| Date |
Topics |
| Jan 5, 2026 |
Introduction to inverse and optimization problems, linear regression
[MP4]
[PDF]
|
| Jan 8, 2026 |
Introduction to deep learning, perceptron, neurons, activation functions, loss functions, simple linear regression, steepest descent method
[MP4]
[PDF]
|
| Jan 12, 2026 |
Polynomial regression, multiple linear regression, metric space, normed space, inner product space, Hilbert space, Euclidean space, linear functional, Riesz representation theorem
[MP4]
[PDF]
|
| Jan 15, 2026 |
Various spaces, Frechet and Gateaux derivatives, batch gradient descent (BGD), stochastic gradient descent (SGD), minibatch gradient descent (MGD)
[MP4]
[PDF]
|
| Jan 19, 2026 |
Linear conjugate gradient, underdetermined linear system and a minimum-norm straint, Tikhonov regularization
[MP4 (part 1),MP4 (part2)]
[PDF]
|
| Jan 26, 2026 |
Approximations in Hilbert spaces, methods for discretizing continuous problems, linear inverse problems governed by the Fredholm integral of first kind, singular value decomposition
[MP4]
[PDF]
|
| Feb 2, 2026 |
Methods for choosing regularization parameters |
| Feb 9, 2026 |
Nonlinear least-squares, Gauss-Newton and Levenberg-Marquardt methods |
| Feb 16, 2026 |
Metaheuristics |
| Feb 23, 2026 |
Metaheuristics (continued) |
| Mar 9, 2026 |
Adjoint method |
| Mar 16, 2026 |
Case study: Kirchhoff migration |
| Mar 23, 2026 |
Case study: Computed tomography |
| Mar 30, 2026 |
Case study: first-arrival traveltime tomography |
| Apr 20, 2026 |
Case study: full-waveform inversion |
| May 11, 2026 |
Project presentation |