ML4EO Abstractions

Goals¶

• Objective

• Task

Estimation vs Learning¶

Using models as a means of estimating or predicting a QoI.

Using models as a means of learning.

Modeling & Simulation¶

• Earth System

• Abstraction -> Model

• Measurements -> Data

• Model -> Predictions

Hierarchical Assemblage of Hypothesis¶

• Conservation Laws

• System Discretization

• Process Parameterization

• Uncertainty Quantification

• Solution Procedure

• Sensitivity Analysis

• Iterative Hypothesis Refinement

ML4EO¶

Geo Tasks¶

• Interpolation - Missingness

• Extrapolation - Data Drift, Distribution Shift, Bad Generalization

• Variable Transformation - Multivariate, High Correlation

• Feature Extraction - Ad-hoc, Foundation Models, Downstream Tasks, Transfer Learning

Geo Issues¶

• Measurements

• Data Shape

• Model

• Solution Procedure

Geo Operations¶

Game of Spatiotemporal Dependencies¶

• IID

• Partial

• Global

• Autoregressive

Operator Learning¶

• Space

• Time

• Quantity

• Shape

• Transformation

Hierarchical Sequence of Decisions¶

Data-Driven Modeling Elements¶

• Measurements

• State

• Quantity of Interest

• Latent Variable

Bayesian Modeling¶

• Data Likelihood

• Prior

• Posterior

• Marginal Likelihood

• Prior Prediction

• Posterior Prediction

• Sampling

• Inference

Discretization¶

• Regular

• Rectilinear

• Curvilinear

• Unstructured - FEM/FVM/GNNs (line segments, triangles, quadrilateral, tetrahedral)

• Point Clouds

Parameterization Complexity¶

Parametric

• Linear

• Basis Function

• Neural Network

Functional

• Neural Fields

• Deep ONets

• Neural Operators

Machine Learning Abstractions¶

• Data Module

• Model

• Criteria

• Optimizer

• Learner

Model Form¶

• Parametric

• Generative

• Conditional Parametric

• Conditional Generative

• Dynamical

Software¶

• Hardware Agnostic Tensor Libraries

• AutoDifferentiation

• Deep Learning

• Probabilistic Programming Libraries

• Data Pipelines