Scientific Machine Learning

Scientific machine learning is a subfield of Artificial Intelligence and constitues computional technologies grounded in scientific approaches that via algorithms learn from data to augment or automate human skills and insights. The adoption of scientific machine learning is transformational across science and engineering adnd enable explainable predictive modelling and learning from data and seek to secure robustness and reliability for practical use cases via proper use and design of algorithms. Many new capabilities are offered for solving complex problems relying on data, mathematical modelling, mathematical optimization and proper design of powerful computational processes.

Scientific Machine Learning brings many opportunities for advancing industrial applications, data-driven ressource optimization and digital innovation related to Internet of Things, Digital Twin concepts, Acceleration of advanced simulations, Design Optimization workflows, Visual Computing, etc.


The improvement or replacement of dedicated simulations by data-driven methods and guided by physical measurements, by low-rank approximations and by reduced modeling strategies combined with high performance computing approaches is an active field of research that is quickly finding its way into industrial applications. To address this, the objective is to research, improve, develop and apply fast and efficient state-of-the-art data-efficient numerical algorithms, based on machine learning (ML) and scientific computing (SC). The methods should be robust, reliable, scalable and fast on modern computing systems to solve high-dimensional problems, utilize uncertainty quantification, mathematical optimization, model-based simulation, take into account measurements, machine learning / artificial intelligence and surrogate modelling utilizing high-performance computing. The research focus on theoretical developments as well as practical applications via software development and open source frameworks. The impact of methods and their applications within sustainability is considered.

Study group

Examples of Application Areas

Dynamical systems
Design optimization
Real-time prediction

Recent student research projects

Courses with Scientific Machine Learning content

  • 01666 Project work - Bachelor of Mathematics and Technology
  • 02456 Deep Learning, project work
  • 02623 Finite Element Method of Differential Equations
  • 02687 Scientific Computing for Ordinary and Partial Differential Equations
  • 02689 Advanced Numerical Methods for Differential Equations

Peer-Reviewed Publications related to data-driven methodologies and applications

Other publications / preprints / reports

Workshops / Summer schools

Research and innovation projects


Function Approximation using Smolyak Sparse Grid
Function approximation using Spectral Tensor-Train Decomposition
Efficient Uncertainty Quantification using Spectral Methods
Massively parallel multi-GPU accelerated multigrid methods for large-scale simulations
Anomaly detection using self-supervised learning
Spectral Element Reduced Basis Method
Physics Informed Neural Networks for Parameter Estimation
Adaptive Mesh Refinement Techniques