Research Article
Neural Network Axiomatic Solver Coaching AGI Method for Solving Scientific and Practical Problems
Evgeny Bryndin*
Issue:
Volume 10, Issue 4, December 2025
Pages:
110-120
Received:
2 September 2025
Accepted:
13 September 2025
Published:
9 October 2025
Abstract: Modern neural network methods combine work with an axiomatic mathematical description (laws, equations, invariants, logical rules) and the power of neural networks for learning from data, pattern recognition and differentiation through complex spaces. This combination produces systems that can learn from data, observe given laws and, as a result, make predictions, solve problems and even discover new hypotheses. Quality depends on the formulation of axioms and the presence of correct formulations, the complexity of scaling to very large axiomatic bases, trade-offs between the accuracy of fitting to data and compliance with laws, interpretation and verification of results. Modern neural network methods with an axiomatic mathematical description have better generalization and physical interpretability due to compliance with axioms, the ability to work with small data due to built-in laws and the ability to discover new dependencies within the framework of formalized rules. Theoretical principles and formal axioms set requirements for neural networks and their training so that solutions to scientific problems correspond to the laws of nature, invariances, data characteristics and other desired properties. Power: an axiomatic neural network tends to be accurately modeled given its sufficient complexity and large scientific data and knowledge. The author proposes a neural network axiomatic solver coaching AGI method for solving scientific and practical problems according to their formulations and developed systems of axioms.
Abstract: Modern neural network methods combine work with an axiomatic mathematical description (laws, equations, invariants, logical rules) and the power of neural networks for learning from data, pattern recognition and differentiation through complex spaces. This combination produces systems that can learn from data, observe given laws and, as a result, m...
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Research Article
Modeling Pulmonary Tuberculosis-Pneumonia Co-dynamics Incorporating Drug Resistance with Optimal Control
Issue:
Volume 10, Issue 4, December 2025
Pages:
121-144
Received:
9 August 2025
Accepted:
21 August 2025
Published:
14 October 2025
DOI:
10.11648/j.ajmcm.20251004.12
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Abstract: In this paper, a deterministic mathematical model illustrating the transmission dynamics of pulmonary tuberculosis and pneumonia co-infection is formulated, incorporating a drug-resistant strain. The model employs a Holling-type functional response to capture the impact of natural immunity on the progression from latent tuberculosis infection to active disease, as well as its role in controlling drug-resistant pulmonary tuberculosis-pneumonia co-infections. The model is extended to include optimal control theory, aimed at identifying strategies to minimize co-infections using prevention, screening of latently infected individuals, and treatment as control variables. Pontryagin’s Maximum Principle is applied to characterize the optimal control system. The resulting optimality system is then solved numerically using the Runge-Kutta-based forward-backward sweep method. Numerical simulations demonstrate that enhancing natural immunity among latently infected individuals significantly reduces the number of co-infected cases. The optimal control analysis indicates that the most effective strategy for controlling or reducing co-infections of drug-resistant tuberculosis and pneumonia is the combined optimization of infection prevention and screening of latently infected individuals. These findings underscore the importance of scaling up preventive measures against pulmonary tuberculosis and opportunistic pneumonia, alongside screening efforts, to effectively control co-infections. Additionally, the study recommends strengthening immunity among latently infected populations to further reduce the prevalence of co-infections.
Abstract: In this paper, a deterministic mathematical model illustrating the transmission dynamics of pulmonary tuberculosis and pneumonia co-infection is formulated, incorporating a drug-resistant strain. The model employs a Holling-type functional response to capture the impact of natural immunity on the progression from latent tuberculosis infection to ac...
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