Innovations in Artificial Neural Network Applications

1. Introduction

Artificial neural networks (ANNs) are widely used for nonlinear approximation, data analysis, prediction, and optimization in scientific and engineering applications [1]. Research has also increasingly investigated the integration of neural models with established mathematical descriptions and physical constraints [2,3]. Neural operators and multi-fidelity methods offer additional possibilities for reducing the computational cost of repeated simulations and design procedures [4,5,6].

Despite these developments, model generalization, interpretability, computational efficiency, and the reliability of predictions remain relevant challenges. The Special Issue “Innovations in Artificial Neural Network Applications” was established to address methodological improvements in ANN-based systems, the integration of symbolic reasoning and first principles, and greater transparency and reliability. This Editorial summarizes selected developments and research gaps, considers the contributions of the Special Issue, and focuses primarily on future research directions.

2. Recent Developments and Remaining Research Gaps

Physics-informed machine learning combines data-driven methods with prior scientific knowledge, including physical laws and mathematical constraints [2,3,7]. Such approaches can be useful when observations are limited or when the physical consistency of predictions is important. However, the choice of how prior knowledge is incorporated remains problem-dependent, and the stability and generalization of the resulting models require further investigation.

Neuro-symbolic research addresses the integration of learned representations with explicit logical or knowledge-based reasoning [8,9,10]. Important unresolved issues include consistency between neural and symbolic components, the representation of uncertainty, and suitable criteria for evaluating the resulting hybrid systems. Similarly, advances in explainable artificial intelligence provide methods for analyzing individual predictions and feature contributions [11], but post hoc explanations do not necessarily establish that a model is interpretable or reliable. In some applications, intrinsically interpretable alternatives may be preferable [12]. Trustworthiness should therefore be assessed using distinct, application-relevant properties rather than a single performance metric [13].

Reliable deployment also depends on prediction calibration, uncertainty estimation, and performance under distribution shifts [14,15,16]. Improvements in accuracy on selected datasets do not establish equivalent performance under different operating conditions. These considerations indicate that progress in ANN applications requires both methodological innovation and more systematic evaluation of model limitations.

3. Contribution of the Special Issue

The Special Issue comprises 17 research articles published in Applied Sciences in 2025 and 2026. Their topics include scientific computing, engineering modeling and optimization, environmental and energy applications, computer vision, information processing, and security. The contributions are heterogeneous in objective and methodology; consequently, their findings are better considered as examples of problem-specific advances than as directly comparable results.

Three studies illustrate approaches particularly relevant to the original objectives of the Special Issue. Hmida et al. [17] developed a compositional neural operator framework for parametrized partial differential equations, incorporating the structure of differential operators and explicit treatment of boundary conditions. Tzotzis et al. [18] combined experimental data with adaptive neuro-fuzzy modeling and multi-objective optimization to investigate the machining of additively manufactured composites. Szymanik et al. [19] integrated numerical simulations, microwave thermography, and neural network-based analysis for the non-destructive detection of steel reinforcement in concrete, including experimental evaluation of the proposed methodology.

Other studies in the Special Issue address neural architecture design, computational efficiency, forecasting, synthetic data generation, measurement, and specialized information systems. Taken together, the contributions show how ANN methodologies can be adapted to particular scientific and engineering requirements and combined with established numerical or experimental procedures. They primarily address methodological and application-specific advances; comprehensive neuro-symbolic integration, general interpretability, and systematic reliability assessment remain less extensively covered and therefore warrant further study.

4. Future Research Directions

4.1. Integration with Scientific Knowledge

Future research should examine how physical laws, conservation principles, and mathematical constraints can be incorporated into ANN models in a systematic and verifiable manner. It is important to distinguish training with simulation-generated data from adding physics-based penalty terms or explicitly enforcing mathematical constraints, since these approaches provide different guarantees. Evaluations should address accuracy, stability, computational cost, and generalization when physical parameters, spatial resolution, or boundary conditions change. For hybrid numerical–neural procedures, comparisons with established solvers should account for the complete computational cost and the errors introduced by neural approximations.

4.2. Neuro-Symbolic Integration

Combining neural learning with explicit rules and knowledge representations may be useful for problems requiring both adaptation to data and structured reasoning. Methodological work should focus on consistent knowledge representation, mechanisms for enforcing or checking logical constraints, and the treatment of uncertainty or conflicting information. Evaluation should include logical consistency, validity of the inferred relationships, computational requirements, and the demonstrable benefit of hybrid models relative to their neural-only and symbolic-only counterparts. Neuro-fuzzy systems provide one class of hybrid methods but do not by themselves resolve the more general problem of neuro-symbolic integration.

4.3. Interpretability, Uncertainty, and Reliability

Interpretability and reliability should be evaluated independently of predictive accuracy. The appropriate explanation method depends on the application, and future studies should investigate whether reported explanations remain stable under plausible changes in inputs or model parameters. Uncertainty estimates should account, where feasible, for measurement noise, limited training data, and model assumptions. Methods such as conformal prediction provide useful statistical tools under stated assumptions [20], but these assumptions and their validity under distribution shifts must be examined. For scientific and engineering decisions, clear distinctions are needed between an explanation of model behavior, physical plausibility, and evidence of dependable operation.

4.4. Generalization, Validation, and Reproducibility

Models should be tested on independent data and, where possible, under conditions different from those used during development. Relevant variations include geometry, material properties, environmental conditions, instrument characteristics, and boundary conditions. Evaluation protocols should report reference methods, data separation, model selection, computational requirements, and sensitivity analyses. In particular, data leakage can lead to substantially overestimated performance [21]. Reproducibility and the maintenance of data dependencies are also important when models are incorporated into operational systems [22]. These requirements should be addressed as part of experimental design rather than treated as secondary reporting details.

4.5. Computational Efficiency and Implementation

Future ANN development should assess computational efficiency alongside accuracy and robustness. Quantization, compact architectures, efficient training, and surrogate modeling may reduce resource requirements, although their benefits depend on the full workflow, including training, inference, validation, and updating. The computational and environmental costs of machine learning have been emphasized in previous research [23,24]. For simulation-driven optimization, further research should address the integration of ANN-based surrogate models with numerical solvers and multi-fidelity modeling strategies to reduce the number of computationally expensive evaluations. Particular attention should be given to the influence of surrogate approximation errors on the accuracy and robustness of optimized solutions, as well as on the overall computational cost. For engineering applications, practical evaluations should further consider compatibility with existing numerical models, measurements, and decision-support procedures rather than model performance in isolation.

5. Conclusions

The 17 articles in the Special Issue “Innovations in Artificial Neural Network Applications” report methodological developments and applications of ANN-based approaches across a broad range of scientific and engineering problems. Selected contributions demonstrate the value of integrating artificial neural models with mathematical structures, experimental investigations, and numerical simulations. These results support the continued development of application-specific neural methodologies but do not eliminate the wider challenges associated with their general use.

Further progress should emphasize the incorporation of scientific and symbolic knowledge, transparent modeling, uncertainty assessment, independent validation, reproducibility, and computational efficiency. Addressing these issues is important in extending ANN applications to more demanding scientific and engineering tasks.

The Guest Editors thank the authors for their contributions, the reviewers for their careful evaluations and constructive comments, and the editorial staff of Applied Sciences for their support throughout the publication process.