Section 2 Conventions
Subsection 2.1 Mathematical Notation
A reference for mathematical notation used throughout the notes.
- \(\mathbf{u},\mathbf{v}\)
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Vectors in the vector space \(\mathcal{V}_n\in\mathbb{R}^n\text{.}\)
- \((\mathbf{q},\mathbf{p})\)
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A point in phase space where \(\mathbf{q}\) represents the generalized coordinates and \(\mathbf{p}\) represents the conjugate momenta.For this work, we will assume \(q=\|\mathbf{q}\|\) denotes the magnitude of the coordinate vector and \(p=\|\mathbf{p}\|\) denotes the magnitude of the momentum vector, respectively.
- \(\{A, B\}\)
-
The Poisson bracket between two scalar functions \(A(\mathbf{q},\mathbf{p})\) and \(B(\mathbf{q},\mathbf{p})\text{.}\)
Subsection 2.2 Abbreviations
- GA
-
Geometric Algebra
- psd
-
positive semi-definite
- PSD
-
power spectral density
- PIML
-
Physics-Informed Machine Learning
- PINN
-
Physics-Informed Neural Networks
