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, datadriven 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.
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.
Applied Artificial Intelligence / Scientific Machine Learning
 The AI Denmark initiative directed at practical use cases is supported.
 The Danish Data Science Academy (DDSA) initiative directed at growing a strong data science comunity in Denmark is supported.
Events
 PhD school 02901 Advanced Topics in Machine Learning: Physics meets Machine Learning, August 1923, 2024
 HAMLET/Physics 2024  How to Apply Machine Learning to Experimental and Theoretical Physics, August 1921, 2024

Danish Digitalization, Data Science and AI  D3A 1.0, 12 Feb, 2024
with a session on "Deep Learning in Science & Physical Systems", including talks on "Scientific Machine Learning for Computational Science and Engineering Applications" by Allan P. EngsigKarup (DTU Compute). 
Mathematics of Data Science seminar series, supported by DDSA.
 Jan S. Hesthaven, Enabling digital twins through modeling, data, and learning â a few examples , May 17th, 2024
 Dirk Hartmann, Executable Digital Twins, Feb 6, 2024
 Esteban Ferrer, New avenues in high order fluid dynamics, June 16, 2023
 Gianluigi Rozza, Reduced Order Modelling in Computational Mechanics: state of the art, challenges and applications, March 7, 2023
 George Em Karniadakis, Physicsinformed machine learning: blending data and physics for fast predictions, November 9, 2022
 DTU Compute special course on "DataDriven Science and Engineering", Feb  Jun, 2023, new course developed by Allan P. EngsigKarup
 2022 Sep  2023 Feb, DDSA Mentoring Programme  Pilog Mentoring Programme
 DTU Compute PhD school on "Scientific Machine Learning", June 1317, 2022, cf. DTU Course 02977. The course is supported by DTU Compute PhD school, Danish Data Science Academy (DDSA), DCAMM, EUROTECH and CERE.

DTU Compute SciML Lunch Seminar 8/32022 12:00  12:45:
"Markov Chain GenerativeAdversarial Neural Networks for
Solving Bayesian Inverse Problems" by Nicolaj Takata
Mucke
Recording: LINK  DCAMM Annual Speaker 2022 "PhysicsInformed Machine Learning: Blending data and physics for fast predictions", George Em Karniadakis, Brown University, USA (November 10, 2022)

20222023 Inspirational seminar series on Mathematics of Data
Science supported by Danish Data Science Academy (DDSA) and Danish
Center for Applied Mathematics and Mechanics (DCAMM)
 November 9, 2022, Prof. George Em Karnidakis: "Physicsinformed machine learning: Blending data and physics for fast predictions"
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.
 Workshops DTU Environment/DTU Compute : Hydraulic Modelling (Since Autumn 2021)
Examples of Application Areas
Dynamical systems and scalable simulations  
Design optimization  
Realtime prediction  
Physicsinformed surrogate modelling for acceleration  
Accelerated computing using operator learning  
Physicsinformed Generative learning and data generation for nonlinear dynamical systems  
Uncertainty quantification and uncertaintyaware acctive learning for engineering systems 
Recent student research projects
 PhysicsInformed Neural Networks for Solving the Linear Elasticity Equations in Continuum Mechanics (MSc, FebJul, 2024)
 Fourier Neural OperatorDriven MultiFidelity Surrogate of RANSbased Wind Farm Wake Simulations (MSc, FebJul, 2024)
 Numerical solutions of PDE’s assisted by Neural Networks (Minor project, FebJun, 2024)
 Integration of Scientific Computing Agents in LangChain Powered by Language Models (Minor project, FebJun, 2024)
 Comparative analysis of deep learning based sound event detection methods in the urban environmental audio domain (MSc, FebJul, 2024)
 Fidelity Enhancement of Wind farm wake simulations using the Fourier Neural Operator (MSc, Jan  Jun, 2024)
 Datadriven surrogate models for physicsbased numerical models (MSc, Sep, 2023  Feb, 2024)
 Predicting bacterial infections using machine learning (MSc, Aug, 2023  Mar, 2024)
 Physicsinformed Neural Networks for Wind Turbine Wake flow predictions (Special course, Sep  Dec, 2023)
 Reduced order modelling for computational engineering (Special course, Feb  Jun, 2023)
 Augmenting a Neural Operator with the Finite Element Method to Develop a Hybrid PDEsolver (Special course, Mar  Jun, 2023)
 Machine learning methods for modelling of dynamic systems (MSc thesis, Feb  Sep, 2023)
 Uncertainty Quantification in Machine Learning models using Conformal Prediction (BSc thesis, FebJun, 2023)
 Machine Learning for UneXploded Ordinance (UXO) Detection from drone surveys (BSc thesis, FebJun, 2023)
 Automating solar panel fault detection from image data (BSc thesis, FebJun, 2023)
 Datadriven techniques for learning nonlinear dynamics of physical systems (M.Sc., Aug 2022  Jan 2023)
 Dynamic 2D flood simulations using scientific machine learning (MSc., Aug 2022  Feb 2023)
 Datadriven Neural Operator Techniques for Efficient Surrogate Modelling (M.Sc., Aug 2022  Jan 2023)
 Using datadriven stateoftheart machine learning and conformal prediction for track irregularities from observed dynamics of inservice railway vehicles (M.Sc.,Feb Aug, 2022 )
 Neural Operators (Special course, JunJul, 2022)
 Variational Auto Encoders (VAE) for Differential Equations (Special course, JunJul, 2022)
 A neural operator for solving the wave equation (Special course, SepDec, 2022)
 Scientific machine learning for discovering basal dynamics of Greenland outlet glaciers (M.Sc., Jan  Aug, 2022)
 Surrogate Modelling for Estimating Sound Speed Profiles (PhD special course, Feb  May, 2022)
 Physicsinformed datadriven techniques for parameter estimation and discovery of hidden physics with application to models for spread of diseases (special course, Sep  Dec, 2021)
 PhysicsConstrained Surrogate Modelling for Computational Hydraulics (M.Sc., Sep 2021  Feb 2022)
 Acceleration of PhysicsInformed Neural Networks (B.Sc., Sep  Dec, 2021)
 PhysicsInformed Neural Networks for Solving Coupled Partial Differential Equations (special course, Aug 2021)
 Mathematical modelling of Covid19 epidemic (B.Sc., Feb  June 2021)
 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
See posters via the link.  02623 Finite Element Method of Differential Equations
 026XX DataDriven 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
PeerReviewed Publications related to datadriven methodologies, analysis and science and engineering applications
 Datadriven MultiFidelity Modelling for Timedependent Partial Differential Equations using Convolutional Neural Networks (May, 2024)
 Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators (Jan, 2024)
 Improving Deep LearningBased Defect Classification in Solar Cells Using Conformal Prediction (Jun, 2023)
 Reduced order modelling using parameterized nonuniform boundary conditions in room acoustic simulations (Apr, 2023))
 Efficient Uncertainty Quantification and VarianceBased Sensitivity Analysis in Epidemic Modelling Using Polynomial Chaos (May, 2022)
 Machine learningbased room acoustics using flow maps and physicsinformed neural networks (Apr 2022)
 Physicsinformed neural networks for onedimensional sound field predictions with parameterized sources and impedance boundaries (Dec 2021)
 Assessment of the National Test Strategy on the Development of the COVID19 Pandemic in Denmark (Nov 2021)
 Efficient pMultigrid Spectral Element Model for Water Waves and Marine Offshore Structures (May 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
 PhysicsInformed Holomorphic Neural Networks (PIHNNs): Solving Linear Elasticity Problems (July, 2024)
 A sensitivity analysis on the effect of hyperparameters in deep neural operators applied to sound propagation (2023, Forum Acousticum, proceedings)
 Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators (August, 2023, submitted)
 Improving deep learningbased defect classification in solar cells using conformal prediction (January, 2023, XXX, proceedings)
 Enabling Interactive Virtual Reality for Room Acoustics in Enclosed Spaced Using Numerical Methods (October, 2022, ICA 2022, proceedings)
 DeepONet: Learning the sound propagation in 1D with parameterized sources using deep learning for approximating the wave equation operators (October, 2022, ICA 2022, proceedings)
 Accelerating hydrodynamic simulations of urban drainage systems with physicsguided machine learning (June 2022, preprint))
 Machine learningbased room acoustics using flow maps and physicsinformed neural networks (April 2022, submitted)
 Reduced Order Modelling for Dispersive and Nonlinear Water Wave Modelling (Jan 2022, submitted)
 Making Waves: How emerging physicsinformed machine learning techniques can change established hydrodynamic modelling paradigms (Nov 2021, submitted)
 Physicsinformed neural networks for 1D sound field predictions with parameterized sources and impedance boundaries (Sep 2021, preprint)
 Efficient Uncertainty Quantification and Sensitivity Analysis in Epidemic Modelling using Polynomial Chaos (Sep 2021, submitted)
 Efficient numerical room acoustic simulations with parametrized boundaries using the spectral element and reduced basis method (Mar 2021, submitted)
 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

Scientific machine learning of environmental systems
(20232026)
PhD student Anton SÃÂ¸rensen (DTU Sustain / DTU Compute, cosupervisor)  Efficient Added Mass Calculations for Large and Complex
Floating Offshore Structures (2023)
PhD student, Jens Haakon Visbech Christensen (COWIFONDEN / DTU Compute, principal investigator, main supervisor) 
Interactive auditory virtual reality using reduced order
modeling (2022)
PhD student, Hermes Sampedro Llopis (DTU Electro / DTU Compute / Ecophon / Ramboll / Virsabi / Treble technologies / Danish Sound Cluster, cosupervisor)
RBSEM virtual acoustics (proofofconcept) 
Reduced Order Modelling based Scientific Machine
Learning (20212023)
PostDoc, Fatma Guler (DTU Compute / Bartin University / TUBITAK, main supervisor) 
Robust Surrogate Modelling for Antenna Design
Applications (20202023)
Industrial PhD student, Sabine Fie Hansen (DTU Compute / TICRA / EPFL, main supervisor) 
Accurate and Fast Auditory Virtual Reality Implementation (20192022)
PhD student, Nikolas BorrelJensen (DTU Electro / DTU Compute / Eindhoven University of Technology / EuroTech, cosupervisor)
PhD thesis: Accelerated methods fo\ r computing acoustic sound fields in dynamic virtual environments with moving sources, oral lecture (youtube)
New position: Software developer, Meta, Redmond  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 
Realtime 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 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 the Taylor Greeen Vortex
solution in computational fluid dynamics (CFD) 

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 

Low rank approximation and modelling from data using
dynamic mode decomposition 