Generalized neural closure models with interpretability.

Area of Science:

• Computational Physics
• Machine Learning
• Scientific Computing

Background:

• Dynamical models in computational physics often lack predictive capability and are computationally expensive.
• Existing machine learning approaches struggle with interpretability and generalization across various conditions.

Purpose of the Study:

• To develop a versatile methodology that addresses interpretability, generalization, and computational cost challenges in augmenting dynamical models with machine learning.
• To introduce unified neural partial delay differential equations for enhanced predictive modeling.

Main Methods:

• Augmenting existing partial differential equation (PDE) models with Markovian and non-Markovian neural network (NN) closure parameterizations.
• Developing a flexible framework for designing unknown closure terms using various NN architectures and input libraries.
• Obtaining adjoint PDEs for direct implementation across diverse computational physics codes and ML frameworks.

Main Results:

• The generalized neural closure models (gnCMs) framework demonstrated improved generalization across different resolutions, conditions, and parameters.
• Learned gnCMs successfully discovered missing physics, identified numerical error terms, and provided interpretable insights.
• The framework showed computational advantages and compensated for limitations in simpler models.

Conclusions:

• Unified neural partial delay differential equations offer a powerful approach to enhance dynamical models in computational physics.
• The developed gnCMs framework achieves significant improvements in interpretability, generalization, and computational efficiency.
• This methodology paves the way for more robust and versatile physics-informed machine learning applications.