Quelles sont les meilleures méthodes et mesures pour quantifier l’incertitude dans les modèles CFD à l’aide de l’apprentissage automatique ?

I've used Machine learning (ML) to improve uncertainty quantification (UQ) in CFD models, such as turbulence modeling. An example is using a Random Forest (RF) regressor to assess uncertainty. First, collect and preprocess data from turbulence simulations. Divide the dataset into training (80%) and test (20%) sets. Train the RF model on the training set, optimizing hyperparameters using cross-validation. Evaluate the model's predictive performance on the test set using metrics like R-squared, RMSE, and MAE. Uncertainty is quantified through the variance in RF predictions, calculated as the variance of individual decision tree predictions within the forest. Such ML-based UQ approach enhances understanding of uncertainties in CFD models.

Before applying ML/UQ methods to CFD, it's first important to define an appropriate response variable for the given engineering application. The choice is not always obvious, but is usually some integral of a CFD field, e.g. impeller power input or average kLa, or another scalar quantity, e.g. mixing time. With a suitable response variable defined, ML approaches can be used to approximate the discrepancy between models of different fidelity and between models and experiments. Neural networks are one choice to do this given enough data. Other approaches, such as the Kennedy-O'Hagan model, use Bayesian methods instead.

Key Metrics for Uncertainty Quantification in CFD Models: 1. Mean Squared Error (MSE) - Measures average prediction error. 2. Predictive Interval Coverage Probability (PICP) - Assesses the proportion of true outcomes within the predicted interval. 3. Width of the Prediction Interval (WPI) - Evaluates the uncertainty range. These metrics together provide a thorough assessment of model reliability, ensuring robust CFD predictions.

Best Methods for Quantifying Uncertainty in CFD Models Using Machine Learning: 1. Bayesian Neural Networks (BNNs) - Provides a probabilistic approach & Yields a distribution of predictions. 2. Monte Carlo Dropout - Randomly drops neurons during training; Approximates Bayesian methods & Captures model uncertainty effectively. These methods help make CFD simulations more reliable by accounting for prediction variability.

Bayesian methods using Monte Carlo sampling of the posterior distribution are powerful uncertainty and parameter estimators that can combine data from low fidelity models, high fidelity models, and experiments within one framework. However, the computational cost of these methods is often quite high when applied to CFD models because drawing each random sample requires solving the CFD model again. Reduced-order/surrogate model approximations that can be rapidly evaluated, e.g. response surfaces or Gaussian process models, are therefore essential to applying these methods in practice.

Parametric modelling maybe able to bridge some challenges in code - using grasshopper and Rhino for the actual structure under analysis.