Research Exchanges in the Mathematics of Deep Learning with Applications

Project Information

REMODEL

Grant agreement ID: 101131557

DOI

10.3030/101131557

EC signature date 16 October 2023

Start date 1 January 2024

End date 31 December 2027

Funded under

• Marie Skłodowska-Curie Actions (MSCA)

Total cost

No data

EU contribution

€ 473 800,00

Coordinated by

NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET NTNU
Norway

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Deliverables

Documents, reports (1)

Report on deep leaning models and deep physical models

Report on completed study on discovering dynamics with incomplete data and invariance.

Data Management Plan (1)

Data management plan

Data management plan submitted at mid-term and updated towards the end of the project if needed.

Publications

Peer reviewed articles (41)

Neural networks for the approximation of Euler’s elastica

Author(s): Elena Celledoni, Ergys Çokaj, Andrea Leone, Sigrid Leyendecker, Davide Murari, Brynjulf Owren, Rodrigo T. Sato Martín de Almagro, Martina Stavole
Published in: Computer Methods in Applied Mechanics and Engineering, Issue 435, 2025, ISSN 0045-7825
Publisher: Elsevier BV
DOI: 10.1016/J.CMA.2024.117584

The Troublesome Kernel: On Hallucinations, No Free Lunches, and the Accuracy-Stability Tradeoff in Inverse Problems

Author(s): Nina M. Gottschling, Vegard Antun, Anders C. Hansen, Ben Adcock
Published in: SIAM Review, Issue 67, 2025, ISSN 0036-1445
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/23M1568739

Proximal Langevin Sampling with Inexact Proximal Mapping

Author(s): Matthias J. Ehrhardt, Lorenz Kuger, Carola-Bibiane Schönlieb
Published in: SIAM Journal on Imaging Sciences, Issue 17, 2024, ISSN 1936-4954
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/23M1593565

PDE-CNNs: Axiomatic Derivations and Applications

Author(s): Gijs Bellaard, Sei Sakata, Bart M. N. Smets, Remco Duits
Published in: Journal of Mathematical Imaging and Vision, Issue 67, 2025, ISSN 0924-9907
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S10851-025-01230-4

Closing the ODE–SDE gap in score-based diffusion models through the Fokker–Planck equation

Author(s): Teo Deveney, Jan Stanczuk, Lisa Kreusser, Chris Budd, Carola-Bibiane Schönlieb
Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Issue 383, 2025, ISSN 1364-503X
Publisher: The Royal Society
DOI: 10.1098/RSTA.2024.0503

Advancing the Frontiers of Deep Learning for Low-Dose 3D Cone-Beam CT Reconstruction

Author(s): Ander Biguri, Subhadip Mukherjee, Xuzhi Zhao, Xi Liu, Xinyi Wang, Rui Yang, Yi Du, Yahui Peng, Mikael Brudfors, Mark Graham, Hyungon Ryu, Oliver Kutter, Andreas Hauptmann, Mustafa Al-Rubaye, Miika T. Nieminen, Mikael A. K. Brix, Austin Yunker, Rajkumar Kettimuthu, John C. Roeske, Sasidhar Alavala, Subrahmanyam Gorthi, Carola-Bibiane Schönlieb
Published in: IEEE Open Journal of Signal Processing, Issue 6, 2025, ISSN 2644-1322
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
DOI: 10.1109/OJSP.2025.3593189

Scientific machine learning

Author(s): Felix Dietrich, Wil Schilders
Published in: Mathematische Semesterberichte, Issue 72, 2025, ISSN 0720-728X
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S00591-025-00399-4

An Adaptively Inexact Method for Bilevel Learning Using Primal–Dual-Style Differentiation

Author(s): Lea Bogensperger, Matthias J. Ehrhardt, Thomas Pock, Mohammad Sadegh Salehi, Hok Shing Wong
Published in: Journal of Mathematical Imaging and Vision, Issue 67, 2025, ISSN 0924-9907
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S10851-025-01262-W

Learning dynamical systems from noisy data with inverse-explicit integrators

Author(s): Elena Celledoni, Sølve Eidnes, Håkon Noren Myhr
Published in: Physica D: Nonlinear Phenomena, Issue 472, 2025, ISSN 0167-2789
Publisher: Elsevier BV
DOI: 10.1016/J.PHYSD.2024.134471

Near-optimal learning of Banach-valued, high-dimensional functions via deep neural networks

Author(s): Ben Adcock, Simone Brugiapaglia, Nick Dexter, Sebastian Moraga
Published in: Neural Networks, Issue 181, 2025, ISSN 0893-6080
Publisher: Elsevier BV
DOI: 10.1016/J.NEUNET.2024.106761

Physics-informed two-tier neural network for non-linear model order reduction

Author(s): Yankun Hong, Harshit Bansal, Karen Veroy
Published in: Advanced Modeling and Simulation in Engineering Sciences, Issue 11, 2024, ISSN 2213-7467
Publisher: Springer Science and Business Media LLC
DOI: 10.1186/S40323-024-00273-3

Inverse Evolution Layers: Physics-Informed Regularizers for Image Segmentation

Author(s): Chaoyu Liu, Zhonghua Qiao, Chao Li, Carola-Bibiane Schönlieb
Published in: SIAM Journal on Mathematics of Data Science, Issue 7, 2025, ISSN 2577-0187
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/24M1633662

Deep Block Proximal Linearized Minimization Algorithm for Nonconvex Inverse Problems

Author(s): Chaoyan Huang, Zhongming Wu, Yanqi Cheng, Tieyong Zeng, Carola-Bibiane Schönlieb, Angelica I. Aviles-Rivero
Published in: SIAM Journal on Mathematics of Data Science, Issue 7, 2025, ISSN 2577-0187
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/24M1682464

Constraint-Satisfying Krylov Solvers for Structure-Preserving Discretizations

Author(s): James Jackaman, Scott MacLachlan
Published in: SIAM Journal on Matrix Analysis and Applications, Issue 45, 2024, ISSN 0895-4798
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/22M1540624

A <i>posteriori</i> error estimation of numerical solutions of PINNs for the Navier–Stokes equations under the Dirichlet boundary condition with external force

Author(s): Baige Xu, Takaharu Yaguchi
Published in: International Journal of Mathematics for Industry, 2025, ISSN 2661-3352
Publisher: World Scientific Pub Co Pte Ltd
DOI: 10.1142/S2661335225500108

Geodesic Tracking via New Data-Driven Connections of Cartan Type for Vascular Tree Tracking

Author(s): Nicky J. van den Berg, Bart M. N. Smets, Gautam Pai, Jean-Marie Mirebeau, Remco Duits
Published in: Journal of Mathematical Imaging and Vision, Issue 66, 2024, ISSN 0924-9907
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S10851-023-01170-X

Optimal Transport on the Lie Group of Roto-translations

Author(s): Daan Bon, Gautam Pai, Gijs Bellaard, Olga Mula, Remco Duits
Published in: SIAM Journal on Imaging Sciences, Issue 18, 2025, ISSN 1936-4954
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/24M1641531

Learning Task-Specific Sampling Strategy for Sparse-View CT Reconstruction

Author(s): Liutao Yang, Jiahao Huang, Yingying Fang, Angelica I Aviles-Rivero, Carola-Bibiane Schönlieb, Daoqiang Zhang, Guang Yang
Published in: IEEE Transactions on Instrumentation and Measurement, Issue 74, 2025, ISSN 0018-9456
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
DOI: 10.1109/TIM.2025.3554318

Motion Constrained Point Cloud Matching for Maritime Tracking

Author(s): Nicholas Dalhaug, Martin Baerveldt, Angelica I. Aviles-Rivero, Carola-Bibiane Schönlieb, Annette Stahl, Rudolf Mester, Edmund Førland Brekke
Published in: IEEE Access, Issue 13, 2025, ISSN 2169-3536
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
DOI: 10.1109/ACCESS.2025.3582327

Enhancing Dynamic CT Image Reconstruction with Neural Fields and Optical Flow

Author(s): Pablo Arratia, Matthias J. Ehrhardt, Lisa Kreusser
Published in: Journal of Mathematical Imaging and Vision, Issue 67, 2025, ISSN 0924-9907
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S10851-025-01259-5

Systematic Construction of Continuous-Time Neural Networks for Linear Dynamical Systems

Author(s): Chinmay Datar, Adwait Datar, Felix Dietrich, Wil Schilders
Published in: SIAM Journal on Scientific Computing, Issue 47, 2025, ISSN 1064-8275
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/24M1648946

A Neural Network Approach for Stochastic Optimal Control

Author(s): Xingjian Li, Deepanshu Verma, Lars Ruthotto
Published in: SIAM Journal on Scientific Computing, Issue 46, 2024, ISSN 1064-8275
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/23M155832X

An Adaptive Hierarchical Ensemble Kalman Filter with Reduced Basis Models

Author(s): Francesco A. B. Silva, Cecilia Pagliantini, Karen Veroy
Published in: SIAM/ASA Journal on Uncertainty Quantification, Issue 13, 2025, ISSN 2166-2525
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/24M1653690

Designing stable neural networks using convex analysis and ODEs

Author(s): Ferdia Sherry, Elena Celledoni, Matthias J. Ehrhardt, Davide Murari, Brynjulf Owren, Carola-Bibiane Schönlieb
Published in: Physica D: Nonlinear Phenomena, Issue 463, 2025, ISSN 0167-2789
Publisher: Elsevier BV
DOI: 10.1016/J.PHYSD.2024.134159

B-stability of numerical integrators on Riemannian manifolds

Author(s): Martin Arnold, null null, Elena Celledoni, Ergys Çokaj, Brynjulf Owren, Denise Tumiotto, null null
Published in: Journal of Computational Dynamics, Issue 11, 2024, ISSN 2158-2491
Publisher: American Institute of Mathematical Sciences (AIMS)
DOI: 10.3934/JCD.2024002

Artificial Intelligence-Led Whole Coronary Artery OCT Analysis; Validation and Identification of Drug Efficacy and Higher-Risk Plaques

Author(s): Benn Jessney, Xu Chen, Sophie Gu, Yuan Huang, Martin Goddard, Adam Brown, Daniel Obaid, Michael Mahmoudi, Hector M. Garcia Garcia, Stephen P. Hoole, Lorenz Räber, Francesco Prati, Carola-Bibiane Schönlieb, Michael Roberts, Martin Bennett
Published in: Circulation: Cardiovascular Imaging, Issue 18, 2025, ISSN 1941-9651
Publisher: Ovid Technologies (Wolters Kluwer Health)
DOI: 10.1161/CIRCIMAGING.125.018133

ACID: A comprehensive toolbox for image processing and modeling of brain, spinal cord, and ex vivo diffusion MRI data

Author(s): Gergely David, Björn Fricke, Jan Malte Oeschger, Lars Ruthotto, Francisco J. Fritz, Ora Ohana, Laurin Mordhorst, Thomas Sauvigny, Patrick Freund, Karsten Tabelow, Siawoosh Mohammadi
Published in: Imaging Neuroscience, Issue 2, 2025, ISSN 2837-6056
Publisher: MIT Press
DOI: 10.1162/IMAG_A_00288

Hyperbolic partial differential equations generalize LSSL with the HiPPO matrix

Author(s): Atsushi Takabatake, Takaharu Yaguchi
Published in: Japan Journal of Industrial and Applied Mathematics, Issue 42, 2025, ISSN 0916-7005
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S13160-025-00731-4

Reduced‐Order Modeling for Second‐Order Computational Homogenization With Applications to Geometrically Parameterized Elastomeric Metamaterials

Author(s): T. Guo, V. G. Kouznetsova, M. G. D. Geers, K. Veroy, O. Rokoš
Published in: International Journal for Numerical Methods in Engineering, Issue 126, 2025, ISSN 0029-5981
Publisher: Wiley
DOI: 10.1002/NME.7604

Restarts Subject to Approximate Sharpness: A Parameter-Free and Optimal Scheme For First-Order Methods

Author(s): Ben Adcock, Matthew J. Colbrook, Maksym Neyra-Nesterenko
Published in: Foundations of Computational Mathematics, 2025, ISSN 1615-3375
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S10208-024-09673-8

Predictions based on pixel data: Insights from PDEs and finite differences

Author(s): Elena Celledoni, James Jackaman, Davide Murari, Brynjulf Owren
Published in: Journal of Computational Physics, Issue 538, 2025, ISSN 0021-9991
Publisher: Elsevier BV
DOI: 10.1016/J.JCP.2025.114166

Polytope Division Method: A Scalable Sampling Method for Problems with High-Dimensional Parameters

Author(s): Evie Nielen, Oliver Tse, Karen Veroy
Published in: SIAM Journal on Scientific Computing, Issue 47, 2025, ISSN 1064-8275
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/24M1704506

Derivative-free discrete gradient methods

Author(s): Håkon Noren Myhr, Sølve Eidnes
Published in: Journal of Computational Dynamics, Issue 11, 2024, ISSN 2158-2491
Publisher: American Institute of Mathematical Sciences (AIMS)
DOI: 10.3934/JCD.2024004

Practical Acceleration of the Condat–Vũ Algorithm

Author(s): Derek Driggs, Matthias J. Ehrhardt, Carola-Bibiane Schönlieb, Junqi Tang
Published in: SIAM Journal on Imaging Sciences, Issue 17, 2024, ISSN 1936-4954
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/23M159473X

Learning Hamiltonians of constrained mechanical systems

Author(s): Elena Celledoni, Andrea Leone, Davide Murari, Brynjulf Owren
Published in: Journal of Computational and Applied Mathematics, Issue 417, 2025, ISSN 0377-0427
Publisher: Elsevier BV
DOI: 10.1016/J.CAM.2022.114608

Practical Operator Sketching Framework for Accelerating Iterative Data-Driven Solutions in Linear Inverse Problems

Author(s): Junqi Tang, Guixian Xu, Subhadip Mukherjee, Carola-Bibiane Schönlieb
Published in: Journal of Mathematical Imaging and Vision, Issue 67, 2025, ISSN 0924-9907
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/S10851-025-01263-9

Dynamical Systems–Based Neural Networks

Author(s): Elena Celledoni, Davide Murari, Brynjulf Owren, Carola-Bibiane Schönlieb, Ferdia Sherry
Published in: SIAM Journal on Scientific Computing, Issue 45, 2023, ISSN 1064-8275
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/22M1527337

Stochastic optimization of large-scale parametrized dynamical systems

Author(s): Pascal den Boef, Jos Maubach, Wil Schilders, Nathan van de Wouw
Published in: Automatica, Issue 179, 2025, ISSN 0005-1098
Publisher: Elsevier BV
DOI: 10.1016/J.AUTOMATICA.2025.112388

Loss function inversion for improved crack segmentation in steel bridges using a CNN framework

Author(s): Andrii Kompanets, Remco Duits, Gautam Pai, Davide Leonetti, H.H. (Bert) Snijder
Published in: Automation in Construction, Issue 170, 2025, ISSN 0926-5805
Publisher: Elsevier BV
DOI: 10.1016/J.AUTCON.2024.105896

Inverse evolution data augmentation for neural PDE solvers

Author(s): Chaoyu Liu, Chris Budd, Carola-Bibiane Schönlieb
Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Issue 383, 2025, ISSN 1364-503X
Publisher: The Royal Society
DOI: 10.1098/RSTA.2024.0242

Index‐aware learning of circuits

Author(s): Idoia Cortes Garcia, Peter Förster, Lennart Jansen, Wil Schilders, Sebastian Schöps
Published in: International Journal of Circuit Theory and Applications, Issue 52, 2024, ISSN 0098-9886
Publisher: Wiley
DOI: 10.1002/CTA.4024

Book chapters (2)

Universal Collection of Euclidean Invariants Between Pairs of Position-Orientations

Author(s): Gijs Bellaard, Bart M. N. Smets, Remco Duits
Published in: Lecture Notes in Computer Science, Geometric Science of Information, 2025
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-03918-7_3

Implicit U-KAN2.0: Dynamic, Efficient and Interpretable Medical Image Segmentation

Author(s): Chun-Wun Cheng, Yining Zhao, Yanqi Cheng, Javier A. Montoya-Zegarra, Carola-Bibiane Schönlieb, Angelica I. Aviles-Rivero
Published in: Lecture Notes in Computer Science, Medical Image Computing and Computer Assisted Intervention – MICCAI 2025, 2025
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-032-05141-7_30