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, datadriven ressource optimization and digital innovation related to Internet of Things, Digital Twin concepts, Acceleration of advanced simulations, Design Optimization workflows, Visual Computing, etc.
Mission
The improvement or replacement of dedicated simulations by datadriven methods and guided by physical measurements, by lowrank 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 stateoftheart dataefficient 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 highdimensional problems, utilize uncertainty quantification, mathematical optimization, modelbased simulation, take into account measurements, machine learning / artificial intelligence and surrogate modelling utilizing highperformance 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
 We form study groups every semester on the topics of Scientic Machine Learning that is rapidly evolving. Drop an email if you are interested to take part and contribute.
Examples of Application Areas
Dynamical systems  
Design optimization  
Realtime prediction 
Recent student research projects
 Mathematical modelling of Covid19 (B.Sc., Feb  June 2021)
 Finite Element Method for partial differential equations  Discovey of Advection Equation (Special course, Feb 2021)
 Scientific Machine Learning (Special course, Feb  Jun 2021)
 Physicsinformed Neural Networks (Special course, Sep  Dec 2020)
 Predictive Maintenance of Ship Engines using Machine Learning (M.Sc., Apr  Sep 2020)
 Machine Learning for matching transaction data with invoice data (B.Sc., Apr  Sep 2020)
 Drag loss for wavebody interaction (Minor, Jun 2020)
 Machine Learning for Predictive Root Cause Analysis in Log Data in an Enterprise (B.Sc., Feb  Jun 2020)
 Sparse Grid Methods for High Dimensional Function Approximation (M.Sc. Project, Feb 2019  July 2019)
 Music Composing with Artifical Intelligence (Minor project, Feb 2019  June 2019)
 Optimal Control of Nonlinear PDE Systems Using Reduced Order Modeling and Neural Networks (M.Sc., Aug 2018  Jan 2019)
 Numerical Solutions to Nonlinear Partial Differential Equations via PhysicsInformed Neural Networks (B.Sc., Feb 2018  Jul 2018)
 Reduced Basis Methods for parametrized PDEs (Special, Oct 2017  Jan 2018)
 Applied Machine Learning for Prediction (Project, Sep 2017  Dec 2017)
 Function approximation using Artificial Neural Networks (B.Sc., Feb 2017  Jun 2017)
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
PeerReviewed Publications related to datadriven methodologies and applications
 Efficient pMultigrid Spectral Element Model for Water Waves and Marine Offshore Structures (2021)
 Reduced Order Modeling for Nonlinear PDEconstrained Optimization using Neural Networks (Apr 2019)
 A massively scalable distributed multigrid framework for nonlinear marine hydrodynamics (Feb 2019)
 Spectral TensorTrain Decomposition (2016)
Other publications / preprints / reports
 Efficient numerical room acoustic simulations with parametrized boundaries using the spectral element and reduced basis method (Mar 2021)
 Agedependent Epidemic Modelling of COVID19 using a Nodal Discontinuous Galerkin Method (Feb 2021)
Workshops / Summer schools
 2020, Model Order Reduction Summer School (MORSS) 2020 organized by EPFL (Ecole polytechnique federale Lausanne), DTU  Technical University of Denmark, a Eindhoven University of Technology (EuroTech Universities Alliance)
Research and innovation projects

Reduced Order Modelling based Scientific Machine
Learning (20212022)
PostDoc, Fatma Guler (DTU Compute / TUBITAK, main supervisor) 
Robust Surrogate Modelling for Antenna Design
Applications (20202023)
Industrial PhD student, Sabine Fie Hansen (DTU Compute / TICRA / EPFL, main supervisor)  Estimation, Simulation and Control for Optimal Containment of COVID19 (2020)
PostDoc, Kristian Meyer (DTU Compute / AAU / Novo Nordisk foundation, main supervisor)
Research Assistant, Anders Dalsgaard Melander (DTU Compute / AAU / Novo Nordisk foundation, main supervisor) 
Acoustic Virtual Reality for Architectural Design (20192022)
Industrial PhD student, Hermes Sampedro Llopis (DTU Electro / DTU Compute / EPFL / Ramboll // Ecophon, cosupervisor)
Talk given at the Model Order Reduction Summer School (MORSS) 2020: RB models for realtime wavebased virtual acoustics simulations 
Uncertainty Quantification for Engineering Applications (20112014)
PhD Student, Daniele Bigoni (DTU Compute, main supervisor)
PhD thesis: Uncertainty Quantification with Application to Engineering Problems
Position after PhD: PostDoc at Department of Aeronautics and Astronautics, Massachusetts Institute of Technology. Cambridge, USA
Gallery
Function Approximation using Smolyak Sparse Grid 
Function approximation using Spectral TensorTrain
Decomposition 
Efficient Uncertainty
Quantification using Spectral
Methods (Polynomial Chaos) 
Massively parallel multiGPU accelerated multigrid
methods for largescale
simulations 
Anomaly detection using selfsupervised 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


Physicsinformed neural network for NavierStokes equations 

Physics Informed Neural Network for Taylor Greeen Vortex 

Datadriven physicsconstrained real time estimation of effective transmission of the spread of covid19 for Denmark 

Deep Neural Networks for datadriven physicsconstrained
simulation of a nonlinear coupled ODE system 
