Physics-Informed Machine Learning: Methodologies and Applications
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".
Deadline for manuscript submissions: 31 December 2025 | Viewed by 56
Special Issue Editors
Interests: physics-Informed machine learning; generative AI; large language models; multi-agent systems
Special Issue Information
Dear Colleagues,
This Special Issue explores the rapidly growing field of physics-informed machine learning (PiML), which integrates machine learning techniques with physical laws and domain knowledge to advance scientific computing and modeling. By incorporating governing equations such as partial differential equations (PDEs) into the learning process, PiML provides powerful tools to address forward and inverse problems, improve accuracy and generalization, and reduce computational costs. This issue features contributions encompassing foundational methodologies—such as physics-informed neural networks (PINNs), operator learning, graph-based approaches, and architecture-imposed conditions—and their diverse applications in areas such as fluid dynamics, structural analysis, material science, and climate modeling. This collection addresses current challenges, including scalability, generalization, and robustness, while highlighting emerging trends and open questions in this transformative field.
Dr. Kuangdai Leng
Dr. Lu Lu
Guest Editors
Manuscript Submission Information
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Keywords
- physics-informed machine learning
- neural networks
- partial differential equations
- scientific computing
- operator learning
- physics-based modeling
- inverse problems
- computational science
- uncertainty quantification
- data-driven simulations
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