Data-based methods have been in use for model order reduction (MOR) for several decades. Established model reduction techniques like Proper Orthogonal Decomposition follow the idea of using data to fit and optimize a model for a given physical problem. With the ever-increasing availability of both data and computing resources and the recent trends towards the inclusion of machine learning (ML) in scientific computing, data-driven methods have gained new interest and application fields in MOR. In contrast to the more classical approaches, these are often entirely data-driven. While model-free or non-intrusive approaches have their success stories, additional benefits can be achieved by including model information as it is the principle of physics-informed neural networks.
In view of the efficient and automated handling of models for real-world problems, data and system-theoretic considerations are similarly important. Theoretical results can provide generally valid approaches and reliable performance guarantees, whereas the inclusion of data can tailor the model to a specific but possibly highly complex setup. Finding good compromises between mathematical rigour and data-based heuristics is the goal of this Research Topic.
This Research Topic covers classical methods and recent developments, trends, and applications in Model Order Reduction or Reduced Order Modelling with data and applications as the common divisor. We invite original research papers with:
- developments and applications of classical though data-oriented MOR methods like Proper Orthogonal Decomposition, Dynamic Mode Decomposition, Loewner, Reduced Bases, Operator Inference, Empirical Gramians, Vector Fitting etc.
- mathematical analysis and systematic studies of machine learning based approaches for reduced order modelling, possibly, in comparison or combination with classical methods.
All contributions should present a real-world application or proven feasibility for relevant mathematical models. Manuscripts that focus on the application of methods to a problem are welcome too, provided the setup is relevant to practitioners and proper comparative studies are performed.
Data-based methods have been in use for model order reduction (MOR) for several decades. Established model reduction techniques like Proper Orthogonal Decomposition follow the idea of using data to fit and optimize a model for a given physical problem. With the ever-increasing availability of both data and computing resources and the recent trends towards the inclusion of machine learning (ML) in scientific computing, data-driven methods have gained new interest and application fields in MOR. In contrast to the more classical approaches, these are often entirely data-driven. While model-free or non-intrusive approaches have their success stories, additional benefits can be achieved by including model information as it is the principle of physics-informed neural networks.
In view of the efficient and automated handling of models for real-world problems, data and system-theoretic considerations are similarly important. Theoretical results can provide generally valid approaches and reliable performance guarantees, whereas the inclusion of data can tailor the model to a specific but possibly highly complex setup. Finding good compromises between mathematical rigour and data-based heuristics is the goal of this Research Topic.
This Research Topic covers classical methods and recent developments, trends, and applications in Model Order Reduction or Reduced Order Modelling with data and applications as the common divisor. We invite original research papers with:
- developments and applications of classical though data-oriented MOR methods like Proper Orthogonal Decomposition, Dynamic Mode Decomposition, Loewner, Reduced Bases, Operator Inference, Empirical Gramians, Vector Fitting etc.
- mathematical analysis and systematic studies of machine learning based approaches for reduced order modelling, possibly, in comparison or combination with classical methods.
All contributions should present a real-world application or proven feasibility for relevant mathematical models. Manuscripts that focus on the application of methods to a problem are welcome too, provided the setup is relevant to practitioners and proper comparative studies are performed.
