New Advances in Physics-Informed Machine Learning
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E4: Mathematical Physics".
Deadline for manuscript submissions: 20 March 2026 | Viewed by 4
Special Issue Editor
Special Issue Information
Dear Colleagues,
Artificial intelligence methods have recently evolved into a dominant approach for solving differential equations, finding widespread applications across various applied mathematics fields such as fluid mechanics, optics, and engineering, known as physics-informed machine learning (PIML) methods. While PIML has demonstrated significant advantages over traditional numerical methods—including the ability to solve unsteady solutions and inverse problems of partial differential equations and even directly derive differential equations from pure data—it still faces critical challenges that require urgent solutions, such as increased complexity and optimization difficulties of loss functions when dealing with large computational domains (with an increased number of residual points), as well as issues of low accuracy and slow computation in operator learning for batch PDE solutions. To address these bottlenecks, the journal Mathematics issues a Special Issue entitled "New Advances in Physics-Informed Machine Learning", which aims to publish the latest progress in PIML approaches for solving differential equations.
Dr. Jingjing Su
Guest Editor
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Keywords
- AI for science
- AI for PDE
- physics-informed machine learning
- operator learning
- neural network
- nonlinearity
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