Submitted manuscripts (under review)

• Parallel Trust-Region Approaches in Neural Network Training: Beyond Traditional Methods (2023), S. Cruz, K. Trotti, A. Kopaničáková, R. Krause, Under review. [BibTeX] [Preprint]

  @article{trotti_23,
    title = {{Parallel Trust-Region Approaches in Neural Network Training: Beyond Traditional Methods}},
    author  = {Cruz, Samuel and Trotti, Ken and Kopani{\v c}{\'a}kov{\'a}, Alena and Krause, Rolf},
    year={2023},
    archivePrefix="arXiv",
    eprint={2312.13677},
  }
  
  

• Two-level Overlapping Additive Schwarz preconditioning for training of scientific machine-learning applications (2024), Y.Lee, A. Kopaničáková, G. Karniadakis, Under review. [BibTeX] [Preprint]

  @article{kopanicakova2024_j3,
    title = {{Two-level Overlapping Additive Schwarz preconditioning for training of scientific machine-learning applications}},
    author  = {Lee Youngku and Kopani{\v c}{\'a}kov{\'a}, Alena and Karniadakis, George},
    year={2024},
    archivePrefix="arXiv",
    eprint={2312.2406.10997},
  }
  
  

• The limitations of a standard phase-field model in reproducing jointing in sedimentary rock layers (2024), E. Pezzuli, P. Zulian, A. Kopaničáková, R. Krause, T. Driesner, Under review. [BibTeX] [Preprint]

  @article{kopanicakova2024_j5,
    title = {{The limitations of a standard phase-field model in reproducing jointing in sedimentary rock layers.}},
    author  = {Pezzuli, Edoardo and Zulian, Patrick and Kopani{\v c}{\'a}kov{\'a}, Alena and Krause, Rolf and Driesner, Thomas},
    year={2024},
    archivePrefix="arXiv",
    eprint={2408.14449},
  }
  
  

• Two-level trust-region method with random subspaces (2024), A. Angino, A. Kopaničáková, R. Krause, Under review. [BibTeX] [Preprint]

  @article{kopanicakova2024_j6,
    title = {{Two-level trust-region method with random subspaces.}},
    author  = {Angino, Andrea and Kopani{\v c}{\'a}kov{\'a}, Alena and Krause, Rolf},
    year={2024},
    archivePrefix="arXiv",
    eprint={2409.05479},
  }
  
  

Publications in peer-reviewed journals and book chapters

• Blending neural operators and relaxation methods in PDE numerical solvers (2024), E. Zhang, A. Kahana, A. Kopaničáková, E. Turkel, R. Ranade, J. Pathak, G. Em Karniadakis, Nature Machine Intelligence [Link] [BibTeX] [Preprint]

  @unpublished{kopanicakova_2024_4,
    title={Blending neural operators and relaxation methods in PDE numerical solvers},
    author={Zhang Enrui and Kahana Adar and Kopani{\v c}{\'a}kov{\'a} Alena and Turkel Eli and Ranade Rishikesh and Pathak Jay and Karniadakis George Em},
    year={2024},
    journal={Nature Machine Intelligence},
    year={2024},
    archivePrefix="arXiv",
    eprint={2208.13273},
    doi = {10.1038/s42256-024-00910-x},
  }
  
  

• DeepONet Based Preconditioning Strategies for Solving Parametric Linear Systems of Equations (2024), A. Kopaničáková, G. Em Karniadakis, Accepted for publication in SISC. [Link] [BibTeX] [Preprint]

  @article{kopanicakova_2024_j1,
    title = {{DeepONet Based Preconditioning Strategies for Solving Parametric Linear Systems of Equations}},
    author={Kopani{\v c}{\'a}kov{\'a} Alena and Karniadakis George Em},
    year={2024},
    archivePrefix="arXiv",
    eprint={2401.02016},
  }
  
  

• Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies (2023), A. Kopaničáková, H. Kothari, G. Em Karniadakis, R. Krause, SIAM Journal on Scientific Computing (SISC) [Link] [BibTeX] [Preprint]

  @article{kopanicakova_pinnspqn_2023,
    title={Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies},
    author={Kopani{\v c}{\'a}kov{\'a} Alena and Kothari Hardik and Karniadakis George Em and Krause Rolf},
    year={2023},
    journal={SIAM Journal on Scientific Computing},
    pages={S46--S67},
    year={2024},
    publisher={SIAM}          
    archivePrefix="arXiv",
    eprint={2306.17648},
    doi = {10.1137/23M1583375},
  }
  
  

• Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training (2023), S. Gratton, A. Kopaničáková, Ph. Toint, SIAM Journal on Optimization [Link] [BibTeX] [Preprint]

  @article{Kopanicakova_2023a,
    author = {Gratton, Serge and {Kopani\v{c}\'{a}kov\'{a}}, Alena and Toint, Philippe L.},
    title = {Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training},
    journal = {SIAM Journal on Optimization},
    volume = {33},
    number = {4},
    pages = {2772-2800},
    year = {2023},
    doi = {10.1137/23M1553455},
  }
  
  

• Globally convergent multilevel training of deep residual networks (2023), A. Kopaničáková, R. Krause, SIAM Journal on Scientific Computing [Link] [BibTeX] [Preprint]

  @article{Kopanicakova_2021g,
    author  = {Kopani{\v c}{\'a}kov{\'a},  Alena and Krause, Rolf},
    title = {{G}lobally {C}onvergent {M}ultilevel {T}raining of {D}eep {R}esidual {N}etworks},
    journal = {SIAM Journal on Scientific Computing},
    volume = {0},
    number = {0},
    pages = {S254-S280},
    doi = {10.1137/21M1434076},
    year = {2022},
  }        
  
  

• Nonlinear field-split preconditioners for solving monolithic phase-field models of brittle fracture (2023), A. Kopaničáková, H. Kothari, R. Krause, Computer Methods in Applied Mechanics and Engineering [Link] [BibTeX] [Preprint]

  @article{Kopanicakova_2021f,
      title={Nonlinear field-split preconditioners for solving monolithic phase-field models of brittle fracture},
      author={Kopani{\v c}{\'a}kov{\'a}, Alena and Kothari, Hardik and Krause, Rolf},
      journal={Computer Methods in Applied Mechanics and Engineering},
      volume={403},
      pages={115733},
      year={2023},
      publisher={Elsevier},
  }
  
  

• A Phase-Field Approach to Pneumatic Fracture (2022), C. Bilgen, A. Kopaničáková, R. Krause, K. Weinberg, Non-standard Discretisation Methods in Solid Mechanics [Link] [BibTeX] [Preprint]

  @article{Kopanicakova_2022b,
    author="Bilgen, Carola and Kopani{\v c}{\'a}kov{\'a},  Alena and Krause, Rolf and Weinberg, Kerstin",
    editor="Schr{\"o}der, J{\"o}rg and Wriggers, Peter",
    title="A Phase-Field Approach to Pneumatic Fracture",
    bookTitle="Non-standard Discretisation Methods in Solid Mechanics",
    year="2022",
    pages="217--241",
  }
  
  

• Large scale simulation of pressure induced phase‐field fracture propagation using Utopia (2021), P. Zulian*, A. Kopaničáková*, M. Nestola, N. Fadel, A. Fink, J. VandeVondele, R. Krause, CCF Transactions on High Performance Computing [Link] [BibTeX] [Preprint]

  @article{Kopanicakova_2021a,
    author = {Zulian{*}, Patrick and {Kopani{\v{c}}{\'a}kov{\'a}*},  Alena and Nestola, Maria G C and Fadel, Nur and Fink, Andreas and VandeVondele, Joost and Krause, Rolf},
    title = {Large scale simulation of pressure induced phase‐field fracture propagation using {U}topia},
    journal = {CCF Transactions on High Performance Computing},
    year = {2021},
    doi = {10.1007/s42514-021-00069-6},
  }
  
  

• Efficient Identification of Scars using Heterogeneous Model Hierarchies. (2021), F. Chegini, A. Kopaničáková, R. Krause, M. Weiser, EP Europace [Link] [BibTeX] [Preprint]

  @article{Kopanicakova_2020b,
      author={Chegini, Fatemeh and {Kopani{\v{c}}{\'{a}}kov{\'{a}}},  Alena and Krause, Rolf and Weiser, Martin},
      title={Efficient Identification of Scars using Heterogeneous Model Hierarchies},
      journal={EP Europace},
      volume={23},
      number={Supplement\_1},
      pages={i113--i122},
      year={2021},
      publisher={Oxford University Press},
  }
  
  

• A detailed investigation of the model influencing parameters of the phase-field fracture approach. (2020), C. Bilgen, A. Kopaničáková, R. Krause, K. Weinberg, GAMM-Mitteilungen [Link] [BibTeX] [Preprint]

  @article{Kopanicakova_2019c,
      author  = {Bilgen, Carola and {Kopani{\v{c}}{\'{a}}kov{\'{a}}},  Alena and Krause, Rolf and Weinberg, Kerstin},
      title   = {{A} detailed investigation of the model influencing parameters of the phase-field fracture approach.},
      journal={GAMM-Mitteilungen},
      volume={43},
      number={2},
      pages={e202000005},
      year={2020},
      publisher={Wiley Online Library},
  }
  
  

• Recursive multilevel trust region method with application to fully monolithic phase-field models of brittle fracture (2020), A. Kopaničáková, R. Krause, Computer Methods in Applied Mechanics and Engineering [Link] [BibTeX] [Preprint]

  @article{Kopanicakova_2019b,
    author  = {{Kopani{\v{c}}{\'{a}}kov{\'{a}}},  Alena and Krause, Rolf},
    title   = {{R}ecursive multilevel trust region method with application to fully monolithic phase-field models of brittle fracture.},
    journal={Computer Methods in Applied Mechanics and Engineering},
    volume={360},
    pages={112720},
    year={2020},
    publisher={Elsevier},  
  }
  
  

• Subdivision-Based Nonlinear Multiscale Cloth Simulation (2019), A. Kopaničáková, R. Krause, R. Tamstorf, SIAM Journal on Scientific Computing [Link] [BibTeX] [Preprint]

  @article{Kopanicakova_2019a,
    author  = {{Kopani{\v c}{\'a}kov{\'a}},  Alena and Krause, Rolf and Tamstorf, Rasmus},
    title = {Subdivision-Based Nonlinear Multiscale Cloth Simulation},
    journal = {SIAM Journal on Scientific Computing},
    volume = {41},
    number = {5},
    pages = {S433-S461},
    year = {2019},
    doi = {10.1137/18M1194870},
    URL = { https://doi.org/10.1137/18M1194870},
  }
  
  

• A phase-field approach to conchoidal fracture (2017), C. Bilgen, A. Kopaničáková, R. Krause, K. Weinberg, Meccanica [Link] [BibTeX] [Preprint]

  @article{kopanicakova_nonlinear_2023,
    author  = {Bilgen, Carola and {Kopani{\v c}{\'a}kov{\'a}},  {A}lena and Krause, Rolf and Weinberg, Kerstin},
    title   = {{A} phase-field approach to conchoidal fracture},
    journal = {Meccanica},
    year    = {2017},
    pages   = {1--17},     
  }
  
  

Publications in peer-reviewed conference proceedings

• On the use of hybrid coarse-level models in multilevel minimization methods (2024), A. Kopaničáková, Domain Decomposition Methods in Science and Engineering XXVII [Link] [BibTeX] [Preprint]

  @unpublished{Kopanicakova_2022f,
    title={On the use of hybrid coarse-level models in multilevel minimization methods},
    author={Alena Kopaničáková},
    booktitle={International Conference on Domain Decomposition Methods},
    pages={303--310},
    year={2022},
    organization={Springer}
  }
  
  

• Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints (2024), H. Kothari, A. Kopaničáková, R. Krause, Accepted for publication in Domain Decomposition Methods in Science and Engineering XXVII [Link] [BibTeX] [Preprint]

  @unpublished{kothari_raspqn_const_2022,
    title={Nonlinear {S}chwarz preconditioning for nonlinear optimization problems with bound constraints},
    author={Hardik Kothari and Alena Kopaničáková and Rolf Krause},
    booktitle={International Conference on Domain Decomposition Methods},
    pages={319--326},
    year={2022},
    organization={Springer}
  }
  
  

• A Multigrid Preconditioner for Jacobian-free Newton-Krylov Methods (2023), H. Kothari, A. Kopaničáková, R. Krause, Domain Decomposition Methods in Science and Engineering XXVI [Link] [BibTeX] [Preprint]

  @InProceedings{kothari_multigrid_2023,
    author="Kothari, Hardik
            and Kopani{\v{c}}{\'a}kov{\'a}, Alena
            and Krause, Rolf",
    editor="Brenner, Susanne C.
            and Chung, Eric
            and Klawonn, Axel
            and Kwok, Felix
            and Xu, Jinchao
            and Zou, Jun",
    title="A Multigrid Preconditioner for Jacobian-free Newton--Krylov Methods",
    booktitle="Domain Decomposition Methods in Science and Engineering XXVI",
    year="2023",
    publisher="Springer International Publishing",
    address="Cham",
    pages="365--372",
  }
  
  

• Multilevel Active-Set Trust-Region (MASTR) Method for Bound Constrained Minimization (2023), A. Kopaničáková, R. Krause, Domain Decomposition Methods in Science and Engineering XXVI [Link] [BibTeX] [Preprint]

  @InProceedings{Kopanicakova_2021c,
    author="Kopani{\v{c}}{\'a}kov{\'a}, Alena
            and Krause, Rolf",
    editor="Brenner, Susanne C.
            and Chung, Eric
            and Klawonn, Axel
            and Kwok, Felix
            and Xu, Jinchao
            and Zou, Jun",
    title="{M}ultilevel {A}ctive-{S}et {T}rust-{R}egion {(MASTR)} {M}ethod for {B}ound {C}onstrained {M}inimization}",
    booktitle="Domain Decomposition Methods in Science and Engineering XXVI",
    year="2023",
    publisher="Springer International Publishing",
    address="Cham",
    pages="355--363",
  }
  
  

• Quantitative Analysis of Nonlinear Multifidelity Optimization for Inverse Electrophysiology (2023), F. Chegini, A. Kopaničáková, R. Krause, M. Weiser, Domain Decomposition Methods in Science and Engineering XXVI [Link] [BibTeX] [Preprint]

  @InProceedings{Kopanicakova_2021d,
    author="Chegini Fatemeh
            and Kopani{\v{c}}{\'a}kov{\'a}, Alena
            and Krause, Rolf
            and Weiser, Martin",
    editor="Brenner, Susanne C.
            and Chung, Eric
            and Klawonn, Axel
            and Kwok, Felix
            and Xu, Jinchao
            and Zou, Jun",
    title="Quantitative Analysis of Nonlinear Multifidelity Optimization for Inverse Electrophysiology",
    booktitle="Domain Decomposition Methods in Science and Engineering XXVI",
    year="2023",
    publisher="Springer International Publishing",
    address="Cham",
    pages="67--78",
  }
  
  

• Training of residual networks with stochastic MG/Opt (2021), C. von Planta, A. Kopaničáková, R. Krause, ICML 2021 Workshop Beyond First Order Methods in Machine Learning [Link] [BibTeX] [Preprint]

  @InProceedings{Kopanicakova_2021e,
    title={Training of residual networks with stochastic {MG}/{O}pt},
    author={von Planta, Cyrill and {Kopani{\v{c}}{\'a}kov{\'a}}, Alena and Krause, Rolf},
    booktitle={ICML 2021 Workshop: Beyond First Order Methods in Machine Learning},
    year={2021}, 
  }
  
  

• Multilevel minimization for deep residual networks (2021), L. Gaedke-Merzhauser*, A. Kopaničáková*, R. Krause, ESAIM Proceedings [Link] [BibTeX] [Preprint]

  @InProceedings{Kopanicakova_2020c,
    title={Multilevel minimization for deep residual networks},
    author={Gaedke-Merzh{\"a}user*, Lisa and Kopani{\v{c}}{\'a}kov{\'a}*,  Alena and Krause, Rolf},
    booktitle={In ESAIM Proceedings and Surveys},
    volume={71}, 
    pages={131-144},
    year={2021},
  }        
  
  

• A Multilevel Approach to Training (2020), V. Braglia*, A. Kopaničáková*, R. Krause, ICML 2020 Workshop Beyond First Order Methods in Machine Learning [Link] [BibTeX] [Preprint]

  @InProceedings{Kopanicakova_2020d,
      title={A Multilevel Approach to Training},
      author={Braglia*, Vanessa and Kopani{\v{c}}{\'a}kov{\'a}*,  Alena and Krause, Rolf},
      booktitle={ICML 2020 Workshop: Beyond First Order Methods in Machine Learning},
      year={2020},
  }
  
  

• A phase-field approach to pneumatic fracture (2017), C. Bilgen, A. Kopaničáková, R. Krause, K. Weinberg, PAMM [Link] [BibTeX] [Preprint]

  @InProceedings{Bilgen17b,
    author        = {Bilgen, Carola and Kopani{\v c}{\'a}kov{\'a},  Alena and Krause, Rolf and Weinberg, Kerstin},
    title         = {{A} phase-field approach to pneumatic fracture},
    booktitle       = {{PAMM}},
    year          = {2017},
    volume        = {17},
    number        = {1},
    pages         = {71-74},
    doi           = {10.1002/pamm.201710022},
  }
  
  

• Gesture recognition using DTW and its application potential in human-centered robotics (2013), A. Kopaničáková, M. Vircikova, P. Sincak, Proceedings of the 13th Scientific Conference of Young Researchers of Faculty of Electrical Engineering and Informatics Technical University of Košice [Link] [BibTeX] [Preprint]

  @InProceedings{kopanivcakova2013gesture,
      title={Gesture recognition using {D}{T}{W} and its application potential in human-centered robotics},
      author={{K}opani{\v{c}}{\'a}kov{\'a}, Alena and Vir{\v{c}}{\'\i}kov{\'a}, M{\'a}ria and Sin{\v{c}}\'ak, Peter},
      booktitle={Proceedings of the 13th Scientific Conference of Young Researchers of Faculty of Electrical Engineering and Informatics
    Technical University of Ko\v{s}ice},
      year={2013}, 
  }
  
  

Thesis

• Multilevel minimization in trust-region framework - Algorithmic and software developments. PhD thesis, Università della Svizzera italiana, 2020