Function Approximation and Mathematical Modeling

Topic Information

Dear Colleagues,

Function approximation is quite a broad area of mathematics that ranges from functional analysis to numerical methods, including more modern areas such as machine learning, neural networks, and deep learning. Mathematical modeling aims to represent real-world systems through mathematically structured formulations derived from physical principles, domain knowledge, or simplifying assumptions. Function approximation can be part of a mathematical model because models often involve the use of functions to describe phenomena or are the solution to some equations. As part of the topic “Function Approximation and Mathematical Modeling”, we are interested in both subjects, with a special interest in the interplay between both—that is, in approaches that combine both perspectives, embedding function approximation within models.

Prof. Dr. Luis M. Garcia-Raffi
Prof. Dr. Vaclav Skala
Topic Editors

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
AppliedMath appliedmath	1.4	1.4	2021	20.4 Days	CHF 1200	Submit
Axioms axioms	1.5	-	2012	21.6 Days	CHF 2400	Submit
Foundations foundations	-	-	2021	24.3 Days	CHF 1000	Submit
Mathematics mathematics	2.3	5.4	2013	17.4 Days	CHF 2600	Submit
Symmetry symmetry	2.2	5.2	2009	16.3 Days	CHF 2400	Submit

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Published Papers (2 papers)

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All AppliedMath Axioms Mathematics Symmetry Foundations

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23 pages, 1022 KB  

Open AccessArticle

Activation-Induced Symmetric Kernels for Neural Network Approximation with Quantitative Error Analysis

by George A. Anastassiou, Seda Karateke and Metin Zontul

AppliedMath 2026, 6(8), 119; https://doi.org/10.3390/appliedmath6080119 - 23 Jul 2026

Viewed by 176

Abstract

This paper studies symmetrized neural network (SNN) operators generated by an adjustable half-hyperbolic tangent activation function. The construction is based on the paired density kernels ${\aleph }_t$ and ${\aleph }_{1/t}$, whose average defines the symmetric kernel $\mathcal{F}.$ This kernel [...] Read more.

This paper studies symmetrized neural network (SNN) operators generated by an adjustable half-hyperbolic tangent activation function. The construction is based on the paired density kernels ${\aleph }_t$ and ${\aleph }_{1/t}$, whose average defines the symmetric kernel $\mathcal{F}.$ This kernel is positive, even, normalized, and preserves the partition of unity. Using $\mathcal{F}$, we define finite-interval and whole-line SNN operators in the Banach space-valued setting. Pointwise and uniform convergence estimates are obtained through the first modulus of continuity. Higher-order and fractional approximation estimates are also derived, the latter using Caputo–Bochner fractional derivatives. The numerical part compares the nonsymmetrized operator ${\mathcal{L}}_n$ and the symmetrized operator ${\mathcal{L}}_n^s$. For $n=80$, the uniform error decreases from $0.010463$ to $0.003479$, the root mean square error (RMSE) decreases from $0.006530$ to $0.000826$, and the coefficient of determination ($R^2$) improves from $0.999675$ to $0.999995$. This improvement is accompanied by an increase in central processing unit (CPU) time from $0.014161$ s to $0.027088$ s. The parameter tests further show that the performance depends on the joint choice of n, t, and $\xi$. Overall, the results indicate that symmetrization improves approximation accuracy, while parameter tuning remains necessary. Full article

(This article belongs to the Topic Function Approximation and Mathematical Modeling)

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25 pages, 2477 KB  

Open AccessArticle

A Dynamic Framework for Defensive Pressure Assessment in Football

by César Catalán, José M. Calabuig, Luis M. García-Raffi and Enrique A. Sánchez-Pérez

AppliedMath 2026, 6(6), 82; https://doi.org/10.3390/appliedmath6060082 - 22 May 2026

Viewed by 591

Abstract

This study introduces a novel physics-inspired framework to quantify defensive pressure in football from tracking data. We model defender–attacker interactions as a variable-mass dynamical system, translating Newtonian mechanics into operational metrics that combine spatial configuration and motion. From this formulation we derive interpretable [...] Read more.

This study introduces a novel physics-inspired framework to quantify defensive pressure in football from tracking data. We model defender–attacker interactions as a variable-mass dynamical system, translating Newtonian mechanics into operational metrics that combine spatial configuration and motion. From this formulation we derive interpretable quantities at dyad, player, and team level, including a Center of Pressure (CP), Defensive Momentum, Defensive Force, and Defensive Work. We illustrate the framework in a single-match proof-of-concept using professional optical tracking data, analysing both full-match behaviour and football-specific phases such as counter-pressing, set-pieces, and throw-ins. Results show how the proposed metrics separate persistent spatial constraint (pressure) from energetically demanding defensive actions (work), enable identification of high-cost match-ups and workload concentration, and support time-resolved descriptions of coordinated pressing sequences. The framework provides a transferable, mechanically grounded toolkit for applied defensive performance analysis and motivates future validation on larger datasets. Full article

(This article belongs to the Topic Function Approximation and Mathematical Modeling)

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