Scientific Machine Learning

Scientific machine learning is a subfield of Artificial Intelligence and constitues computional techniues and 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 and 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, utilize mathematical modelling and domain expertise, employing mathematical optimization and using 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, Accelerated simulations, 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.

Applied Artificial Intelligence / Scientific Machine Learning


Study group

Examples of Application Areas

Dynamical systems and scalable simulations
Design optimization
Real-time prediction
Physics-informed surrogate modelling for acceleration
Accelerated computing using operator learning
Physics-informed Generative learning and data generation for nonlinear dynamical systems
Uncertainty quantification and uncertainty-aware acctive learning for engineering systems

Recent student research projects

Courses with Scientific Machine Learning content

  • 01666 Project work - Bachelor of Mathematics and Technology
  • 02456 Deep Learning, project work
    See posters via the link.
  • 02623 Finite Element Method of Differential Equations
  • 026XX Data-Driven Computional Science and Engineering (since 2023)
  • 02687 Scientific Computing for Ordinary and Partial Differential Equations
  • 02689 Advanced Numerical Methods for Differential Equations
  • 02977 Scientific Machine Learning

Peer-Reviewed Publications related to data-driven methodologies, analysis and science and engineering 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
Real-time acoustic simulation in complex geometries using neural operator framework DeepONet
Fast acoustic simulations using reduced order modelling (ROM) vs full order models (FOM) for virtual environments
Efficient Uncertainty Quantification using Spectral Methods (Polynomial Chaos)
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
Neural Network Residual (ResNet) Arrchitetcures for Dynamical systems
Physics-informed neural network for Navier-Stokes equations
Physics Informed Neural Network for the Taylor Greeen Vortex solution in computational fluid dynamics (CFD)
Data-driven physics-constrained real time estimation of effective transmission of the spread of covid-19 for Denmark
Deep Neural Networks for data-driven physics-constrained simulation of a nonlinear coupled ODE system
Low rank approximation and modelling from data using dynamic mode decomposition