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

2025-10-28

AI Summary

This work addresses spatial dimensionality reduction for turbulent flow data. We propose a coordinate-based Conditional Neural Field (CNF) framework and systematically investigate three conditional modulation mechanisms—Feature-wise Linear Modulation (FiLM), Feature Projection (FP), and final-layer coupling—while incorporating a domain decomposition architecture to localize modeling complexity. Under a unified evaluation protocol, CNFs are benchmarked against Proper Orthogonal Decomposition (POD) and convolutional autoencoders. Results show that CNF-FP achieves the lowest reconstruction error in interpolation tasks, whereas CNF-FiLM exhibits superior generalization in extrapolation. Domain decomposition significantly improves extrapolation accuracy for high-gradient and non-stationary turbulent flows. To our knowledge, this is the first study to systematically decouple, evaluate, and validate the applicability boundaries of distinct conditional mechanisms in turbulence modeling. The proposed methodology provides an interpretable, reusable foundation for physics-informed neural field-based dimensionality reduction.

Technology Category

• Machine Learning: Dimensionality Reduction/Feature Selection
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Multi-modal Vision

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Comparing neural fields with traditional methods for turbulence data compression
• Evaluating conditioning mechanisms for spatial dimensionality reduction of flows
• Assessing domain decomposition to improve extrapolation accuracy in turbulence

Innovation

• Conditional neural fields reduce turbulence data dimensions
• Domain-decomposed CNF localizes complexities for accuracy
• CNF-FP achieves lowest errors with low-rank modulation