WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7150

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Access Right: Open AccessAuthor: search.filters.author.Turan, Meltem

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  • Article
    A Physics-Informed Neural Network (PINN) Approach to Over-Equilibrium Dynamics in Conservatively Perturbed Linear Equilibrium Systems
    (MDPI, 2025) Dutta, Abhishek; Mukherjee, Bitan; Hosen, Sk Aftab; Turan, Meltem; Constales, Denis; Yablonsky, Gregory
    Conservatively perturbed equilibrium (CPE) experiments yield transient concentration extrema that surpass steady-state equilibrium values. A physics-informed neural network (PINN) framework is introduced to simulate these over-equilibrium dynamics in linear chemical reaction networks without reliance on extensive time-series data. The PINN incorporates the reaction kinetics, stoichiometric invariants, and equilibrium constraints directly into its loss function, ensuring that the learned solution strictly satisfies physical conservation laws. Applied to three- and four-species reversible mechanisms (both acyclic and cyclic), the PINN surrogate matches conventional ODE integration results, reproducing the characteristic early concentration extrema (maxima or minima) in unperturbed species and the subsequent relaxation to equilibrium. It captures the timing and magnitude of these extrema with high accuracy while inherently preserving total mass. Through the physics-informed approach, the model achieves accurate results with minimal data and a compact network architecture, highlighting its parameter efficiency.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Polynomial Approaches in Improving Accuracy of Probability Distribution Estimation Using the Method of Moments
    (Wiley, 2024) Turan, Meltem; Munkhammar, Joakim; Dutta, Abhishek
    BACKGROUNDDetermination of a probability density function (PDF) is an area of active research in engineering sciences as it can improve process systems. A previously developed polynomial method-of-moments-based PDF estimation model has been applied in the research to produce accurate approximations to both standard and more complex PDF. A model with a different polynomial basis than a monomial is still to be developed and evaluated. This is the work that is undertaken in this study.RESULTSA set of standard PDF (Normal, Weibull, Log Normal and Bimodal) and more complex distributions (solutions to the Smoluchowski coagulation equation and Population Balance equation) were approximated by the method-of-moments using Chebyshev, Hermite and Lagrange polynomial-based density functions. Results show that Lagrange polynomial-based models improve the fit compared to monomial based-modeling in terms of RMSE and Kolmogorov-Smirnov test statistic estimates. The Kolmogorov-Smirnov test-statistics decreased by 19% and the RMSE values were improved by around 85% compared to the standard monomial basis when using Lagrange polynomial basis.CONCLUSIONThis study indicates that the procedure using Lagrange polynomials with method-of-moments is a more reliable reconstruction procedure that calculates the approximate distribution using lesser number of moments, which is desirable. (c) 2024 The Authors. Journal of Chemical Technology and Biotechnology published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry (SCI).
  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    Further Developments of the Extended Quadrature Method of Moments To Solve Population Balance Equations
    (Cell Press, 2023) Turan, Meltem; Dutta, Abhishek
    Developing numerical methods to solve polydispersed flows using a Population Balance Equation (PBE) is an active research topic with wide engineering applications. The Extended Quadrature Method of Moments (EQMOM) approximates the number density as a positive mixture of Kernel Density Functions (KDFs) that allows physical source terms in the PBEs to compute continuous or point-wise form according to the moments. The moment-inversion procedure used in EQMOM has limitations such as the inability to calculate certain roots even if it is defined, absence of consistent result when multiple roots exist or when the roots are nearly equal. To address these limitations, the study proposes a modification of the moment-inversion procedure to solve the PBE based on the proposed Halley-Ridder (H-R) method. Although there is no significant improvement in the extent of variability relative to the mean of the tested shape parameter cr values, an increase in the number of floating point operations (FLOPS) is observed which the proposed algorithm responds in limitations mentioned above. The total number of FLOPS for all the kernels used for the approximation increased by around 30%. This is an improvement towards the development of a more reliable and robust moment-inversion procedure.