These blogs aim to (1) simplify abstract concepts for newcomers and (2) provide the broader ML/DL community with a quick overview of my research areas. Coding examples are provided to illustrate these concepts. The code is much simpler compared to complex libraries, but it includes the essential functionalities needed to grasp the underlying concepts. The goal is to ensure that anyone can easily follow each line of code and run the experiments within minutes on almost any laptop, computer, or Google Colab.

The code accompanying these blogs can be found Here.

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Technical BLOGs

  • All
  • Equivariance
  • Neural PDE Solvers
  • Generative Models
  • Others

Group CNNs

- Lift the features to the group space
- Input Transformation → Output transformation
- Used more often in computer vision
- With broader applications to many fields

Geometric GNNs

- Taking 3D geometric graphs as inputs
- Ensure Euclidean (Roto-translation) symmetries
- Used more often in 3D molecular learning
- Broader applications to any geometric point clouds

Unconstrained Methods

- Offset the symmetries to the data
- The model can be of any architecture
- Does not constrain the features or operations
- Broad applications to any geometric data

Operator Learning

- Learning mappings between function spaces
- Data-driven PDEs solving
- Bridging physics and data
- Weather forecast, fluid dynamics, etc.

PINN in 5 Minutes

- Solving PDEs with neural networks
- Physics constraints in loss functions
- Can train without data
- No explicit numerical discretization

DeepONet

- Operator with learned basis functions
- No explicit discretization for the output
- Fixed sensor points for the input
- Based on universal approximation

Fourier Neural Operator

- Integral neural operator
- Learn in the frequency domain directly
- Global sinusoidal filters
- Fast and accurate

Intro: Generative Models

- Generative model → Probability distribution
- Sampling → Generation
- Discriminative vs. Generative
- Broad applications beyond generation

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