Norsk English

Supervision of master theses

Supervising master’s students is integral to our research. Here, we outline current directions where we offer thesis supervision in applied computational science.

Contact person

Research in the Applied Computational Science group at SINTEF Digital  covers a wide range of topics — from flow and transport in porous media to urban flooding, ocean dynamics, electrochemical systems, and agentic AI. We build and maintain open-source software and other community tools used by researchers and industry worldwide.

Over the past two decades, the group has supervised  close to 100 master’s and PhD theses, often in collaboration with NTNU’s Industrial Mathematics programme. Many of these projects have led to scientific publications and continued research through PhD studies or industrial careers.

Each year we offer a selection of master projects and research directions where students can contribute to ongoing research. The projects typically combine:

  • mathematical and numerical modelling,
  • implementation in existing simulation frameworks, and
  • application to real-world energy or environmental problems.

Research directions

Below are our current research directions where we offer master’s projects. Rather than listing predefined assignments, we outline broader themes. Our experience shows that defining the specific project together with the student — based on their interests, background, and progress — leads to stronger engagement and better scientific results. The final scope can range from numerical analysis and algorithm development to software implementation or applied case studies.

1. Rapid prototyping and AI-agentic simulation ecosystems

We develop flexible and modular simulation frameworks where users — or AI agents — can interact with simulators as active collaborators. This direction combines rapid prototyping of differentiable models with intelligent interfaces that support exploration, optimisation, and discovery in complex physical systems.

  • Build modular simulation environments (grids, discretisations, solvers) that enable fast development and integration of new physical models.
  • Embed automatic differentiation and computational-graph representations to make parts of the simulator trainable and optimisable.
  • Design AI-driven user interfaces and agent-based workflows that allow the simulator to respond to natural language or programmatic commands, analyse errors, and suggest improvements.

Typical tools: differentiable simulation, automatic differentiation, AI-agent workflows, modular solver frameworks.
Contact: Olav Møyner, Knut-Andreas Lie, Jakob Torben, Elling Svee (NTNU)
Read more: Rapid prototyping of differentiable simulators, Discussing with your simulator.

2. Graph- and AI-inspired methods for PDEs

We explore how numerical PDE models can be viewed and enhanced through graph and machine-learning concepts. By treating discretisations or reduced-order models as computational graphs, we develop hybrid approaches that merge physics-based structure with adaptive, data-driven components.

  • Replace fixed constitutive laws with trainable functional forms (e.g., neural networks) embedded inside simulators, so that parameters adapt through simulation to match observed system responses.
  • Combine physics-based reduced-order models (e.g., SINTEF’s CGNet) with neural-network correctors that learn residual discrepancies, improving predictive accuracy while retaining physical consistency.
  • Develop and analyse graph-based formulations of PDE solvers for efficient, interpretable model reduction.

Typical tools: optimisation, graph theory, machine learning, numerical PDEs.
Contact: Knut Andreas Lie, Øystein Klemetsdal, Stein Krogstad.
Read more:  Machine learning for physics-based modeling

3. Surface-water dynamics and urban flood resilience

Urban flooding is becoming an increasingly urgent challenge — especially in small-town settings where rivers and built environment meet. One interesting question to address is how to model the interplay of heavy rainfall, river overflow, and flood defence in towns such as Nesbyen (where the where the rivers Hallingdalselva and its tributary Rukkedøla surged during the Hans extreme weather in August 2023).

  • Develop high-resolution urban surface-water and river coupling models (e.g., using SWIM) to simulate extreme rainfall and river-overflow scenarios in towns like Nesbyen.
  • Assess the flood resilience of proposed defence works (for example the 6-m high levee system planned in Nesbyen) — investigate how such structures change flooding extents, return periods and inundation depths.
  • Develop modeling tools apropriate to quantify socio-hydraulic impacts: inundation of streets and buildings, evacuation zones, infrastructure at risk, and scenarios with and without mitigation works.
  • Integrate climate-change projections (e.g., heavier rain events, increased river flows) and multi-hazard coupling (flood + debris flow) in flood-risk modelling frameworks.

Typical tools: shallow-water equations, watershed analysis, urban hydraulics, stochastic rainfall/run-off modelling.
Contact: Odd Andersen, Kjetil Olsen Lye, Knut-Andreas Lie
Read more: Surface-water research, SWIM software.

4. Ocean and environmental forecasting

We develop simplified, GPU-accelerated ocean models (rotational shallow water, multi-layer, thermal variants) that can be initialised from operational forecasts and used for drift prediction and ensemble simulations.

  • Numerical methods for multi-layer shallow-water systems (hyperbolicity, stabilisation).
  • Thermal or stratified extensions and comparison with operational models.
  • Data assimilation and ensemble forecasting for Norwegian coastal regions.

Typical tools: GPU computing, finite-volume schemes, data assimilation.
Contact: Håvard Heitlo Holm.
Read more: Ocean modelling, GPUOcean.

5. Subsurface energy storage and carbon management

Underground hydrogen storage (UHS) and CO2 storage are essential technologies for the energy transition. We study how to optimise injection–withdrawal cycles, model caprock integrity, and develop reduced-order flow models.

  • Construct proxy or diagnostic models from high-fidelity MRST simulations.
  • Optimise operating cycles under caprock and pressure constraints.
  • Develop graph-based or machine-learning-inspired reduced models.

Typical tools: MRST, optimisation, porous-media flow.
Contact: Odd Andersen, Elyes Ahmed.
Read more: Carbon storage, hydrogen storage, MRST-co2lab

6. Electrochemical and energy-conversion systems

We model the coupled physics in batteries and electrolysers, focusing on degradation, swelling, bubble formation, and other effects that limit lifetime and efficiency.

  • Model degradation mechanisms in lithium-ion batteries (plating, SEI growth, swelling).
  • Simulate membrane degradation or gas transport in electrolysers.
  • Couple microscopic effects to macroscopic cell performance.

Typical tools: multi-physics modelling, PDE/ODE coupling, numerical simulation.
Contact: Xavier Raynaud, August Johansson.
Read more: Electrochemical modelling, BattMo.

7. Gridding, discretization, and robust solvers

Many of our simulation targets involve complex geometries that require flexible polyhedral/Voronoi-type grids and discretizations that preserve local conservation. On top of this, large-scale simulations depend on efficient linear and nonlinear solvers tailored to these grids.

  • Develop and test fast generators for conforming Voronoi/polytopal grids and assess grid quality for flow and mechanics.
  • Design and benchmark discretizations (FV, VEM, mimetic) for coupled flow–geomechanics on irregular grids.
  • Study iterative and multilevel solvers for the resulting linear systems, including preconditioners adapted to polytopal grids.
  • Explore nonlinear and domain-decomposition–based strategies for strongly coupled problems.

Typical tools: computational geometry, finite-volume/VEM/mimetic methods, iterative and nonlinear solvers.
Contact: Øystein Klemetsdal, Knut-Andreas Lie, Olav Møyner
Read more: Gridding and discretization, numerical solvers and solution algorithms.

8. Smart-city and network-flow models

Urban traffic flow can be formulated as a system of nonlinear conservation laws on a network, coupled with discrete optimisation for signal timing and control.

  • Model traffic flow using PDEs on complex road networks.
  • Optimise traffic-light switching or speed limits to minimise congestion.
  • Include data assimilation from sensor or camera data.

Typical tools: conservation laws, integer optimisation, network PDEs.
Contact: Kjetil Olsen Lye, Franz Fuchs.

9. Coupled mechanics, fracture, and phase-field problems

To simulate deformation and fracturing in porous media, we study coupled flow–mechanics systems using phase-field formulations and compatible discretisations on irregular grids.

  • Implement a phase-field fracture model coupled to elasticity.
  • Test consistent discretization methods for these PDE systems.
  • Apply to subsurface or structural simulation benchmarks.

Typical tools: PDE coupling, elasticity, phase-field models, VEM.
Contact: Xavier Raynaud, Halvor Møll Nilsen
Read more:  Geomechanics and its interaction with flow

10. Quantum Computing

Quantum computing provides a fundamentally different paradigm from classi- cal computation. Although the theoretical foundations were established in the 1980s, significant hardware progress has taken place only in the past decade. As devices continue to mature, advances on the algorithmic, modelling, and circuit-engineering side are equally important.

A central theme in quantum optimisation is the Quantum Approximate Optimization Algorithm (QAOA). It is well suited for problems that can be ex- pressed as Quadratic Unconstrained Binary Optimisation (QUBO), which en- compass a wide class of scheduling, routing, and resource-allocation tasks. A key research direction is the construction of mixer Hamiltonians that respect constraints and exploit structure such as symmetries, sparsity, or graph topol- ogy. Related work investigates constrained integer problems, advanced mixer families, and systematic approaches to modelling classical tasks in QUBO form.

Another active area is quantum circuit synthesis and hardware-aware compi- lation. This includes structured Hamiltonian decompositions, symmetry-preserving circuit constructions, qubit mapping, routing strategies, and methods for gen- erating shallow, hardware-efficient circuits suitable for both NISQ devices and future fault-tolerant platforms.

Students can work on topics such as:

  • QAOA for constrained combinatorial optimisation
  • Variational quantum eigensolvers for chemistry
  • Quantum random walks and their algorithmic applications
  • Circuit synthesis and decomposition
  • Qubit mapping and hardware-aware compilation

Typical tools: optimisation, QAOA, random walks, Qiskit
Contact:  Franz G. Fuchs, Alexander J. Stasik
Read more: NeQst, QC4DS, Q-NRI, NordIQuEst
Past theses: Rokne (2021), Uthayamoorthy (2002), 

Master theses supervised

2025
  1. Peder Brekke (NTNU): Digital twins for geothermal reservoirs. Advisors: K-A Lie, Ø. Klemetsdal, Stein Krogstad, Jakob Torben, Odd Andersen.
  2. Arianna Cagali (Politecnico Milano/NTNU): Hybrid optimization and neural network approaches for inverse learning in battery modeling. Advisors: F. Regazzoni, K-A Lie, X. Raynaud, K.O. Lye.
  3. Trygve Johan Kjellemo Tegnander (NTNU): An efficient finite volume solver for the shallow water equations on triangular meshes. Advisors: K-A Lie, K.O. Lye, Franz G. Fuchs.
  4. Trond Skaret Johansen (NTNU): Neural methods for reconstruction of organic shape. Advisors: X. Raynaud, G. Muntingh.
  5. Ylva Schüch (NTNU): Generalized Grover optimization for quantum random walks. Advisors: F. G. Fuchs.
2024
  1. Kristian Hægstad (NTNU): Reducing potential for urban flooding: Parameter optimization in a shallow-water model. Advisors: K-A Lie, H.H. Holm.
  2. Kristian Holme (NTNU): Grid orientation effects and consistent discretizations for simulation of geologic carbon storage: A study of the SPE11 benchmark. Advisors: K-A Lie, A. Johansson, O. Møyner.
  3. Torjei Helset (NTNU): Speed limit and traffic-light control for traffic-flow networks. Advisors: K-A Lie, K.O. Lye, F. Fuchs.
2023
  1. Ingvild S. Devold (NTNU): Graph-based methods for data-driven reservoir modeling. Advisors: K-A Lie, S. Krogstad, Ø. Klemetsdal.
  2. Sondre Husøy (NTNU): Constrained generation of Voronoi meshes using inscribed sphere distance. Advisors: K-A Lie, A. Johansson, Ø. Klemetsdal.
  3. Vetle Nevland (UiO): An extended fully-implicit hybrid model for geological CO₂ storage. Advisors: K-A Lie, O. Andersen, H. Hellevang.
  4. Bendik S. Waade (NTNU): Numerics-informed neural networks and inverse problems with hyperbolic balance laws. Advisors: K.O. Lye, E.R. Jakobsen.
2022
  1. Andreas Bjelland Berg (NTNU): Combining Gmsh and MRST – Developing software for more efficient grid creation in two dimensions. Advisors: K-A Lie, A. Johansson, Ø. Klemetsdal.
  2. Duy Duc Khuat (NTNU): Improved optimization methods for adjoint-based training of reduced-order models. Advisors: K-A Lie, S. Krogstad.
  3. VIroshaan Uthayamoorthy (NTNU): Quantum machine learning for variational quantum algorithms. Advisors: F. G. Fuchs, A.J. Stasik, J. Danon, H.M. Nilsen.
  4. Boye Gravningen Sjo (NTNU): Banditry and quantum agents. Advisors: G. Taraldsen, F. G. Fuchs.
  5. Ida Asperheim Holsæter (NTNU): An efficient adaptive variational quantum eigensolver. Advisors: F. G. Fuchs.
2021
  1. Anders Håøy Rokne (NTNU): Quantum error mitigation for CNOT-gates. Advisors: K-A Lie, F.G. Fuchs, J. Danon.
  2. Marius C. Landsverk (NTNU): Inductive bias and the information bottleneck method. Advisors: K-A Lie, S. Riemer-Sørensen.
2020
  1. Thibault Edward Gaudet (NTNU): Upscaling the effect of thin low-permeability shale layers on the vertical migration of CO₂. Advisors: K-A Lie.
2019
  1. Mona-Lena Norheim (NTNU): Investigating iterative solvers of Poisson-type equations discretized by the two-point flux-approximation scheme. Advisors: K-A Lie, O. Møyner.
  2. Sindre Grøstad (NTNU): Automatic differentiation in Julia with application to numerical solution of PDEs. Advisors: K-A Lie, O. Møyner, A.F. Rasmussen.
2018
  1. Pia-Kristina Heigrestad (NTNU): Nonlinear two-point flux approximation schemes. Advisors: K-A Lie, O. Møyner.
  2. Raymond Toft (NTNU): Two-phase reservoir simulation with the full approximation scheme. Advisors: K-A Lie, O. Møyner.
  3. Roman Bohne (NTNU): Machine-learning algorithms for the computation of upscaled permeabilities. Advisors: K-A Lie, X. Raynaud.
  4. Håkon Jarvis Westergård (KTH/NTNU): Fast marching and fast sweeping in optimal path planning. Advisors: K-A Lie, S. Zahedi, S. Krogstad.
  5. Asgeir Nyvoll (NTNU): Correlating recovery factors with measures of reservoir heterogeneity. Advisors: C.F. Berg, S. Krogstad.
  6. Ferenc Szekely (NTNU): Mathematical modeling and numerical study of viscous fingering. Advisors: X. Raynaud, H.M. Nilsen.
2017
  1. Anders Opskar Voldsund (NTNU): A mathematical model for calculating river hydrographs using high resolution digital elevation models. Advisors: K-A Lie, A. Brodtkorb, O. Andersen.
  2. Espen Høgh Sørum (NTNU):  CO2 sequestration - a near-well study. Advisors: X. Raynaud, O. Andersen.
2016
  1. Fredrik Johannesen (NTNU): Accelerated computation with the multiscale restriction-smoothed-basis method on distributed memory systems. Advisors: K-A Lie, O. Møyner.
  2. Andreas Almlien Røssland (NTNU): PRST – Python Reservoir Simulation Toolbox. Advisors: K-A Lie, O. Møyner.
  3. Ingeborg Gjerde (NTNU): Simulations of underground storage of natural gas. Advisors: K-A Lie, H.M. Nilsen.
  4. Runar Lie Berge (NTNU): Unstructured PEBI grids adapting to geological features in subsurface reservoirs. Advisors: K-A Lie.
  5. Magnus Jordstad (NTNU): Multigrid preconditioning of linear elasticity in anisotropic porous media. Advisors: K-A Lie, T. Kvamsdal.
  6. Stine Vennemo (NTNU): Multiscale simulation of thermal flow in porous media. Advisors: K-A Lie, O. Møyner.
2015
  1. Swej Shah (TU Delft): The multiscale restriction smoothed basis method for fractured porous media. Advisors: K-A Lie, H. Hajibeygi, O. Møyner, M. Tene.
  2. Aleksander Amundsen (NTNU/DTU): Microbial enhanced oil recovery – modeling and numerical simulations. Advisors: K-A Lie, X. Raynaud, S.M. Nielsen.
  3. Henrik Vikøren (NTNU): Towards a parallel multiphase solver based on potential ordering. Advisors: K-A Lie.
  4. Jens Kristoffer Reitan Markussen (UiO): An open-source framework for solving hyperbolic conservation and balance laws on GPUs. Advisors: K-A Lie, A.R. Brodtkorb.
  5. Cecilia Halmøy (NTNU): Estimation of pressure propagation in reservoirs using the fast-marching method. Advisors: K-A Lie.
  6. Guro Seternes (NTNU): Simulations of CO₂ migration with a fully-integrated VE model on the GPU. Advisors: K-A Lie, H.M. Nilsen, A. Brodtkorb.
  7. Tor Gramann Nærland (UiO): Accelerating Reactive Transport Modeling. Advisors: K-A Lie, A. Brodtkorb.
2014
  1. Håvard Heitlo Holm (NTNU): A CUDA back-end for the Equelle compiler. Advisors: H. Holden, F. Rasmussen.
  2. Svein Morten Drejer (NTNU): Optimal non-linear solvers: applications in reservoir simulation. Advisors: K-A Lie, H. Holden.
  3. Thea Knudsen (NTNU): Full implicit WENO scheme for two phase flow in reservoir simulation.. Advisors: K-A Lie, H. Holden, X. Raynaud.
  4. Elisabeth K. Prestegård (NTNU): A GPU accelerated simulator for CO2 storage. Advisors: H. M. Nilsen, H. Holden, A.R. Brodtkorb.
  5. Joachim Dyrdahl (NTNU): Thermal flow in fractured porous media and operator splitting. Advisors: A. F. Rasmussen.
  6. Vegard Ove Endresen Kjelseth (UiO): Efficient calculation of derivatives using automatic differentiation. Advisors: S. Krogstad.
  7. Sveinung Fossås (UiO): Level-of-detail metoder for visualisering av store isogeometriske modeller. Advisor: F.G. Fuchs.
2013
  1. Kristin A. Larssen (UiO): Steady-state upscaling of polymer flow. Advisors: K-A Lie, Daniel W. Schmid, Marcin Dabrowski.
  2. Espen Graff Berglie (NTNU): Higher-order methods for the shallow-water equations on GPUs. Advisors: K-A Lie, H. Holden, A.R. Brodtkorb.
2012
  1. Are Gabriel Høyland (UiB): Multiscale methods in reservoir simulation. Advisors: K-A Lie, H. Dahle.
  2. Jens Birkevold (NTNU): Divergence-free isogeometric methods for flow in porous media. Advisors: K-A Lie, T. Kvamsdal.
  3. Ruben Bø (NTNU): Mimetic discretizations on grids with curved surfaces. Advisors: K-A Lie, S. Krogstad, H. Holden.
  4. Simen Lønsethagen (NTNU): Krylov subspace accelerated algebraic multigrid for mimetic finite differences on GPUs. Advisors: K-A Lie, B. Skaflestad, H. Holden.
  5. Anders Hoff (NTNU): A parallel multiscale mixed finite element method for the Matlab Reservoir Simulation Toolbox. Advisors: K-A Lie, B. Skaflestad, H. Holden.
  6. Christine M. Ø. Haugland (NTNU): Applying hybrid methods to reduce nonphysical cycles in the flux field. Advisors: K-A Lie, S. Krogstad, H. Holden.
  7. O. Møyner (NTNU): Multiscale finite-volume methods on unstructured grids. Advisors: K-A Lie, B. Skaflestad, H. Holden.
  8. Lars Jahr Røine (UiO): Visualization of subsurface grids in Octave. Advisors: K-A Lie, C. Dyken.
  9. André Boganskij Amundsen (UiO): Auto-tuning shallow water simulations on GPUs. Advisor: F.G. Fuchs.
  10. Gard Skevik (UiO): Auto-tuning flood simulations on CPUs and GPUs. Advisor: F.G. Fuchs.
  11. Gorm Skevik (UiO): Load-balancing multi-GPU shallow water simulations on small clusters. Advisor: F.G. Fuchs.
2011
  1. Martin Ertsås (UiO): Vertically integrated models of CO₂ migration: GPU accelerated simulations. Advisors: K-A Lie, J.R. Natvig, M. Reimers.
2010
  1. Karianne H. Christensen (NTNU): Adaptive Voronoi grids in the MATLAB Reservoir Simulation Toolbox. Advisors: K-A Lie, J.R. Natvig, H. Holden.
  2. Gagandeep Singh (NTNU): Mimetic finite difference method on GPU. Application in reservoir simulation and well modeling.. Advisors: K-A Lie, B. Skaflestad, T. Kvamsdal.
2009
  1. Audun Torp (NTNU): Sparse linear algebra on a GPU (with applications to flow in porous media). Advisors: K-A Lie, T. Kvamsdal.
  2. Asbjørn Bydal (UiA): GPU-accelerated simulation of flow through porous medium. Advisors: K-A Lie, T.R. Hagen, O.-C. Granmo.
2008
  1. Ingeborg Skjelkvåle Ligaarden (UiO): Well models for mimetic finite difference methods and improved representation of wells in multiscale methods. Advisors: K-A Lie, S. Krogstad.
2007
  1. Lars Moastuen (UiO): Real-time simulation of the incompressible Navier-Stokes equations on the GPU. Advisors: K-A Lie, T.R. Hagen.
  2. Martin Lilleeng Sætra (UiO): Solving systems of hyperbolic PDEs using multiple GPUs. Advisors: K-A Lie, T.R. Hagen.
  3. Andre Rigland Brodtkorb (UiO): A Matlab interface to the GPU. Advisors: K-A Lie, T.R. Hagen.
  4. Trygve Fladby (UiO): Efficient linear algebra on heterogeneous processors. Advisors: K-A Lie, T.R. Hagen.
  5. Thomas Lunde (UiO): Comparison between mimetic and two-point flux-approximation schemes on PEBI-grids. Advisors: K-A Lie, J.E. Aarnes.
  6. Hanne Moen (UiO): Wavelet transforms and efficient implementation on the GPU. Advisors: K-A Lie, T.R. Hagen.
2006
  1. Ola Iver Røe (NTNU): Discontinous Galerkin methods with optimal ordering for fast reservoir simulation on unstructured tetrahedral grids. Advisors: K-A Lie, J.R. Natvig, H. Holden.
2003
  1. Jan-Frode Stene (NTNU): Central difference schemes for gas dynamics. Advisors: K-A Lie, H. Holden.
  2. Kjetil Bergh-Ånonsen (NTNU): Central difference schemes for gas dynamics. Advisors: K-A Lie, H. Holden.
  3. Vegard Kippe (NTNU): Streamline methods for reservoir simulation. Advisors: K-A Lie, H. Holden.
1999
  1. Thomas F. Skjønhaug (UiO): Finite volume methods for the two-phase pressure equation. Advisors: K-A Lie, A. Tveito.
1998
  1. Jostein R. Natvig (NTNU/UiB): Front tracking and operator splitting methods for the polymer system. Advisors: K-A Lie, H. Holden, K.H. Karlsen.
  2. Runar Holdahl (NTNU): Front tracking and operator splitting methods for the shallow water equations. Advisors: K-A Lie, H. Holden.