[Paper Review] Using Machine Learning for Model Physics: an Overview

Vladimir M. Krasnopolsky, Belochitski, Aleksei A.|arXiv (Cornell University)|Feb 2, 2020

Computational Physics and Python Applications39 references4 citations

TL;DR

This paper presents a comprehensive overview of using machine learning (ML) to improve model physics in atmospheric and oceanic simulations. It introduces a generic mathematical framework—mapping—to represent physical parameterizations, and reviews ML techniques for emulating, approximating, and enhancing these mappings while preserving physical constraints and improving accuracy.

ABSTRACT

In the overview, a generic mathematical object (mapping) is introduced, and its relation to model physics parameterization is explained. Machine learning (ML) tools that can be used to emulate and/or approximate mappings are introduced. Applications of ML to emulate existing parameterizations, to develop new parameterizations, to ensure physical constraints, and control the accuracy of developed applications are described. Some ML approaches that allow developers to go beyond the standard parameterization paradigm are discussed.

Motivation & Objective

• To establish a unified mathematical framework—mapping—for representing model physics parameterizations in atmospheric and oceanic models.
• To identify and evaluate machine learning tools capable of emulating or approximating complex physical mappings in climate models.
• To explore how ML can be used to develop new, more accurate parameterizations beyond traditional empirical approaches.
• To ensure physical consistency and constraint adherence in ML-based parameterizations, avoiding unphysical behavior.
• To improve the accuracy and reliability of climate model simulations through data-driven, physics-informed ML techniques.

Proposed method

• Introduces a generic mathematical object called a 'mapping' to represent the relationship between large-scale model variables and subgrid-scale physical processes.
• Reviews various machine learning models (e.g., neural networks, Gaussian processes) suitable for approximating complex, nonlinear mappings in model physics.
• Proposes using ML to replace or refine existing parameterizations by learning from high-resolution simulations or observational data.
• Applies physical constraints (e.g., conservation laws, monotonicity) as inductive biases in ML models to ensure physically plausible outputs.
• Employs loss functions that incorporate both data fidelity and physical consistency to train ML models for model physics.
• Discusses advanced ML approaches such as physics-informed neural networks and differentiable physics to go beyond standard parameterization paradigms.

Experimental results

Research questions

• RQ1 How can machine learning be systematically applied to represent and improve model physics parameterizations in climate models?
• RQ2 What types of machine learning models are most effective for approximating complex, nonlinear physical mappings in atmospheric and oceanic systems?
• RQ3 How can physical constraints be embedded into machine learning models to ensure consistency with fundamental laws of physics?
• RQ4 Can ML-based parameterizations outperform traditional empirical parameterizations in terms of accuracy and generalizability?
• RQ5 What are the limitations and opportunities of moving beyond the standard parameterization paradigm using ML techniques?

Key findings

• The mapping framework provides a unifying mathematical language for expressing model physics, enabling systematic application of ML techniques.
• Machine learning models such as feedforward neural networks and Gaussian processes can effectively emulate existing parameterizations with high accuracy.
• Incorporating physical constraints into ML models significantly improves their reliability and generalization, especially in extrapolation scenarios.
• Physics-informed ML approaches can produce parameterizations that are both data-driven and consistent with conservation laws and thermodynamic principles.
• ML-based parameterizations show potential to reduce biases in climate models and improve simulation fidelity without requiring full-scale high-resolution modeling.
• The paper identifies key challenges, including interpretability, uncertainty quantification, and computational cost, in deploying ML for operational model physics.