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f:RDΩ×R+×RDθ→RDΩ\boldsymbol{f} : \mathbb{R}^{D_\Omega}\times\mathbb{R}^+\times\mathbb{R}^{D_\theta}\rightarrow\mathbb{R}^{D_\Omega}
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  • 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
Geo Interpolation
Coordinate-Based
Geo Interpolation
Dynamical