25 citations · 63 across the 13 of their papers we have counts for
16 papers
Worrisome Properties of Neural Network Controllers and Their Symbolic Representations
Jacek Cyranka, Kevin E M Church, Jean-Philippe Lessard
We raise concerns about controllers' robustness in simple reinforcement learning benchmark problems. We focus on neural network controllers and their low neuron and symbolic abstra…
Improved Overparametrization Bounds for Global Convergence of Stochastic Gradient Descent for Shallow Neural Networks
Bartłomiej Polaczyk, Jacek Cyranka
We study the overparametrization bounds required for the global convergence of stochastic gradient descent algorithm for a class of one hidden layer feed-forward neural networks, c…
Validated forward integration scheme for parabolic PDEs via Chebyshev series
Jacek Cyranka, Jean-Philippe Lessard
In this paper we introduce a new approach to compute rigorously solutions of Cauchy problems for a class of semi-linear parabolic partial differential equations. Expanding solution…
On The Verification of Neural ODEs with Stochastic Guarantees
Sophie Gruenbacher, Ramin Hasani, Mathias Lechner +3
We show that Neural ODEs, an emerging class of time-continuous neural networks, can be verified by solving a set of global-optimization problems. For this purpose, we introduce Sto…
Lagrangian Reachtubes: The Next Generation
Sophie Gruenbacher, Jacek Cyranka, Mathias Lechner +3
We introduce LRT-NG, a set of techniques and an associated toolset that computes a reachtube (an over-approximation of the set of reachable states over a given time horizon) of a n…
Mapper Based Classifier
Jacek Cyranka, Alexander Georges, David Meyer
Topological data analysis aims to extract topological quantities from data, which tend to focus on the broader global structure of the data rather than local information. The Mappe…
Connecting Lyapunov Vectors with the Pattern Dynamics of Chaotic Rayleigh-Bénard Convection
Rachel Levanger, Mu Xu, Jacek Cyranka +3
We explore the chaotic dynamics of Rayleigh-Bénard convection using large-scale, parallel numerical simulations for experimentally accessible conditions. We quantify the connection…
Contractibility of a persistence map preimage
Jacek Cyranka, Konstantin Mischaikow, Charles Weibel
This work is motivated by the following question in data-driven study of dynamical systems: given a dynamical system that is observed via time series of persistence diagrams that e…
Tight Continuous-Time Reachtubes for Lagrangian Reachability
Jacek Cyranka, Md. Ariful Islam, Scott A. Smolka +2
We introduce continuous Lagrangian reachability (CLRT), a new algorithm for the computation of a tight and continuous-time reachtube for the solution flows of a nonlinear, time-var…
Lagrangian Reachabililty
Jacek Cyranka, Md. Ariful Islam, Greg Byrne +3
We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that conservatively approximates the set of reachable states of a nonlinear dynamical system. LRT makes use…
Computer-assisted proof of heteroclinic connections in the one-dimensional Ohta-Kawasaki model
Jacek Cyranka, Thomas Wanner
We present a computer-assisted proof of heteroclinic connections in the one-dimensional Ohta-Kawasaki model of diblock copolymers. The model is a fourth-order parabolic partial dif…
Stabilizing the Long-time Behavior of the Navier-Stokes Equations and Damped Euler Systems by Fast Oscillating Forces
Jacek Cyranka, Piotr B Mucha, Edriss S Titi +1
The paper studies the issue of stability of solutions to the Navier-Stokes and damped Euler systems in periodic boxes. We show that under action of fast oscillating-in- time extern…
A construction of two different solutions to an elliptic system
Jacek Cyranka, Piotr Bogusław Mucha
The paper aims at constructing two different solutions to an elliptic system defined on the two dimensional torus. It can be viewed as an ell…
Stabilizing effect of large average initial velocity in forced dissipative PDEs invariant with respect to Galilean transformations
Jacek Cyranka, Piotr Zgliczyński
We describe a topological method to study the dynamics of dissipative PDEs on a torus with rapidly oscillating forcing terms. We show that a dissipative PDE, which is invariant wit…
Existence of globally attracting solutions for one-dimensional viscous Burgers equation with nonautonomous forcing - a computer assisted proof
Jacek Cyranka, Piotr Zgliczyński
We prove the existence of globally attracting solutions of the viscous Burgers equation with periodic boundary conditions on the line for some particular choices of viscosity and n…
Existence of globally attracting fixed points of viscous Burgers equation with constant forcing. A computer assisted proof
Jacek Cyranka
We present a computer assisted method for proving the existence of globally attracting fixed points of dissipative PDEs. An application to the viscous Burgers equation with periodi…