Mathematical modelling and artificial intelligence with applications

Computer Science

Mathematical modelling and artificial intelligence with applications

Numerical methods, scientific computing, mathematical modelling, machine learning, coding theory.

Design and implementation of numerical methods and applications;
Generalized inverses;
Neural networks;
Source coding and quantizer design;

Mathematical modelling and applications:
- Finite element methods
- Nonlinear, linear and combinatorial optimization methods
- Numerical methods for ordinary and stochastic differential equations
- Applications to problems in engineering, finance, etc.

Computation of matrix generalized inverses:
- Design and implementation of direct and iterative numerical methods for computing matrix generalized inverses and solutions of the matrix equations;

Machine learning:
- Gradient and zeroing neural networks and applications to linear algebra problems;
- Convolutional neural networks and combinatorial designs;
- Quantization of the coefficients of the neural networks;

Coding theory:
- Design and implementation of the source coding algorithms with applications to audio, image and video coding;

• Germany-Serbian Bilateral Reseach Project: Modern techniques for optimisation of plasma modelling codes; Project leader in Serbia: Marko Petković; Project leader in Germany: Marcus Becker, Leibniz Institute for Plasma Science and Technology (INP), Greifswald, Germany. Project No: 337-00-253/2023-05/14; Duration: 2024-2025.

- Vladimir Stojanović, Marko Petković, Dynamic stability of vibrations and critical velocity of a complex bogie system moving on a flexibly supported infinity track, Journal of Sound and Vibration 434 (2018) 475-501. (M21, IF=3.123)
- Zoran Perić, Marko Petković, Jelena Nikolić, Aleksandra Jovanović, Support region estimation of the product polar companded quantizer for Gaussian source, Signal Processing 143 (2018), 140-145. (M21, IF=4.086)
- Predrag Stanimirović, Marko Petković, Dimitrios Gerontitis, Gradient neural network with nonlinear activation for computing inner inverses and the Drazin inverse, Neural Processing Letters 48:1 (2018), 109-133. (M22, IF=2.591)
- Vladimir Stojanović, Marko Petković, Jian Deng, Stability of vibrations of a moving railway vehicle along an infinite complex three-part viscoelastic system, International Journal of Mechanical Sciences 136 (2018), 155-168. (M21a, IF=4.134)
- Vladimir Stojanović, Marko Petković, Jian Deng, Instability of vehicle systems moving along an infinite beam on a viscoelastic foundation, European Journal of Mechanics A: Solids 69 (2018), 238-254. (M21, IF=2.931)
- Marko Petković, Predrag Stanimirović, Vasilios Katsikis, Modified discrete iterations for computing the inverse and pseudoinverse of the time-varying matrix, Neurocomputing 289 (2018), 155-165. (M21, IF=4.072)
- Predrag Stanimirović, Marko Petković, Gradient neural dynamics for solving matrix equations and their applications, Neurocomputing 306 (2018), 200-212. (M21, IF=4.072)
- Marko Petković, Mihailo Krstić, Kostadin Rajković, Rapid generalized Schultz iterative methods for the computation of outer inverses, Journal of Computational and Applied Mathematics 344 (2018), 572-584. (M21, IF=1.632)
- Predrag Rajković, Slađana Marinković, Marko Petković, A class of orthogonal polynomials related to the generalized Laguerre weight with two parameters, Computational and Applied Mathematics 38:10 (2019). (M22, IF=1.360)
- Vladimir Stojanović, Marko Petković, Jian Deng, Stability and vibrations of an overcritical speed moving multiple discrete oscillators along an infinite continuous structure, European Journal of Mechanics / A Solids 75, 367-380. (M21, IF=3.786)
- Zoran Perić, Jelena Nikolić, Marko Petković, Class of tight bounds on the Q-Function with closed-form upper bound on relative error, Mathematical Methods in the Applied Sciences 42:6 (2019), 1786-1794. (M21, IF=1.626)
- Vladimir Stojanović, Marko Petković, Jian Deng, Stability of parametric vibrations of an isolated symmetric cross-ply laminated plate, Composites part B: Engineering 167 (2019), 631-642. (M21a, IF=7.635)
- Tanay Saha, Shwetabh Srivastava, Swanand Khare, Predrag Stanimirović, Marko Petković, An improved algorithm for basis pursuit problem and its applications, Applied Mathematics and Computation 355 (2019), 385-398. (M21a, IF=3.472)
- Predrag Stanimirović, Marko Petković, Improved GNN models for constant matrix inversion, Neural Processing Letters 50:1 (2019), 321-339. (M22, IF=2.891)
- Vladimir Stojanović, Marko Petković, Dunja Milić, Nonlinear vibrations of a coupled beam-arch bridge system, Journal of Sound and Vibration 464 (2020), 115000. (M21, IF=3.429)
- Predrag Stanimirović, Marko Petković, Dijana Mosić, Exact solutions and convergence of gradient based dynamical systems for computing outer inverses, Applied Mathematics and Computation 412 (2022), 126588. (M21a, IF=4.091)
- Zoran Perić, Aleksandar Marković, Nataša Kontrec, Jelena Nikolić, Marko Petković, Aleksandra Jovanović, Two Interval Upper-Bound Q-Function Approximations with Applications, Mathematics 10 (2022), 3590. (M21a, IF=2.592)
- Dunja Milić, Jian Deng, Vladimir Stojanović, Marko Petković, Effects of Kerr-type viscoelastic coupling layer with different stiffnesses on stochastic stability of Rayleigh double beams, Mechanics Research Communications 132 (2023), 104181. (M22, IF=2.749)
- Vladimir Stojanović, Jian Deng, Dunja Milić, Marko Petković, Non-stability of a bogie moving along a specific infinite complex flexibly beam-layer structure, Engineering Structures 295 (2023), 116788. (M21, IF=5.582)
- Vladimir Stojanović, Jian Deng, Dunja Milić, Marko Petković, MDOF Stochastic Stability Analysis and Applications to a Coupled Rotating Shaft System, Probabilistic Engineering Mechanics 74 (2023), 103509. (M21, IF=2.954)
- Radica Bojičić, Marko Petković, Oscillation criteria for a second order half-linear differential equation with delay, with monotone nondecreasing delay function, Computational and Applied Mathematics 42 (2023), 326. (M21, IF=2.998)
- Vladimir Stojanović, Jian Deng, Dunja Milić, Marko Petković, Dynamics of moving coupled objects with stabilizers and unconventional couplings, Journal of Sound and Vibration 570 (2024), 118020. (M21, IF=4.761)
- Vladimir Stojanović, Jian Deng, Dunja Milić, Marko Petković, Structures with varying discontinuities and curvatures: A Dynamic analysis approach by the p-version finite element method, Finite Elements in Analysis & Design 229 (2024), 104066. (M21a, IF=3.100)
- Dunja Milić, Vladimir Stojanović, Jian Deng, Marko Petković, Dynamic stability of the sandwich nano-beam system, International Journal of Engineering Science 194 (2024), 103973. (M21a, IF=7.155)
- Vladimir Stojanović, Jian Deng, Dunja Milić, Marko Petković, Vibrational analysis of a coupled damaged Timoshenko beam-arch mechanical system with von Kármán nonlinearities and layer discontinuity, Mathematics and Computers in Simulation 218 (2024), 334-356. (M21a, IF=4.600)
- Predrag Rajković, Slađana Marinković, Miomir Stanković, Marko Petković, Differential properties of the reduced Mittag-Leffler polynomials, U.P.B. Scientific Bulletin, Series A 86:1 (2024). (M23, IF=1.100)
- Jelena Dakić, Marko Petković, Gradient neural network model for the system of two linear matrix equations and applications, Applied Mathematics and Computation 481:15 (2024), 128930. (M21a, IF=4.000)
- Marko Petković, Predrag Stanimirović, Zeroing neural network based on the equation AXA = A, Information and Computation, 301:B (2024), 105207. (M23, IF=0.800)
- Jelena Pejić, Marko Petković, Sandra Klinge, Exploring spatial reasoning performances of CNN on linear layout dataset, Machine Learning: Science and Technology 5:4 (2024), 045056. (M21, IF=6.300)
- Radica Bojičić, Marko Petković, Paul Barry, Hankel transform of linear combination of three consecutive Catalan numbers, Hacettepe Journal of Mathematics and Statistics, to appear (M22, IF=0.700)
- Radica Bojičić, Marko Petković, Predrag Rajković, Paul Barry, On the Hankel transform of the number of closed walks on regular trees, FILOMAT, to appear. (M22, IF=0.800)