Journal of Scientific Computing - Topical Collection: Beyond traditional AI: the impact of Machine Learning on Scientific Computing

Guest Editors 

Francesco Piccialli, francesco.piccialli@unina.it (this opens in a new tab)
Salvatore Cuomo, salvatore.cuomo@unina.it (this opens in a new tab)
Boumediene Hamzi, b.hamzi@imperial.ac.uk (this opens in a new tab)
Jan Hesthaven, Jan.Hesthaven@epfl.ch (this opens in a new tab)

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 models
ii)  how have ML and DL approaches adopted the research results in numerical analysis, scientific computing, and more in general computational science
iii)  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 extended: February 28, 2022

List of Topics

• Machine learning-based numerical algorithm for solving high dimensional PDEs 
• Machine learning for multi-scale problems
• Physics-Informed Deep-Learning for Scientific Computing
• Supervised Learning for High Dimension parametric PDEs
• Machine learning-based algorithms for high dimensional problems
• Machine learning approach for efficient uncertainty quantification
• Neural-network machine learning-based methods for stochastic control problems
• Mathematical methods for Kernel Learning 
• Machine Learning methodologies for Graph signals
• Multivariate data approximation by Deep Learning methodologies
• Data Classification through Deep Learning 
• Stochastic approaches in Deep Reinforcement Learning
• Non-linear approximation through Deep Neural Networks
• Scientific Computing approaches for time series forecasting

Submission: Manuscripts should be submitted electronically to https://www.editorialmanager.com/jomp/default.aspx (this opens in a new tab)