Teaching¶

Graduate Courses in Mathematics¶

Topic: Computational Inverse Problems and Uncertainty Quantification — From Calculus to Neural Networks

Numerical methods for inverse problems governed by physical models, where the models are systems of partial and ordinary differential equations
Deterministic and Bayesian inverse problems
Ill-posedness, regularization, and variational methods
Large-scale computational solution algorithms
Solution of inverse problems with neural networks

Interfaces that make human–computer interaction efficient and systematic; including terminal, editors, version control, and AI coding agents
The Go language and parallel programming with shared memory and with communication
The C language with MPI for distributed memory computing, and the PETSc library
GPUs with NVIDIA CUDA for massive concurrency

Interfaces is about the tools that make human-computer interaction efficient and systematic, including effective uses of terminals, editors, version control, AI tools, and more.
The Go language has build-in concurrency to challenges our abilities on parallel thinking. It guides us toward understanding concurrency, interdependence of actions, shared memory across workers, distributed memory and communication between workers.
Neural networks with PyTorch allow tapping into massive parallelism. By building on our lower-level skills, we understand – and appreciate – how neural networks are trained even when Python interfaces hide much of the complexity. We will be able to train in parallel using distributed data parallelism.

Concepts and techniques from numerical linear algebra, including iterative methods for solving linear systems and least squares problems, and numerical approaches for solving eigenvalue problems
III-posed inverse problems such as parameter estimation, and numerical methods for computing solutions to inverse problems
Numerical optimization with emphasis on large-scale problems