Conditional neural field for spatial dimension reduction of turbulence data: a comparison study

TL;DR

This study introduces and benchmarks conditional neural fields (CNFs) as mesh-agnostic, coordinate-based decoders conditioned on latent codes for spatial dimension reduction of turbulent flows. A unified encoding–decoding framework is used to compare CNFs against POD and CNN-AEs under identical preprocessing and a rigorous evaluation protocol that separately tests interpolation within the training horizon and extrapolation beyond it. Among conditioning strategies, full latent-driven weight and bias modulation (CNF-FP) delivers the strongest in-range reconstruction, while activation-only modulation (CNF-FiLM) generalizes more robustly to out-of-range data when latent capacity is moderate; a domain-decomposition extension substantially improves extrapolation for demanding turbulent datasets. These results provide physics-aware guidance on choosing conditioning, capacity, and localization for turbulence data compression and reconstruction, and suggest future directions including amortized encoders, overlap-aware tiling, and uncertainty quantification for latents. Overall, CNFs, especially with domain decomposition, offer a powerful, flexible tool for accurate turbulence field reconstruction and could underpin improved surrogate modeling and operator learning in CFD contexts.

Abstract

We investigate conditional neural fields (CNFs), mesh-agnostic, coordinate-based decoders conditioned on a low-dimensional latent, for spatial dimensionality reduction of turbulent flows. CNFs are benchmarked against Proper Orthogonal Decomposition and a convolutional autoencoder within a unified encoding-decoding framework and a common evaluation protocol that explicitly separates in-range (interpolative) from out-of-range (strict extrapolative) testing beyond the training horizon, with identical preprocessing, metrics, and fixed splits across all baselines. We examine three conditioning mechanisms: (i) activation-only modulation (often termed FiLM), (ii) low-rank weight and bias modulation (termed FP), and (iii) last-layer inner-product coupling, and introduce a novel domain-decomposed CNF that localizes complexities. Across representative turbulence datasets (WMLES channel inflow, DNS channel inflow, and wall pressure fluctuations over turbulent boundary layers), CNF-FP achieves the lowest training and in-range testing errors, while CNF-FiLM generalizes best for out-of-range scenarios once moderate latent capacity is available. Domain decomposition significantly improves out-of-range accuracy, especially for the more demanding datasets. The study provides a rigorous, physics-aware basis for selecting conditioning, capacity, and domain decomposition when using CNFs for turbulence compression and reconstruction.

Figures (12)

• Figure 1: Schematic illustration of the unified encoding-decoding framework for spatial dimension reduction methods, demonstrating the common structure comprising transformation (blue dashed boxes) and reduction (orange dashed boxes) steps. Representative methods shown include linear (PCA/POD), convolutional neural network autoencoder (CNN-AE), and conditional neural fields (CNF-FiLM and CNF-FP)
• Figure 2: Diagram of different conditioning mechanism
• Figure 3: Demo diagram of dataset splitting strategy
• Figure 4: Wall–normal profiles of the normalized streamwise–velocity fluctuation RMS, $C_{u,\mathrm{rms}}(y^+)$, on the WMLES--Inlet dataset. Columns correspond to latent sizes $r \in\{8,64,256\}$; rows shows evaluation splits: (a) training, (b) in-range testing, (c) out-of-range testing.
• Figure 5: DNS-inlet, out-of-range testing at $r = 128$. Top: reconstructions; bottom: absolute error. (a) Global CNFs (no decomposition): blurred streaks, spurious high–wavenumber textures, larger structured errors. (b) Domain-decomposed CNFs: streak spacing and amplitude recovered; artifacts suppressed.