Current Research Interests

• Neural PDE Solvers Resource Home Page
  • Neural Operators (Learning in infinite-dimensional function spaces, as opposed to traditional neural networks that learn vector-to-vector mappings)
  • Physics Informed Neural Networks (Solving PDEs by penalizing the extent to which the network solution violates the PDE)
• Equivariance (Embedding symmetries into networks) Resource Home Page
  • Group CNN (Lifts features to the group space and performs convolutions in the group space; used more in vision tasks).
  • Geometric GNNs (Restrict features and/or operations to maintain equivariance; used more for geometric data (e.g., point clouds with spatial coordinates)
  • Unconstrained Methods (Offset the symmetries to the data instead of the model; particular useful for large pretrained models, e.g. LLMs)
• Generative Models (Learning the underlying data distribution and generate new, realistic samples that resemble the original data) Resource Home Page
  • Mathematical and statistical aspects of generative models (e.g. accelerating generative models)
  • Generative models for science (e.g. drug designs)

More details and overviews are available in Technical Blogs.