Scientific Machine Learning

Scientific Machine Learning (SciML) is an emerging field that integrates Artificial Intelligence techniques with scientific domain knowledge, such as physical laws and engineering principles, to create more accurate, interpretable, and robust models. Unlike conventional machine learning, which relies exclusively on data to identify patterns, SciML incorporates differential equations, conservation laws, and other physical constraints. This makes it particularly effective in contexts with scarce, noisy, or difficult-to-obtain data, allowing for a more faithful representation of natural phenomena.

Some of SciML’s main applications include:

  • Surrogate Models: These are efficient alternatives to complex simulations, as seen in Computational Engineering, aiming to accelerate design and optimization, which often demand high computational costs. They provide quick predictions, avoiding the need for time-consuming simulations for each design variation.
  • Reduced Order Models (ROMs): These decrease the computational load of high-resolution simulations by creating low-dimensional representations of numerical systems. Unlike many “black box” surrogate models, intrusive ROMs maintain physical and numerical principles, ensuring that reduced solutions adhere to the constraints of the original models. Techniques such as Proper Orthogonal Decomposition (POD), often combined with neural networks, are employed to extract and predict non-linear dynamics.
  • Uncertainty Quantification (UQ): This seeks to evaluate the confidence in model predictions, especially in high-stakes sectors like aeronautics and medicine. UQ distinguishes between aleatoric uncertainty, which is inherent in the data and irreducible, and epistemic uncertainty, which arises from a lack of model knowledge and can be reduced. Common methods include Bayesian Neural Networks (BNNs), Deep Ensembles (DEns), Monte Carlo dropout, Variational Inference (VI), and Laplace Approximation (LA). Deep Ensembles, for example, improve generalization and uncertainty estimation by combining predictions from multiple independently trained neural networks.