Abstractions Overview

Geoscience Tasks¶

Interpolation. Within Convex Hull of points; Missingness

Extrapolation. X-Casting; Problems - Data Drift, Distribution Shift, Bad Generalization

Variable Transformation. Multivariate, High-Correlation, High-Dimensionality

Operator Learning¶

A Space, time, and quantity perspective

Quadrant of Things That Can Go Wrong¶

• Measurements
• Domain Shape
• Model
• Solution Procedure

Designing Models for Dynamical Systems¶

A Hierarchical Sequence of Decisions (Gharari et al, 2021)

Data-Driven Model Elements with PGMs¶

• Pieces - Observations, Covariates, Latent Variables, Quantity of Interest
• Directions - Directional, Bi-Directional, Non-Directional
• Independence

Bayesian Modeling¶

• Data Likelihood, Prior, Marginal Likelihood
• Posterior, Prior Predictive Distribution, Posterior Predictive Distribution
• Variational Posterior

ML Algorithm Abstractions¶

How to read ML papers effectively.

• Data Module
• Model
• Criteria
• Optimizer
• (Learner)

Software Stack¶

• Hardware Agnostic Tensor Library - jax
• AutoDifferentiation - jax
• Deep Learning Library - keras
• Probabilistic Programming Language - numpyro