Abstractions - jejjohnson/research_journal_v2 GitHub Wiki

Hierarchical Assemblages of Hypothesis

  • Conservation Laws - Game of Dependencies, Model Form
  • System Architecture - Discretization
  • Process Parameterization
  • Uncertainty Specification
  • Inference Procedure

Model Components

  • Quantity of Interest
  • Observations
  • Latent Variables
  • Parameters
  • State

Game of Dependencies

  • Time & Space - Independent
  • Time & Space - Partially Dependent
  • Space - Globally Dependent
  • Time - Autoregressive

Model Form

  • Unconditional vs Conditional
  • Parametric vs Generative
  • Static vs Dynamic

Discretization

  • Regular
  • Rectilinear
  • Curvilinear
  • Unstructured Grid - (Finite Element, Finite Volume, Graphs) | (Line Segments, Triangles, Quadilaterals, Tetrahedrals)
  • Point-Clouds

Parameterizations

  • Linear
  • Basis Function
  • Non-Linear
  • Neural Network
  • Functional - Neural Field, DeepONer, Neural Operator

Uncertainty

  • Deterministic
  • Probabilistic
  • Bayesian

Inference

Bayesian Learning Rule

  • MLE
  • Approximate Inference
  • Sampling
  • Hybrid

Task: Learning

  1. Make Hypothesis, 2) Collect System Data, 3) Assess Likelihood, 4) Improve/Fix Hypothesis
  • Check Assumptions about Data —> Data Likelihood
  • State & Parameter Estimation
  • Process Parameterization Estimation
  • System Architecture Estimation