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:
Keywords: Statistical machine learning; uncertainty quantification
Surrogate models of the potential energy surface (PES) approach the accuracy of DFT at a much lower computational cost, and are becoming popular in large-scale material science applications, notably for machine-learning interaction potentials (MLIPs) in molecular dynamics simulations.
Informative and affordable uncertainty quantification (UQ) methods is crucial here, both to put error bars on predictions in the interpolative regime, and also to detect the boundary of the extrapolative regime where surrogate models break down, enabling active learning strategies.
Parametric surrogate models are fitted using a dataset of a high-fidelity method (e.g. from DFT computations), where observation noise is typically negligible. The dominant source of the prediction error is by far the incompleteness or of the model: no choice of the model parameters can explain all the data. In this misspecified regime, we can describe the predictive uncertainty is by defining a probability distribution over model parameters or posterior ensemble, as in Bayesian regression.
The POPS[1] algorithm, recently proposed in[2], has proven to be a scalable method for materials applications[3], but relies on a crude error model. In particular, the error model is independent of the position on the PES. As a result, we expect the standard POPS posterior to overestimate the uncertainty in well-fitted regions of the PES.
The goal of this project is to extend the POPS algorithm with clustering methods in the space of model parameters, allowing the construction of more complex posteriors. By training a classifier to assign configurations to parameter clusters, we will create a refined, configuration-dependent model of the mispecification error, and hopefully obtain better-calibrated uncertainties. This clustered POPS approach is closely related to mixture-of-experts strategies explored in the recent MLIP literature (e.g. [4]).
A first target application is the estimation of defect migration barriers in imperfect crystals, using high-dimensional linear models. If succesful, the approach could be extended to more sophisticated MLIPs, and released within the POPSRegression.jl package.
Requirements: Strong programming skills, ideally Julia (or Python and a willingless to learn Julia); Working knowledge of Bayesian statistics/probabilistic regression; Experience in implementing machine learning models; Experience in running DFT calculations is a plus;
| [2] | T.D. Swinburne & D. Perez (2024). Parameter uncertainties for imperfect surrogate models in the low-noise regime. Machine Learning: Science and Technology, 6(1). DOI 10.1088/2632-2153/ad9fce |
| [3] | D. Perez, A.P.A. Subramanyam, I. Maliyov, T.D. Swinburne (2025). Uncertainty quantification for misspecified machine learned interatomic potentials. npj Computational Materials, 11(1). DOI 10.1038/s41524-025-01758-4 (Preprint: https://arxiv.org/abs/2502.07104) |
| [4] | N.C. Nguyen & D. Sema (2024). Environment-adaptive machine learning potentials. Physical Review B, 110(6). DOI 10.1103/PhysRevB.110.064101 (Preprint: https://arxiv.org/abs/2405.00306) |
| [1] | pointwise optimal parameter sets |
Keywords: Statistical machine learning; Multitask Gaussian process regression;
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 discretisation 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 discretisation (e.g., plane-wave cutoff) chosen a priori (e.g. [5] and [6]), which may not optimally balance computational cost and accuracy across diverse materials.
By leveraging techniques to learn from data of heterogeneous quality [7] 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 optimisation; Experience in running DFT calculations is a bonus; Basic knowledge of numerical methods for partial differential equations is a bonus.
| [5] | 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 |
| [6] | 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 |
| [7] | K. E. Fisher, M. F. Herbst and Y. M. Marzouk. Multitask methods for predicting molecular properties from heterogeneous data. Journal of Chemical Physics 161, 014114 (2024). DOI 10.1063/5.0201681 |
Keywords: Understanding errors in materials models
Density-functional theory (DFT) is one of the most widely used methods for simulations in chemistry and materials science. In a standard Kohn-Sham DFT calculation, the electron density is computed for a given effective potential. Kohn-Sham inversion asks the inverse question: Given an electron density, can we reconstruct the effective potential that produces it? Such inversions can provide insight into exact Kohn-Sham potentials and are useful for developing and benchmarking density-functional approximations. [8][9]
This inverse problem is mathematically and numerically challenging. In exact DFT, the universal density functional is in general not differentiable, such that the corresponding potential cannot always be obtained as a functional derivative. Moreau-Yosida regularisation gives a differentiable formulation and thereby a well-defined regularized density–potential relation.[10]
In this project we will investigate how well high-frequency and strongly localized features of a potential can be reconstructed by Kohn-Sham inversion. We will study how the inversion depends on the numerical resolution, on the consistency of the wavefunction and density grids, and on how errors in the density and potential are measured. The aim is to understand how these choices influence the accuracy and stability of the reconstructed potential. Depending on the interests of the student a more analytical (pen and paper) or numerical (running test calculations) direction of the project is possible.
Requirements: Strong programming skills, ideally Julia; Background in numerical methods, optimisation, and Fourier-based discretisations; Basic knowledge of quantum mechanics and experience in density-functional theory are a bonus.
| [8] | M. F. Herbst, V. H. Bakkestuen, and A. Laestadius. Kohn-Sham inversion with mathematical guarantees. Phys. Rev. B 111, 205143 (2025). DOI 10.1103/PhysRevB.111.205143 |
| [9] | V. H. Bakkestuen, M. F. Herbst, V. Falmår, M. Penz, and A. Laestadius. Moreau-Yosida-based Kohn-Sham Inversion for Periodic Systems. arXiv:2606.19471 (2026). |
| [10] | M. Penz, M. F. Herbst, T. Helgaker, and A. Laestadius. Perspective on Moreau-Yosida Regularisation in Density-Functional Theory. arXiv:2511.06957 (2025). |
Keywords: Understanding errors in materials models
The key approximation in plane-wave density-functional theory (DFT) is the usage of an approximate exchange-correlation (XC) functional. In particular for each chosen XC functional an adapted pseudopotential model needs to be developed as well, which has the purpose to model efficiently and accurately the interactions of atoms and electrons in a way that it matches the XC functional appropriately.
In recent years, new promising XC functionals such as r2SCAN [11] have been developed, however adapted pseudopotentials have not yet become widely available. As a result such promising new functionals are typically used with inconsistent pseudopotentials. In this project, we will analyse the error that this mismatch induces.
The goal of this project is to understand the discrepancy introduced by a mismatch between pseudopotential and DFT functional. Depending on the interests of the student this can be tackled more as an analytical project, where we study mathematically the variation of the model under a change in pseudopotential, or in form of a systematic numerical study, where we understand this effect by conducting numerical experiments on standard DFT test problems.
Requirements for the analytical direction: Numerical methods for partial differential equations; Experience in numerical analysis of PDEs; Experience in running DFT calculations is a bonus;
Requirements for the numerical direction: Strong programming skills, ideally Julia or python; Previous experience with running simulations or with general solid-state physics and materials modelling is a bonus.
| [11] | James W. Furness, Aaron D. Kaplan, Jinliang Ning, John P. Perdew, and Jianwei Sun. Accurate and Numerically Efficient r2SCAN Meta-Generalized Gradient Approximation. The Journal of Physical Chemistry Letters 2020 11 (19), 8208-8215. DOI 10.1021/acs.jpclett.0c02405 |
Keywords: Statistical machine learning; Learning better materials models
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. [12]). 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 optimisation using gradient information. We will explore the learning of pseudopotentials directly in bulk materials, utilizing recent algorithmic differentiation (AD) tools for plane-wave DFT [13]. 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 optimisation methods; Bonus: Prior knowledge about DFT.
| [12] | 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 |
| [13] | 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) |
Keywords: Understanding errors in materials models
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[14] 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.
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;
| [14] | E. Cancès, G. Dusson, G. Kemlin and A. Levitt. SIAM J. Sci. Comp. 44 (2022). ArXiv 2111.01470 |
