Below are examples of projects our group can offer as Bachelor or Master semester projects or Master thesis projects (PdM). This list is not exhaustive and other topics related to our research are equally possible. If you are interested in a project or Master thesis with us, please make yourself familiar with our general guidelines about student projects.
Finally, if you are a student outside EPFL, please take a look at the summer research opportunities listed on our Job Openings website.
Overview of projects:
Density-functional theory simulations allow computing key material properties. In this work we will investigate how reducing the size of the discretisation basis employed for the simulations impacts the quality of the obtained properties (see below). We will employ recent perturbative error estimates[1] in order to quantify the expected error in the obtained properties versus a fully converged discretisation. For this work we will employ the density-functional toolkit (DFTK), a first-principle materials simulation code based on density-functional theory in which the aforementioned error estimates are implemented and readily available. To see how this works in practice, see this Research Demo.
The properties that we want to focus on are:
Geometry - Atom positions: A key step when simulating the properties of a material is structure optimisation. In this process an approximate arrangement of atoms in a crystal is optimised to obtain the most stable configuration, based on the computed interatomic forces.
Geometry - Stresses: Another key step is the computation of the optimal crystal cell parameters, based on the computed stresses.
Equations of state, which relate the volume change of a material to its total energy. The equation of state of a material can be used to extract important properties such as the bulk modulus, as well as a precision benchmark across many DFT codes [2].
Band structures, which are often a first step in the computation of more advanced properties such as electrical resistivity and optical absorption.
Requirements: Strong programming skills, ideally Julia or python; Basic knowledge of numerical methods for partial differential equations; Experience in numerical analysis of PDEs is a bonus; Experience in running DFT calculations is a bonus;
| [1] | E. Cancès, G. Dusson, G. Kemlin and A. Levitt. SIAM J. Sci. Comp. 44 (2022). ArXiv 2111.01470 |
| [2] | Bosoni, E., Beal, L., Bercx, M. et al. How to verify the precision of density-functional-theory implementations via reproducible and universal workflows. Nat Rev Phys 6, 45–58 (2024). |
Density-functional theory (DFT) simulations are a central ingredient in modern materials modelling and such simulations are run in the millions every day across the world's supercomputers. The typical fixed-point problem underlying DFT is solved iteratively using a variant of standard fixed-point iterations termed self-consistent field (SCF) iterations. In particular for challenging materials system the SCF can converge very slowly. Convergence acceleration techniques (such as Anderson acceleration) are thus regularly employed and amount to speed up convergence. In a nutshell these methods build adapted linear combinations by solving a linear regression problem. However, typically the error in the regressed iterates (i.e. the fact that these are polluted with numerical noise) is completely ignored. In this project we want to develop a suitable adaptation of Anderson acceleration by combining this method with ideas from statistical learning in order to take numerical errors into account.
Requirements: Strong programming skills, ideally Julia or python; Background in numerical methods, in particular for solving non-linear problems and eigenvalue problems; Interest or experience with statistical regression, in particular Bayesian methods; Experience in solid-state physics and materials modelling is a bonus;
A central goal of modern materials modelling is to predict the chemical and physical properties of a material. Such properties colloquially describe how the material behaves under a change of external conditions such as a change of electromagnetic field, some external pressure. In the context of density-functional theory (DFT) simulations computing such properties requires the solution of a nested set of linear systems, that is one outer linear system, where each application of the linear operator itself requires solving hundreds of inner linear systems. Our recent research [3] [4] has proposed a framework based on inexact Krylov subspace methods to solve this problem efficiently. In this project we will investigate the adaptation of block Krylov techniques and Krylov subspace recycling techniques (such as [5]) to this challenging application setting.
Requirements: Strong programming skills, ideally Julia or python; Background in numerical methods, in particular for solving non-linear problems and eigenvalue problems; Interest or experience in Krylov subspace methods, such as GMRES or Arnoldi; Experience in solid-state physics and materials modelling is a bonus;
| [3] | E. Cancès, M. F. Herbst, G. Kemlin, A. Levitt, B. Stamm. Numerical stability and efficiency of response property calculations in density functional theory. Lett. Math. Phys. 113, 21 (2023). DOI 10.1007/s11005-023-01645-3 |
| [4] | M. F. Herbst and B. Sun. Efficient Krylov methods for linear response in plane-wave electronic structure calculations. ArXiv 2505.02319 |
| [5] | R. B. Morgan. GMRES with Deflated Restarting SIAM J. Sci. Comp. 24, 20 (2002). |
In almost all plane-wave density-functional theory (DFT) simulations one employs a pseudopotential to model the interactions between atoms and electrons. While this represents an additional approximation (on top of the DFT model and the discretisation basis), this trick contributes considerably to making the numerics feasible in practice. Common pseudopotential models feature a multitude of parameters, which are determined following an involved fitting procedure. In practice the pseudopotential choice and the choice of DFT model are tightly coupled. However, since targeted pseudopotentials are not known for all DFT models, practitioners frequently perform DFT calculations with a mismatching pseudopotential.
The goal of this project is to understand the discrepancy introduced by a mismatch between pseudopotential and DFT functional. This will involve both an analytical component, studying the variation under a change of pseudopotential using perturbation theory as well as a numerical component featuring systematic numerical experiments on standard DFT test problems.
Requirements: Strong programming skills, ideally Julia or python; Basic knowledge of numerical methods for partial differential equations; Experience in numerical analysis of PDEs is a bonus; Experience in running DFT calculations is a bonus;
Data-driven materials modeling plays a crucial role in modern materials discovery. Statistical models trained on large datasets of first-principles simulations provide efficient and accurate predictions of material properties, reducing the need for costly computations. However, datasets generated from density-functional theory (DFT) calculations, which underlie many data-driven approaches, face two key challenges:
Non-uniform computational cost: The cost of DFT calculations varies significantly across materials due to differences in numerical parameters, such as discretization basis, k-point sampling, tolerances, required to achieve a target accuracy.
Data heterogeneity: Training data often come from diverse sources with varying levels of uncertainty, which affects the reliability of predictive models.
Active learning is a promising approach for improving the efficiency of data-driven materials modeling by adaptively selecting the most informative data points for further computations. Currently, a common approach is to compute the entire dataset with a fixed discretization (e.g., plane-wave cutoff) chosen a priori (e.g. [6] and [7]), which may not optimally balance computational cost and accuracy across diverse materials.
The goal of this project is to investigate directions that overcome these challenges by integrating active learning with uncertainty-aware models. This involves formulating an active learning approach that adaptively selects both material structures and numerical parameters to optimize computational resources, while employing Gaussian process regression [8] to effectively propagate and manage uncertainties in heterogeneous datasets. By combining these techniques, the project aims to improve the accuracy, efficiency, and reliability of data-driven materials modeling.
Requirements: Strong programming skills, ideally Julia or Python; Experience with probabilistic machine learning methods, Gaussian processes, Bayesian optimization; Experience in running DFT calculations is a bonus; Basic knowledge of numerical methods for partial differential equations is a bonus.
| [6] | C. van der Oord, M. Sachs, D. P. Kovács, C. Ortner and G. Csányi . Hyperactive learning for data-driven interatomic potentials. npj Comput Mater 9, 168 (2023). DOI 10.1038/s41524-023-01104-6 |
| [7] | A. Merchant, S. Batzner, S. S. Schoenholz, M. Aykol, G. Cheon and E. D. Cubuk. Scaling deep learning for materials discovery. Nature 624, 80–85 (2023). DOI 10.1038/s41586-023-06735-9 |
| [8] | C. E. Rasmussen & C. K. I. Williams, Gaussian Processes for Machine Learning, the MIT Press, 2006. DOI 3206.001.0001 |
Automatic differentiation (AD) is a technique to reinterpret the implementation of an algorithm in order to compute not only the output quantities of the map, but also its Jacobian, that is all derivatives of all outputs versus all inputs. As derivatives play an essential role in physics, it is worthwhile developing such capabilities further. For a showcase example how AD can be used in density-functional theory and materials modelling see this Research Demo.
This project is to extend DFTK's symmetry handling capabilities to work with automatic differentiation. Symmetry handling becomes even more important in the case of partially symmetry-breaking perturbations, for materials properties such as phonons and elastic constants. The project involves deriving methods that combine crystallographic symmetry analysis[9] with derivative computations, helping to optimize density-functional theory calculations [10]. This would be a fruitful contribution to the open-source DFTK framework.
Requirements: Solid numerical programming skills, ideally in Julia or python; Practical knowledge of group theory and representation theory; Bonus: Prior knowledge about DFT.
| [9] | Togo, A., Shinohara, K., & Tanaka, I. (2024). Spglib: a software library for crystal symmetry search. Science and Technology of Advanced Materials: Methods, 4(1). https://doi.org/10.1080/27660400.2024.2384822 |
| [10] | https://docs.dftk.org/stable/developer/symmetries/ |
Pseudopotentials are an essential component of modern plane-wave density-functional theory (DFT) computations for materials. Their construction represents a fundamental trade-off between smoothness (or "softness"), which dictates the computational cost, and transferability across diverse chemical environments.
Standard generation involves a two-phase approach: fitting parameters to isolated atoms, followed by validation in bulk systems (e.g. [11]). In practice, this process is frequently repeated in an iterative trial-and-error fashion to semi-automatically navigate this trade-off.
In this project, we aim at a more targeted optimization using gradient information. We will explore the learning of pseudopotentials directly in bulk materials, utilizing recent algorithmic differentiation (AD) tools for plane-wave DFT [12]. The goal is to minimize errors against high-precision all-electron references automatically, yielding potentials that are both efficient and highly accurate for specific applications.
Requirements: Strong numerical programming skills, ideally Julia or Python; Understanding of gradient-based optimization methods; Bonus: Prior knowledge about DFT.
| [11] | M.J. van Setten, M. Giantomassi, E. Bousquet, M.J. Verstraete, D.R. Hamann, X. Gonze, & G.-M. Rignanese (2018). The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table. Computer Physics Communications, 226, 39-54. DOI 10.1016/j.cpc.2018.01.012 |
| [12] | N. F. Schmitz, B. Ploumhans, M. F. Herbst. (2025) Algorithmic differentiation for plane-wave DFT: materials design, error control and learning model parameters. npj Computational Materials (in press). DOI 10.1038/S41524-025-01880-3 (Preprint: https://arxiv.org/abs/2509.07785) |
