Dynamical-Based Interpolation - Research Notebook

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

Operator Learning Revisited - Universal Differential Equations
Whirlwind Tour - Spatial Operators
Training
- Experimental Setup - OSSE vs OSE
- Online
- Offline
Spatial Operators Deep Dive
- Linear Spatial Operator & MLP
- Convolutions
- FFT Convolutions
- Spectral Convolutions
- Transformers
- Graphical Models
Bayesian Filtering
- State Space Models
- Parameter & State Inference in SSMs
- Linear Models + Exact Inference - KF
- Non-Linear Model + “Exact” Inference - EKF, UKF, ADF
- Whirlwind Tour of Deterministic Inference for SSMs
- Amortized Variational Posteriors (Encoders)
- Whirlwind Tour of Stochastic Inference for SSMs
Nonparametric Revisited
- Markovian Gaussian Processes
- Sparse Markovian Gaussian Processes
Latent Generative Dynamical Models
- Latent State Space Models
- Conjugate Transforms - Conditional Markov Flows
- Stochastic Transform Filters
- Observation Operator Encoders
- Stochastic Differential Equations
- Neural Stochastic Differential Equations