Published papers journal,conference,workshop ( journal , conference)

• Jacek Cyranka and Jean-Philippe Lessard, Validated forward integration scheme for parabolic PDEs via Chebyshev series, 2022, Communications in Nonlinear Science and Numerical Simulation, ArXiv link.

• Sophie Gruenbacher; Ramin Hasani; Mathias Lechner; Jacek Cyranka; Scott A. Smolka; Radu Grosu,   On the Verification of Neural ODEs with Convergence Guarantees, AAAI 2021.

• Sophie Gruenbacher, Jacek Cyranka, Mathias Lechner, Md. Ariful Islam, Scott A. Smolka, Radu Grosu,   Lagrangian Reachtubes: The Next Generation, IEEE CDC 2020.

• Jacek Cyranka, Konstantin Mischaikow, Charles Weibel,  Contractibility of a persistence map preimage, J Appl. and Comput. Topology 4, 509-523, 2020. https://doi.org/10.1007/s41468-020-00059-7

• (workshop) Jacek Cyranka, Alex Georges, David Meyer, Mapper based classifier, TDA in ML workshop at IEEE ICML 2019 conference, Arxiv link.

• (workshop) Sophie Gruenbacher, Jacek Cyranka, Md Ariful Islam, Max Tschaikowski, Scott Smolka, Radu Grosu, Under the Hood of a Stand-Alone Lagrangian Reachability Tool, EPiC Series in Computing 61, 211-219.

• Rachel Levanger, Mu Xu, Jacek Cyranka, Michael Schatz, Konstantin Mischaikow, Mark Paul, Correlations between the Leading Lyapunov Vector and Pattern Defects for Chaotic Rayleigh-Bénard Convection, Chaos 29(5):053103, 2019.

• Jacek Cyranka, Md. Ariful Islam, Scott A. Smolka, Sicun Gao, Radu Grosu,  Tight Continuous-Time Reachtubes for Lagrangian Reachability, IEEE CDC 2018, Arxiv link.

• Jacek Cyranka, Piotr Mucha, A construction of two different solutions to an elliptic system, Journal of Mathematical Analysis and Applications, 2018, 465(1), 500-530, Arxiv link.

• Jacek Cyranka, Thomas Wanner, Computer-assisted proof of heteroclinic connections in the one-dimensional Ohta-Kawasaki model, SIAM Journal on Applied Dynamical Systems (SIADS), 2018, 17(1), 694 -731, Arxiv link.

• Jacek Cyranka, P. B. Mucha, E. S. Titi and P Zgliczyński, Stabilizing the long-time behavior of the forced Navier-Stokes and damped Euler systems by large mean flow, Physica D, vol. 369, 18-29, 2018, Arxiv link.

• Jacek Cyranka, Md. Ariful Islam, Greg Byrne, Paul Jones, Scott A. Smolka and Radu Grosu,  Lagrangian Reachability, COMPUTER AIDED VERIFICATION, CAV 2017, PT I Book Series: Lecture Notes in Computer Science, 10426, 379-400, 2017, Arxiv link

  Jacek Cyranka and P. Zgliczyński, Stabilizing effect of large average initial velocity in forced dissipative PDEs invariant with respect to Galilean transformations, Journal of Differential Equations, Vol. 261, 8 (2016), pp. 4648-4708, Arxiv link

  Jacek Cyranka and P. Zgliczyński, Existence of globally attracting solutions for one-dimensional viscous Burgers equation with nonautonomous forcing - a computer assisted proof SIAM Journal on Applied Dynamical Systems, 14-2 (2015), pp. 787-821, Arxiv link, software, documentation, numerical data and supplement.

  Jacek Cyranka, Existence of globally attracting fixed points of viscous Burgers equation with constant forcing. A computer assisted proof, Topological Methods in Nonlinear Analysis, Vol. 45, 2 (2015), 655–697, Arxiv link, software, documentation, numerical data from computer proofs.

  Jacek Cyranka, Efficient and generic algorithm for rigorous integration forward in time of dPDEs: Part I, Journal of Scientific Computing, Vol. 59, 1 (2014), 28-52, Download the paper, software, documentation, numerical data from tests, software guide.

Preprints

• Bartlomiej Polaczyk, Jacek Cyranka, Improved Overparametrization Bounds for Global Convergence of Stochastic Gradient Descent for Shallow Neural Networks , 2022, ArXiv link.