Impact Score 2.97
Machine Learning (ML) and Deep Learning (DL) are attractive pervasive methodologies across numerous research fields. It is especially true in scientific computing and computational science. Conversely, scientists have often considered such methodologies a magic "black box" not based on solid mathematical formalisms and rigorously explainable principles. Despite these sceptic considerations, learning approaches represent novel paradigms to efficiently and accurately solve problems enhancing classical scientific computing approaches.
Concerning the effectiveness of this new challenge, many crucial and fascinating still open questions have to be addressed. For example:
i) how well-known methodologies of computational mathematics, particularly numerical kernels, can be integrated and improve machine learning modelsii) how have ML and DL approaches adopted the research results in numerical analysis, scientific computing, and more in general computational scienceiii) how ML and DL will influence the choice to adopt complex mathematical models and/or data-driven approaches for solving problems?
Numerous research topics support the effectiveness of the combination of ML and DL and Scientific Computing such as the Nonlinear Black–Scholes equation, the Hamilton–Jacobi–Bellman equation and the Allen–Cahn equation are partial differential equations(PDEs) in high dimensions. Recently, it has been proved that learning-based approaches can handle general high-dimensional PDEs. Conversely, mathematical models based on the Markov decision processes play an essential role in Deep Reinforcement Learning.
In order to add another piece to a complicated but fascinating puzzle, this topical collection aims to attract high-quality contributions to investigate both the role of ML/DL methodologies in applied mathematics and how Scientific Computing can benefit from learning paradigms.
Submission Deadline: December 31, 2021
List of Topics
Submission: Manuscripts should be submitted electronically to https://www.editorialmanager.com/jomp/default.aspx