Scientific Machine Learning (SciML) is a relatively new research field based on both machine learning (ML) and scientific computing tools. Its aim is the development of new methods to solve several kinds of problems, which can be forward multidimensional partial differential equations, identification of parameters, or inverse problems. The methods we seek must be robust, reliable and interpretable. The new SciML tools allow the natural inclusion of data in the numerical simulation in order to generate new results. This new methodology will be at the forefront of the next wave of data-driven scientific discovery in the physical and engineering sciences. More precisely, our goals are:
- to introduce the mathematical concepts lying at the foundation of machine learning as used in scientific computing;
- to give an overview of the different approaches developed to address these problems;
- to give insight on the latest numerical tools in scientific machine learning and data inclusion for the solution of PDEs.