Physics-constrained, low-dimensional models for magnetohydrodynamics: First-principles and data-driven approaches.

Area of Science:

• Plasma physics
• Computational physics
• Nonlinear dynamics

Background:

• Plasmas exhibit complex nonlinear and multiscale behaviors requiring diverse modeling approaches.
• A gap exists in lower-fidelity plasma models below magnetohydrodynamics (MHD) for efficient analysis and control.
• Reduced-order models offer potential for understanding key physical mechanisms and real-time applications.

Purpose of the Study:

• To develop a reduced-order modeling framework for compressible plasmas.
• To bridge projection-based and data-driven modeling techniques for plasma systems.
• To create more accessible and computationally efficient plasma models.

Main Methods:

• Formalized projection-based model reduction for nonlinear magnetohydrodynamics (MHD) systems.
• Introduced an energy inner product to create a unified reduced-order basis for plasma fields.
• Applied Galerkin projection to Hall-MHD equations and demonstrated constraint by conservation laws.

Main Results:

• Developed a dimensionally consistent, reduced-order basis for plasma fields.
• Derived an analytic model via Galerkin projection of Hall-MHD equations.
• Showcased model effectiveness using data from 3D spheromak simulations.

Conclusions:

• The framework effectively integrates projection-based and data-driven modeling for plasmas.
• Conservation laws and symmetries provide crucial constraints for data-driven plasma models.
• This work facilitates principled development of reduced-order plasma models, linking to fluid mechanics literature.