MS045 - Discovering Evolution Equations Using Structure-Preserving Data-Driven Methods
Keywords: data-based methods, machine learning, structure-preserving model
In recent years, there has been a growing interest in integrating data-driven approaches with traditional physics-based modeling to discover evolution equations for mechanical systems. While traditional physics-agnostic learning (natural language, images) have employed structure preserving architectures (e.g. SO(3) invariance, equivariance) to improve sample complexity, structure preservation is arguably more important in physical contexts, where structures related to the underlying geometry and algebraic structure of physics are intricately related. Particularly, more attention is being paid to developing methods that encode and preserve the underlying physical structures, such as symmetries, conservation laws, and thermodynamic consistency, ensuring that these models are both accurate and physically meaningful. This minisymposium will explore the development and application of structure-preserving data-driven methods for discovering evolution equations that can reliably model complex systems while adhering to these fundamental principles.
The focus will be on innovative approaches that incorporate mathematical and physical constraints into machine learning frameworks, ensuring that the resulting models not only predict system behavior accurately but also respect essential physical laws. These approaches are crucial in fields like constitutive model discovery, reduced-order modeling, digital twins, multiscale modeling, fluid mechanics, and material science, where the preservation of these structures is key to developing robust and reliable models.
Topics of interest for this minisymposium include, but are not limited to:
· Machine learning for discovering governing equations while preserving symmetries, conservation laws, thermodynamic constraints, and other physical and mathematical structures.
· Constitutive modeling and multiscale modeling using thermodynamic-consistent data-driven methods.
· Fusion of machine learning with finite element methods, isogeometric analysis, geometric mechanics, and others traditional computational mechanics techniques.
· Model discovery using physically interpretable machine learning techniques.
· Advanced structure and symmetry preserving techniques applied to reduced order modeling.
· Uncertainty quantification of structure-preserving data-driven methods.
The focus will be on innovative approaches that incorporate mathematical and physical constraints into machine learning frameworks, ensuring that the resulting models not only predict system behavior accurately but also respect essential physical laws. These approaches are crucial in fields like constitutive model discovery, reduced-order modeling, digital twins, multiscale modeling, fluid mechanics, and material science, where the preservation of these structures is key to developing robust and reliable models.
Topics of interest for this minisymposium include, but are not limited to:
· Machine learning for discovering governing equations while preserving symmetries, conservation laws, thermodynamic constraints, and other physical and mathematical structures.
· Constitutive modeling and multiscale modeling using thermodynamic-consistent data-driven methods.
· Fusion of machine learning with finite element methods, isogeometric analysis, geometric mechanics, and others traditional computational mechanics techniques.
· Model discovery using physically interpretable machine learning techniques.
· Advanced structure and symmetry preserving techniques applied to reduced order modeling.
· Uncertainty quantification of structure-preserving data-driven methods.
