Scientific machine learning: A symbiosis

This editorial serves as a preface to the "Scientific Machine Learning" (SciML) special issue of the AIMS Foundations of Data Science journal. In this piece, we contend that SciML exists in a symbiotic relationship with the fields of computational science and engineering (CSE) and machine learning (ML). We highlight the progress (and limitations) of CSE and reflect on the recent successes of ML. While ML creates significant possibilities for advancing simulation techniques, it lacks the mathematical guarantees that are typically found in CSE. We argue that as SciML develops and embraces the remarkable capabilities of ML, it will support, not replace, traditional methods of CSE. We then overview some existing challenges and opportunities in this interdisciplinary field and close by introducing the special issue papers.

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