Evaluating Pre-Loss Normalization Across Multiple Loss Functions in Deep Learning for Multivariate Fluid Flow Prediction

Kaya U., EKİCİ Ö.

International Journal of Computational Methods, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1142/s0219876226500295
  • Dergi Adı: International Journal of Computational Methods
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, MathSciNet, zbMATH
  • Anahtar Kelimeler: data-driven, deep learning, fluid flow, loss functions, Normalization techniques
  • Hacettepe Üniversitesi Adresli: Evet

Özet

Multi-scale flow fields can destabilize the training of data-driven models by weighting loss contributions unevenly. This study proposes a loss-independent pre-loss normalization module, used only during training, that independently scales predictions and targets prior to loss computation. Three normalization schemes are tested with four loss functions using a transformer model for laminar developing pipe flow. On the test dataset and two additional flow cases, Pre-Loss Normalization reduces the mean absolute error by 27–81% and improves the R2 value of 0.186–0.630 over unnormalized training. Overall, this approach mitigates multi-scale effects and improves accuracy and robustness.