Seminar Scientific Computing (Martin Klakow)

Generative diffusion models have emerged as a leading approach dir="ltr">

In the field of MRI several different reconstruction methods exist to compute specific tissue properties encoded in modern generative modeling.
These models relaxation times. MRI is based on nuclear magnetic resonance and does not rely on a stochastic process X-rays or ionizing radiation. It has been shown that bridges an unknown data distribution with a wellunderstood
reference distribution. Despite their empirical success, current diffusion models are
subject to several sources Levenberg-Marquardt algorithm is capable of error. These include approximation errors arising from reconstructing the use parameters of neural
networks to estimate intractable quantities, interest.

This master’s project is about understanding and implementing a corresponding forward model based on a discretization errors introduced when simulating
continuous-time processes, of the underlying Bloch dynamics. Since the forward problem is nonlinear, the corresponding Fréchet derivative and truncation errors due to terminating its adjoint are also explicitly derived and implemented with or without a matrix representation. As first attempt, the process at a finite time.iterative Gauss-Newton Method (IRGNM) was used, but it turned out that an accurate solution of the corresponding linear systems in each step is unfeasible. Therefore, it was decided to switch to Landweber iteration.
By integrating tools from numerical analysis As the project is still in process, the talk will cover the theoretical background and stochastic process theory, a rigorous mathematical
understanding the results achieved by the day of diffusion models can be developed, enabling a systematic characterization