
Pressure p

Mid-span 2D slices of the streamwise velocity (left) and pressure (right) from the same fully three-dimensional simulation: elliptical cross-section (n = 2, a/D = 1.46) at Re = 3101 and angle of attack α = 31°. Each TurTLES trajectory comprises 400 time steps of 3D wake dynamics sampled on irregular point clouds with 3–9 million points per frame; the slices shown are for visualisation only.

Abstract

Machine-learning surrogates are increasingly used to accelerate computational fluid dynamics (CFD), yet progress is limited by the lack of benchmarks capturing realistic, time-dependent turbulent flows. We introduce TurTLES, a 13 TB dataset of high-fidelity implicit large-eddy simulations of three-dimensional turbulent cylinder wakes in the shear-layer transition regime. The dataset contains 380 trajectories of 400 time steps each, with 3–9 million points per frame sampled on irregular point clouds, spanning variations in geometry, Reynolds number, and angle of attack. Unlike existing datasets, TurTLES captures fully three-dimensional turbulence with an active energy cascade driven by vortex stretching, combining (i) dense irregular meshes, (ii) long-horizon temporal dynamics, and (iii) physically realistic turbulent behavior. We benchmark state-of-the-art neural operators on long autoregressive rollouts and identify key failure modes, including temporal instability, loss of small-scale energy, and challenges in learning on large irregular domains. TurTLES provides a new standard benchmark for evaluating surrogate models in high-resolution, industrial-scale CFD regimes.

Key Properties

13 TB
High-fidelity 3D iLES data
380
Trajectories × 400 time steps
3–9 M
Points per frame, irregular mesh
4-D
Parameter space (a, n, Re, α)

Dataset Overview

TurTLES is constructed within a four-dimensional parameter space: geometry is parameterised through the super-ellipse (Lamé curve) family, with aspect ratio AR = a/b, exponent n ∈ {1, 2, 5, ∞} (diamond, circular, rounded rectangle, rectangle), Reynolds number Re ∈ [1000, 3900], and inflow angle of attack α ∈ [0°, 45°]. Samples are drawn from a Sobol’ sequence to evenly cover the hypercube. Each case is solved using a high-order Flux Reconstruction iLES scheme on a Gmsh-generated unstructured mesh extruded into the span-wise direction.

Parameter space overview: geometry definitions, Sobol sample distribution, and parameter histograms.
Figure 1. Overview of the four-dimensional parameter sampling space: super-elliptical geometries, the 380 Sobol samples in (Re, α, AR), and histograms of each parameter.
Schematic overview of the simulation domain: 3D view with labelled boundaries and the 2D mesh in the xy-plane.
Figure 2. Schematic overview of the domain. (a) Three-dimensional view illustrating the physical boundaries: inlet (A), outlets (B–D), object surface (E), and periodic side-walls (F, G). (b) xy-plane of the computational mesh, extended into three dimensions via a structured extrusion in the span-wise (z) direction.

Data Structure

Each case is stored as a single set of node coordinates plus solutions at 400 time steps. A solution comprises the three-dimensional pressure p, density ρ, and velocity components (u, v, w). Snapshots are restricted to nodes inside the rectangular box x/D ∈ [−3, 10], y/D ∈ [−3.5, 3.5], z/D ∈ [0, 2π]. The sampling interval Δts is chosen so that the inertial range of the turbulence spectrum is retained while keeping storage tractable.

Diagram of a per-case directory: shared coordinates, 400 time-step solutions, and example renders of the u-velocity and pressure fields.
Figure 3. Overview of the flow case data structure. Each case directory holds one set of node coordinates and the corresponding solutions for all 400 time steps (t0, t1, …, tf = 399). Right: example renders of the u-velocity and pressure fields for a single frame of case Re_3101_alpha31_a1p46_n2.

Contributions

  1. Dense irregular 3D data. Millions of points per frame on unstructured meshes, beyond the resolution of regular-grid or coarse point-cloud benchmarks.
  2. Long-horizon evaluation. Hundreds of autoregressive time steps in chaotic, geometry-dependent wakes.

Benchmarks

We evaluate state-of-the-art neural operators on long autoregressive rollouts and identify recurring failure modes: temporal instability, loss of small-scale energy, and degradation on large irregular domains. Full results, training protocols, and evaluation metrics are reported in the paper.

More Cases

Additional simulation trajectories from the dataset. Each card shows mid-span 2D slices of streamwise velocity (left) and pressure (right) for one case. Use the arrows or swipe to navigate.

Diamond, n = 1

Re = 3842 · α = 36° · a/D = 0.213

Streamwise velocity u
Pressure p

Rounded rectangle, n = 5

Re = 3129 · α = 9° · a/D = 1.063

Streamwise velocity u
Pressure p

Rectangle, n = ∞

Re = 3088 · α = 3° · a/D = 0.453

Streamwise velocity u
Pressure p

Citation

@inproceedings{turtles2026,
  title     = {TurTLES: A Large-Scale Benchmark for Turbulent 3D Neural PDE Surrogates},
  author    = {Anonymous Authors},
  booktitle = {Submitted to NeurIPS 2026 Datasets and Benchmarks Track},
  year      = {2026},
  note      = {Under double-blind review}
}