Interval and fuzzy physics-augmented neural networks (iPANN and fPANN) for uncertainty quantification and propagation in constitutive modeling

Imagine you're designing materials for structures, and you need to predict how they will behave under stress. The challenge is that the data you have might be incomplete or noisy, making it hard to trust your simulations. Traditional methods often struggle with this uncertainty, leading to inaccurate predictions and potential failures in real-world applications. This is what's called uncertainty quantification, and it’s crucial for reliable engineering. To address this, researchers have developed interval and fuzzy physics-augmented neural networks, which help model these uncertainties more effectively. The interval networks create a range of possible stress responses based on the data, while the fuzzy networks take it a step further by allowing for a spectrum of responses, capturing more of the uncertainty in the data. By incorporating physical constraints into the learning process, these models ensure that the predictions remain realistic and interpretable. Compared to previous methods, this approach not only provides tighter bounds on stress predictions but also enhances the ability to propagate uncertainty through simulations, making it a valuable tool for engineers looking to improve the reliability of their designs.

The introduction of interval and fuzzy physics-augmented neural networks represents a meaningful extension in uncertainty-aware modeling.

The evaluation on synthetic data with varying noise conditions provides solid evidence of the framework's effectiveness.