Sharper predictions: The role of loss functions for enhanced turbulent-flow sensing

Accurate estimation of near-wall turbulence from limited surface measurements is critical for various practical and experimental applications; however, it remains challenging due to the complex and multiscale characteristics inherent to turbulent flows. Recent developments in data-driven methods have improved performance over traditional linear approaches but are often limited by loss functions that primarily penalize pointwise errors. In this study, we consider a composite, spectrally informed loss function that augments the conventional mean-squared error with terms that explicitly promote statistical consistency of fluctuation levels and spectral energy distributions. This loss function is evaluated using a baseline convolutional network model applied to direct numerical simulation datasets of turbulent open-channel flow at friction Reynolds numbers, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mtext>Re</a:mtext> <a:mi>τ</a:mi> </a:msub> <a:mo>=</a:mo> <a:mn>180</a:mn> </a:mrow> </a:math> and 550. We show that the considered loss function substantially reduces reconstruction errors of near-wall fluctuation velocity fields obtained from the network model using wall-shear stress and wall-pressure data as inputs. The proposed method recovers up to a threefold improvement in reconstruction accuracy relative to baseline employing mean-squared loss and retains energy content at small-scale structures. We further show that reconstruction accuracy is only mildly affected when the input wall signals are contaminated with 5–100% Gaussian noise and retains energy content in small flow structures when predicting from coarse wall inputs, indicating that the trained models generalize robustly to noisy, experimentally relevant conditions. Our results demonstrate that properly designed loss functions can improve reconstruction accuracy, highlighting the importance of training strategy in achieving efficient, high-performance neural-network models for practical nonintrusive sensing applications. The present study also provides a foundation for future extensions with advanced architectures, such as generative or diffusion-based models to further improve reconstruction of turbulent flow fields in complex settings.