Research Exchanges in the Mathematics of Deep Learning with Applications

Informazioni relative al progetto

REMODEL

ID dell’accordo di sovvenzione: 101131557

DOI

10.3030/101131557

Data della firma CE 16 Ottobre 2023

Data di avvio 1 Gennaio 2024

Data di completamento 31 Dicembre 2027

Finanziato da

• Marie Skłodowska-Curie Actions (MSCA)

Costo totale

Nessun dato

Contributo UE

€ 473 800,00

Coordinato da

NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITET NTNU
Norway

CORDIS fornisce collegamenti ai risultati finali pubblici e alle pubblicazioni dei progetti ORIZZONTE.

I link ai risultati e alle pubblicazioni dei progetti del 7° PQ, così come i link ad alcuni tipi di risultati specifici come dataset e software, sono recuperati dinamicamente da .OpenAIRE .

Risultati finali

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.

Pubblicazioni

Peer reviewed articles (41)

Neural networks for the approximation of Euler’s elastica

Autori: Elena Celledoni, Ergys Çokaj, Andrea Leone, Sigrid Leyendecker, Davide Murari, Brynjulf Owren, Rodrigo T. Sato Martín de Almagro, Martina Stavole
Pubblicato in: Computer Methods in Applied Mechanics and Engineering, Numero 435, 2025, ISSN 0045-7825
Editore: 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

Autori: Nina M. Gottschling, Vegard Antun, Anders C. Hansen, Ben Adcock
Pubblicato in: SIAM Review, Numero 67, 2025, ISSN 0036-1445
Editore: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/23M1568739

Proximal Langevin Sampling with Inexact Proximal Mapping

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

PDE-CNNs: Axiomatic Derivations and Applications

Autori: Gijs Bellaard, Sei Sakata, Bart M. N. Smets, Remco Duits
Pubblicato in: Journal of Mathematical Imaging and Vision, Numero 67, 2025, ISSN 0924-9907
Editore: 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

Autori: Teo Deveney, Jan Stanczuk, Lisa Kreusser, Chris Budd, Carola-Bibiane Schönlieb
Pubblicato in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Numero 383, 2025, ISSN 1364-503X
Editore: The Royal Society
DOI: 10.1098/RSTA.2024.0503

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

Autori: 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
Pubblicato in: IEEE Open Journal of Signal Processing, Numero 6, 2025, ISSN 2644-1322
Editore: Institute of Electrical and Electronics Engineers (IEEE)
DOI: 10.1109/OJSP.2025.3593189

Scientific machine learning

Autori: Felix Dietrich, Wil Schilders
Pubblicato in: Mathematische Semesterberichte, Numero 72, 2025, ISSN 0720-728X
Editore: 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

Autori: Lea Bogensperger, Matthias J. Ehrhardt, Thomas Pock, Mohammad Sadegh Salehi, Hok Shing Wong
Pubblicato in: Journal of Mathematical Imaging and Vision, Numero 67, 2025, ISSN 0924-9907
Editore: Springer Science and Business Media LLC
DOI: 10.1007/S10851-025-01262-W

Learning dynamical systems from noisy data with inverse-explicit integrators

Autori: Elena Celledoni, Sølve Eidnes, Håkon Noren Myhr
Pubblicato in: Physica D: Nonlinear Phenomena, Numero 472, 2025, ISSN 0167-2789
Editore: Elsevier BV
DOI: 10.1016/J.PHYSD.2024.134471

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

Autori: Ben Adcock, Simone Brugiapaglia, Nick Dexter, Sebastian Moraga
Pubblicato in: Neural Networks, Numero 181, 2025, ISSN 0893-6080
Editore: Elsevier BV
DOI: 10.1016/J.NEUNET.2024.106761

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

Autori: Yankun Hong, Harshit Bansal, Karen Veroy
Pubblicato in: Advanced Modeling and Simulation in Engineering Sciences, Numero 11, 2024, ISSN 2213-7467
Editore: Springer Science and Business Media LLC
DOI: 10.1186/S40323-024-00273-3

Inverse Evolution Layers: Physics-Informed Regularizers for Image Segmentation

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

Deep Block Proximal Linearized Minimization Algorithm for Nonconvex Inverse Problems

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

Constraint-Satisfying Krylov Solvers for Structure-Preserving Discretizations

Autori: James Jackaman, Scott MacLachlan
Pubblicato in: SIAM Journal on Matrix Analysis and Applications, Numero 45, 2024, ISSN 0895-4798
Editore: 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

Autori: Baige Xu, Takaharu Yaguchi
Pubblicato in: International Journal of Mathematics for Industry, 2025, ISSN 2661-3352
Editore: World Scientific Pub Co Pte Ltd
DOI: 10.1142/S2661335225500108

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

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

Optimal Transport on the Lie Group of Roto-translations

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

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

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

Motion Constrained Point Cloud Matching for Maritime Tracking

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

Enhancing Dynamic CT Image Reconstruction with Neural Fields and Optical Flow

Autori: Pablo Arratia, Matthias J. Ehrhardt, Lisa Kreusser
Pubblicato in: Journal of Mathematical Imaging and Vision, Numero 67, 2025, ISSN 0924-9907
Editore: Springer Science and Business Media LLC
DOI: 10.1007/S10851-025-01259-5

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

Autori: Chinmay Datar, Adwait Datar, Felix Dietrich, Wil Schilders
Pubblicato in: SIAM Journal on Scientific Computing, Numero 47, 2025, ISSN 1064-8275
Editore: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/24M1648946

A Neural Network Approach for Stochastic Optimal Control

Autori: Xingjian Li, Deepanshu Verma, Lars Ruthotto
Pubblicato in: SIAM Journal on Scientific Computing, Numero 46, 2024, ISSN 1064-8275
Editore: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/23M155832X

An Adaptive Hierarchical Ensemble Kalman Filter with Reduced Basis Models

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

Designing stable neural networks using convex analysis and ODEs

Autori: Ferdia Sherry, Elena Celledoni, Matthias J. Ehrhardt, Davide Murari, Brynjulf Owren, Carola-Bibiane Schönlieb
Pubblicato in: Physica D: Nonlinear Phenomena, Numero 463, 2025, ISSN 0167-2789
Editore: Elsevier BV
DOI: 10.1016/J.PHYSD.2024.134159

B-stability of numerical integrators on Riemannian manifolds

Autori: Martin Arnold, null null, Elena Celledoni, Ergys Çokaj, Brynjulf Owren, Denise Tumiotto, null null
Pubblicato in: Journal of Computational Dynamics, Numero 11, 2024, ISSN 2158-2491
Editore: 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

Autori: 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
Pubblicato in: Circulation: Cardiovascular Imaging, Numero 18, 2025, ISSN 1941-9651
Editore: 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

Autori: Gergely David, Björn Fricke, Jan Malte Oeschger, Lars Ruthotto, Francisco J. Fritz, Ora Ohana, Laurin Mordhorst, Thomas Sauvigny, Patrick Freund, Karsten Tabelow, Siawoosh Mohammadi
Pubblicato in: Imaging Neuroscience, Numero 2, 2025, ISSN 2837-6056
Editore: MIT Press
DOI: 10.1162/IMAG_A_00288

Hyperbolic partial differential equations generalize LSSL with the HiPPO matrix

Autori: Atsushi Takabatake, Takaharu Yaguchi
Pubblicato in: Japan Journal of Industrial and Applied Mathematics, Numero 42, 2025, ISSN 0916-7005
Editore: 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

Autori: T. Guo, V. G. Kouznetsova, M. G. D. Geers, K. Veroy, O. Rokoš
Pubblicato in: International Journal for Numerical Methods in Engineering, Numero 126, 2025, ISSN 0029-5981
Editore: Wiley
DOI: 10.1002/NME.7604

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

Autori: Ben Adcock, Matthew J. Colbrook, Maksym Neyra-Nesterenko
Pubblicato in: Foundations of Computational Mathematics, 2025, ISSN 1615-3375
Editore: Springer Science and Business Media LLC
DOI: 10.1007/S10208-024-09673-8

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

Autori: Elena Celledoni, James Jackaman, Davide Murari, Brynjulf Owren
Pubblicato in: Journal of Computational Physics, Numero 538, 2025, ISSN 0021-9991
Editore: Elsevier BV
DOI: 10.1016/J.JCP.2025.114166

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

Autori: Evie Nielen, Oliver Tse, Karen Veroy
Pubblicato in: SIAM Journal on Scientific Computing, Numero 47, 2025, ISSN 1064-8275
Editore: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/24M1704506

Derivative-free discrete gradient methods

Autori: Håkon Noren Myhr, Sølve Eidnes
Pubblicato in: Journal of Computational Dynamics, Numero 11, 2024, ISSN 2158-2491
Editore: American Institute of Mathematical Sciences (AIMS)
DOI: 10.3934/JCD.2024004

Practical Acceleration of the Condat–Vũ Algorithm

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

Learning Hamiltonians of constrained mechanical systems

Autori: Elena Celledoni, Andrea Leone, Davide Murari, Brynjulf Owren
Pubblicato in: Journal of Computational and Applied Mathematics, Numero 417, 2025, ISSN 0377-0427
Editore: Elsevier BV
DOI: 10.1016/J.CAM.2022.114608

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

Autori: Junqi Tang, Guixian Xu, Subhadip Mukherjee, Carola-Bibiane Schönlieb
Pubblicato in: Journal of Mathematical Imaging and Vision, Numero 67, 2025, ISSN 0924-9907
Editore: Springer Science and Business Media LLC
DOI: 10.1007/S10851-025-01263-9

Dynamical Systems–Based Neural Networks

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

Stochastic optimization of large-scale parametrized dynamical systems

Autori: Pascal den Boef, Jos Maubach, Wil Schilders, Nathan van de Wouw
Pubblicato in: Automatica, Numero 179, 2025, ISSN 0005-1098
Editore: Elsevier BV
DOI: 10.1016/J.AUTOMATICA.2025.112388

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

Autori: Andrii Kompanets, Remco Duits, Gautam Pai, Davide Leonetti, H.H. (Bert) Snijder
Pubblicato in: Automation in Construction, Numero 170, 2025, ISSN 0926-5805
Editore: Elsevier BV
DOI: 10.1016/J.AUTCON.2024.105896

Inverse evolution data augmentation for neural PDE solvers

Autori: Chaoyu Liu, Chris Budd, Carola-Bibiane Schönlieb
Pubblicato in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Numero 383, 2025, ISSN 1364-503X
Editore: The Royal Society
DOI: 10.1098/RSTA.2024.0242

Index‐aware learning of circuits

Autori: Idoia Cortes Garcia, Peter Förster, Lennart Jansen, Wil Schilders, Sebastian Schöps
Pubblicato in: International Journal of Circuit Theory and Applications, Numero 52, 2024, ISSN 0098-9886
Editore: Wiley
DOI: 10.1002/CTA.4024

Book chapters (2)

Universal Collection of Euclidean Invariants Between Pairs of Position-Orientations

Autori: Gijs Bellaard, Bart M. N. Smets, Remco Duits
Pubblicato in: Lecture Notes in Computer Science, Geometric Science of Information, 2025
Editore: Springer Nature Switzerland
DOI: 10.1007/978-3-032-03918-7_3

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

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