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MCA
Special Issues
Numerical and Symbolic Computation: Developments and Applications 2025
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Numerical and Symbolic Computation: Developments and Applications 2025

A special issue of Mathematical and Computational Applications (ISSN 2297-8747).

Deadline for manuscript submissions: closed (30 September 2025) | Viewed by 2986

Special Issue Editor

Dr. Maria Amélia Ramos Loja

E-Mail Website
Guest Editor
1. CIMOSM—Centro de Investigação em Modelação e Otimização de Sistemas Multifuncionais, ISEL, IPL—Instituto Politécnico de Lisboa, Av. Conselheiro Emídio Navarro 1, 1959-007 Lisboa, Portugal
2. IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Avenue Rovisco Pais, 1, 1049-001 Lisboa, Portugal
Interests: computational mechanics of solids; composite materials; adaptive structures; optimization; reverse engineering
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The ECCOMAS Thematic Conference on Numerical and Symbolic Computation: Developments and Applications (SYMCOMP2025) will be the seventh conference in a series that started in 2013, and it aims to bring together academic and scientific communities involved in numerical and symbolic computation across various scientific areas.

Sharing experiences and knowledge about current and emerging research and development areas is a major goal. The multidisciplinary character of this conference makes it a privileged forum to establish and cross-fertilize new multidisciplinary and cross-sector collaborations.

This Special Issue will mainly consist of selected papers presented at the "7th International Conference on Numerical and Symbolic Computation: Developments and Applications". Papers considered to fit the scope of the journal and be of sufficient quality, after evaluation by the reviewers, will be published free of charge.

Dr. Maria Amélia Ramos Loja
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematical and Computational Applications is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • symbolic and numerical applications
  • advanced parallel computing
  • system identification, modelling, and optimization
  • intelligent systems’ control and automation

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Published Papers (2 papers)

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26 pages, 1869 KB  
Article
Error Estimates and Generalized Trial Constructions for Solving ODEs Using Physics-Informed Neural Networks
by Atmane Babni, Ismail Jamiai and José Alberto Rodrigues
Math. Comput. Appl. 2025, 30(6), 127; https://doi.org/10.3390/mca30060127 - 24 Nov 2025
Viewed by 499
Abstract
In this paper, we address the challenge of solving differential equations using physics-informed neural networks (PINNs), an innovative approach that integrates known physical laws into neural network training. The PINN approach involves three main steps: constructing a neural-network-based solution ansatz, defining a suitable [...] Read more.
In this paper, we address the challenge of solving differential equations using physics-informed neural networks (PINNs), an innovative approach that integrates known physical laws into neural network training. The PINN approach involves three main steps: constructing a neural-network-based solution ansatz, defining a suitable loss function, and minimizing this loss via gradient-based optimization. We review two primary PINN formulations: the standard PINN I and an enhanced PINN II. The latter explicitly incorporates initial, final, or boundary conditions. Focusing on first-order differential equations, PINN II methods typically express the approximate solution as u˜(x,θ)=P(x)+Q(x)N(x,θ), where N(x,θ) is the neural network output with parameters θ, and P(x) and Q(x) are polynomial functions. We generalize this formulation by replacing the polynomial Q(x) with a more flexible function ϕ(x). We demonstrate that this generalized form yields a uniform approximation of the true solution, based on Cybenko’s universal approximation theorem. We further show that the approximation error diminishes as the loss function converges. Numerical experiments validate our theoretical findings and illustrate the advantages of the proposed choice of ϕ(x). Finally, we outline how this framework can be extended to higher-order or other classes of differential equations. Full article
(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications 2025)
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13 pages, 2920 KB  
Article
Dynamic Time Warping as Elementary Effects Metric for Morris-Based Global Sensitivity Analysis of High-Dimension Dynamical Models
by Dhan Lord B. Fortela, Ashley P. Mikolajczyk, Rafael Hernandez, Emmanuel Revellame, Wayne Sharp, William Holmes, Daniel Gang and Mark E. Zappi
Math. Comput. Appl. 2024, 29(6), 111; https://doi.org/10.3390/mca29060111 - 27 Nov 2024
Cited by 2 | Viewed by 1368
Abstract
This work focused on demonstrating the use of dynamic time warping (DTW) as a metric for the elementary effects computation in Morris-based global sensitivity analysis (GSA) of model parameters in multivariate dynamical systems. One of the challenges of GSA on multivariate time-dependent dynamics [...] Read more.
This work focused on demonstrating the use of dynamic time warping (DTW) as a metric for the elementary effects computation in Morris-based global sensitivity analysis (GSA) of model parameters in multivariate dynamical systems. One of the challenges of GSA on multivariate time-dependent dynamics is the modeling of parameter perturbation effects propagated to all model outputs while capturing time-dependent patterns. The study establishes and demonstrates the use of DTW as a metric of elementary effects across the time domain and the multivariate output domain, which are all aggregated together via the DTW cost function into a single metric value. Unlike the commonly studied coefficient-based functional approximation and covariance decomposition methods, this new DTW-based Morris GSA algorithm implements curve alignment via dynamic programing for cost computation in every parameter perturbation trajectory, which captures the essence of “elementary effect” in the original Morris formulation. This new algorithm eliminates approximations and assumptions about the model outputs while achieving the objective of capturing perturbations across time and the array of model outputs. The technique was demonstrated using an ordinary differential equation (ODE) system of mixed-order adsorption kinetics, Monod-type microbial kinetics, and the Lorenz attractor for chaotic solutions. DTW as a Morris-based GSA metric enables the modeling of parameter sensitivity effects on the entire array of model output variables evolving in the time domain, resulting in parameter rankings attributed to the entire model dynamics. Full article
(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications 2025)
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