Certified machine learning and its applications in computational biochemistry
Physics-informed neural networks (PINNs) are a powerful method to incorporate a priori available information of the system into a neural network (NN) representing the system. Despite its huge success in diverse application areas, a systematic analysis of the prediction error including rigorous error bounds has not been pursued so far. We use PINNs to discover an approximate solution to a partial or ordinary differential equation. This means especially, that we assume to know the structure and parameters of the surrogate model before applying the method instead of using neural networks to derive the structure or the parameters of the differential equation. During the project, we derive rigorous bounds for the prediction error of a PINN. The theoretical results will be demonstrated numerically with complex problems such as challenges in molecular dynamics research.
- Hillebrecht, B., & Unger, B. (2022). Certified machine learning: A posteriori error estimation for physics-informed neural networks. 2022 International Joint Conference on Neural Networks (IJCNN), 1–8. https://doi.org/10.1109/IJCNN55064.2022.9892569
- Hillebrecht, B., & Unger, B. (2022). Certified machine learning: Rigorous a posteriori error bounds for PDE defined PINNs. https://doi.org/10.48550/arXiv.2210.03426
- Patra, A., Hillebrecht, B., & Nielsen, A. E. B. (2021). Continuum limit of lattice quasielectron wavefunctions. Journal of Statistical Mechanics: Theory and Experiment, 2021(8), Article 8. https://doi.org/10.1088/1742-5468/ac0f63
- Apr 2022 ongoing: PhD student at SimTech, University of Stuttgart, Scholar of International Max Planck Research School for Intelligent Systems (IMPRS-IS)
- Nov 2021 - Mar 2022: Research assistant at SimTech, University of Stuttgart
- 2021 M.Sc. Mathematics, subject area: Applied Algebra and Discrete Mathematics, Fernuni Hagen
- June 2018 - Nov 2018 Scientific employee MPI-PKS Dresden
- 2018 M.Sc. Physics, subject area: Theoretical Biophysics, Technical University Munich
- June 2016 - Aug 2016 Research Internship Cavendish Laboratory, University of Cambridge
- 2015 B.Sc. Mathematics, RWTH Aachen
- 2015 B.Sc. Physics, RWTH Aachen
- 2015 - 2018 Scholar of "Studienstiftung des Deutschen Volkes"
- 2015 - 2016 Erasmus Scholar, KTH Stockholm