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Journal article
A novel Sigmexd Activation Function to enhance Physics-Informed Neural Networks (PINNs) for differential equations with a perspective on the role of activation functions in PINNs
Neurocomputing, Vol.666, pp.1-25
2026
Abstract
Physics-Informed Neural Networks (PINNs) is a rapidly evolving machine learning technique that leverages deep learning strengths to solve physical equations. In PINNs, Activation Functions (AFs) are key to capturing nonlinearities of complex real-world problems. In addition, the inherent randomness of neural-network learning makes ‘seeding’ an important consideration for ensuring reproducibility and consistency. In this background, this investigation focuses on enhancing PINN activation to achieve reliable solutions across diverse differential equations. The key objectives include: a) Evaluating the role of different AFs and seeding arrangements in PINNs; b) Proposing a novel AF specifically suitable for PINN-based computational modeling; and c) Providing preliminary recommendations on PINN activation and seeding selection. In achieving these objectives, nine different differential-equation setups have been considered with three Ordinary Differential Equations (ODEs) and six Partial Differential Equations (PDEs). Six different AFs, including the newly proposed Sigmexd AF and a range of widely-utilized AFs, have been comprehensively compared with respect to PINNs. The Sigmexd AF demonstrates superior performance, achieving up to five-fold improvements compared to the next-best AF. The practical impact of Sigmexd has been clearly demonstrated, as a versatile AF that can consistently deliver high levels of accuracy across a wide range of linear and nonlinear differential equations of varying orders. The analyses further reveal an interesting interaction between seeding arrangements and AFs. A preliminary activation selection setup is recommended for PINN-based modeling, offering foundational-level guidance for optimal activation and seeding. To the best of the authors’ knowledge, this represents the first systematic approach of its kind.
Details
- Title
- A novel Sigmexd Activation Function to enhance Physics-Informed Neural Networks (PINNs) for differential equations with a perspective on the role of activation functions in PINNs
- Authors
- Manoj Kurukulasuriya (Corresponding Author) - Queensland University of TechnologyChanaka Batuwatta-Gamage - Queensland University of TechnologyChaminda Karunasena - University of RuhunaHyogu Jeong - Queensland University of TechnologyKalani Ranathunga - University of the Sunshine Coast, Queensland, School of Science, Technology and EngineeringCharith Rathnayaka (Corresponding Author) - University of the Sunshine Coast, Queensland, School of Science, Technology and EngineeringYuanTong Gu - Queensland University of Technology
- Publication details
- Neurocomputing, Vol.666, pp.1-25
- Publisher
- Elsevier BV
- Date published
- 2026
- DOI
- 10.1016/j.neucom.2025.132364
- ISSN
- 1872-8286; 0925-2312
- Copyright note
- © 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
- Data Availability
- No data was used for the research described in the article.
- Grant note
- Support from the QUT HDR Tuition Fee Sponsorship, QUT Postgraduate Research Award (QUTPRA) Scholarship, QUT High-Performance Computing resources and University of the Sunshine Coast (UniSC) are gratefully acknowledged.
- Organisation Unit
- School of Science, Technology and Engineering
- Language
- English
- Record Identifier
- 991192142902621
- Output Type
- Journal article
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