Field-Based Interpolation - Research Notebook

\boldsymbol{f} : \mathbb{R}^{D_\Omega}\times\mathbb{R}^+\times\mathbb{R}^{D_\theta}\rightarrow\mathbb{R}^{D_\Omega}

Interpolation Operator: A Physics-Informed Approach (Spatiotemporal Decomposition)
Abstraction: Amortization vs Objective-Based
Whirlwind Tour for 3 Architectures - CNNs, Transformers, Graphs
Convolutions
- Explaining Convolutions via Finite Differences
- More on Convolutions - FOV, Separable,
- FFT Convolutions via Pseudospectral Methods
- Missing Values & Masks
- Partial Convolutions
Transformers
- Attention is All You Need
- Transformers & Kernels
- Missing Data - Masked Transformers
Graphical Models
- Graphs and Finite Element Methods
- Missing Data
Dimension Reduction
- Dimensionality Reduction - What is it and why we need it? (SWM vs Linear SWM vs ROM)
- AutoEncoders I - PCA/EOF/SVD/POD
- AutoEncoders II - CNNs
- AutoEncoders III - Transformers (MAE)
- AutoEncoders IV - Graphs
Multiscale
- Introduction to Multiscale - Power Spectrum Approach
- U-Net I - CNN
- U-Net II - Transformers
- U-Net III - Graphs
Objective-Based Approaches
- Implicit Models I - Fixed Point/Root Finding
- Implicit Models II - Argmin Differentiation
- Implicit Models III - Deep Equilibrium Models
- From Scratch
- Packages - JaxOpt, optimistix
Conditional Generative Models
- Latent Variable Models
- Bijective Flows
- Stochastic Flows
- Surjective Flows
- Stochastic Interpolants