Machine learning based ray interpolation in isotropic and anisotropic media

The wavefront construction (WFC) method is a powerful ray‑based technique for computing traveltimes and wavefronts in complex media. A persistent challenge is the interpolation of new rays between existing ones, especially in regions of strong heterogeneity or anisotropy. Traditional geometric interpolation schemes often fail near caustics, in high‑curvature regions, or when the slowness surface is non‑convex. This project explores the use of machine learning (ML) to develop robust, physics‑aware interpolation operators that can be integrated into the wavefront construction method.

Supervisors

Main supervisor: Einar Iversen, UiB-GEO
Co-supervisor: TBD

Project description

The student will begin with simple isotropic models and gradually extend the approach to anisotropic media (VTI, TTI). The core idea is to train a neural network, starting with a so-called multilayer perceptron (MLP), to predict the position and slowness of an ‘intermediate’ ray given its neighbors. A possible later extension is to use a graph neural network (GNN).

Training data will be generated using dense WFC simulations, from which rays are selectively removed to create supervised learning targets.

The project includes:

  1. Implementing ray tracing in isotropic and anisotropic media.
  2. Designing ML architectures for local interpolation.
  3. Incorporating physics‑informed constraints (e.g., Hamiltonian consistency).
  4. Evaluating accuracy, stability, and computational efficiency.
  5. Integrating the ML operator into a WFC prototype.
     

The project is well‑bounded but offers room for innovation. It is suitable for a student with interest in computational geophysics, numerical methods, and machine learning.

Last updated: 19.06.2026