A primer on variational inference for physics-informed deep generative modelling.

Area of Science:

• Computational Physics
• Bayesian Inference
• Machine Learning

Background:

• Variational inference (VI) is a scalable method for approximate Bayesian inference.
• It balances uncertainty quantification accuracy with computational tractability.
• VI is well-suited for generative modeling and inversion tasks in physics.

Purpose of the Study:

• To provide a technical introduction to VI for physics-based forward and inverse problems.
• To guide readers on implementing VI using deep learning.
• To review and unify recent literature on VI applications in physics.

Main Methods:

• Derivation of the VI learning objective tailored to physical models.
• Integration of VI with deep learning frameworks.
• Review of existing literature on VI flexibility in physical inference.

Main Results:

• Demonstration of VI's effectiveness in physics-based problems.
• Highlighting the role of physical model structure in VI.
• Showcasing the flexibility of VI through diverse applications.

Conclusions:

• VI is a powerful tool for uncertainty quantification in physics.
• Deep learning enhances the realization of VI for complex problems.
• This work unifies and expands the understanding of VI in scientific computing.