The development of artificial intelligence (AI) and machine learning (ML) methods over recent decades has had a significant impact on biology and medicine. Traditional mathematical models based on systems of differential equations, stochastic processes, and network structures make it possible to describe and explain fundamental mechanisms of living systems. However, the high complexity of biological processes, the multiscale nature of data, and the large number of uncertain parameters often limit the accuracy and applicability of classical models. AI methods, particularly deep learning, complement and extend mathematical modeling by providing new approaches to data analysis, prediction, and interpretation [1,2].

One of the key directions is the integration of AI with mechanistic models. For example, in modeling the spread of viral and bacterial infections, classical models such as SIR allow the study of infection dynamics at the population level. However, model parameters (infection rate, disease duration, immune interactions) can vary significantly across patients and conditions. The use of AI for automatic parameter identification from observational data (e.g., clinical measurements or experimental time series) enables model personalization and improves predictive accuracy [3]. This approach is particularly important for pandemic analysis and forecasting the effectiveness of infection control measures.

A major area of AI application is the analysis of large-scale biomedical data, including genome sequencing, transcriptomic profiles, proteomic maps, and metabolomic networks. For instance, deep neural networks are successfully used to classify cell types based on single-cell RNA sequencing data and to identify previously unknown cellular states [4]. Combined with mathematical models of regulatory networks, this helps reconstruct mechanisms of cell differentiation, tissue development, and disease progression, such as cancer.

In medicine, AI methods are widely used for diagnostics and medical image analysis. Deep convolutional neural networks can automatically recognize pathological structures in X-ray images, MRI, and CT scans, significantly reducing physicians’ workload and the likelihood of errors [5]. However, integrating these methods with dynamic mathematical models makes it possible to move from static diagnosis to predictive modeling. For example, modeling tumor growth while accounting for intercellular interactions and immune response allows prediction of disease progression and optimization of therapy. In this context, AI is used to estimate model parameters, such as cell proliferation rates or metastasis probabilities, based on clinical and diagnostic data [6].

Of particular interest is the application of AI to drug development and optimization. Machine learning methods are used to predict molecular activity, assess toxicity, and model interactions with cellular targets [7]. Combined with mathematical models of pharmacokinetics and pharmacodynamics, these approaches enable virtual experiments to determine optimal dosages and administration regimens, substantially reducing the cost and duration of preclinical studies.

Despite significant progress, the integration of AI and mathematical modeling faces several challenges. First, deep neural networks often act as “black boxes,” making result interpretation difficult and reducing trust in predictions. Therefore, explainable AI methods are actively being developed to identify key factors driving model behavior [8]. Second, successful AI applications require large volumes of reliable and standardized data. In biomedicine, data acquisition is constrained by ethical considerations, high experimental costs, and patient data confidentiality. Finally, an important unresolved challenge is the unification of empirical AI models and mechanistic mathematical models into a single computational framework that ensures both predictive accuracy and scientific interpretability.

Additional successful examples of integrating AI and mathematical modeling come from studies of blood coagulation and thrombosis. In [9], a model of thrombin generation under blood flow conditions was developed to determine threshold concentrations of coagulation factors required to initiate the coagulation cascade. This model is based on transport equations and chemical kinetics describing the delicate balance between procoagulant and anticoagulant mechanisms. The application of AI in this context enables adaptation of the model to individual patient physiological parameters extracted from clinical data. This makes it possible to use such models to predict thrombosis risk and assess the effectiveness of personalized therapeutic strategies.

Another example concerns the development of methods for predicting thromboembolic complications in patients with COVID-19. In [10], it is shown that combining computational coagulation models with machine learning algorithms allows identification of patient subgroups at high risk of thrombosis. The mathematical model describes thrombus formation dynamics, while AI analyzes clinical indicators, laboratory data, and inflammation parameters. In [11], this idea is further developed: deep neural networks are used to predict an individual patient’s response to anticoagulant therapy under venous flow conditions. The model not only achieves high predictive accuracy but also enables interpretation of the contribution of individual biological parameters, making the solution transparent and clinically meaningful. These approaches demonstrate how the joint use of AI and mechanistic models leads to the emergence of next-generation personalized medicine.

Thus, artificial intelligence does not replace mathematical modeling but expands its capabilities. The combination of mechanistic descriptions of biological processes with advanced data analysis opens the way to personalized medicine, the development of new diagnostic, therapeutic, and preventive methods. The future of biological and medical modeling is closely linked to the continued development of AI, interdisciplinary research, and the creation of new approaches for analyzing complex living systems.

 

[1] Jordan M.I., Mitchell T.M. Machine learning: Trends, perspectives, and prospects. Science, 2015.
[2] LeCun Y., Bengio Y., Hinton G. Deep learning. Nature, 2015.
[3] Bertozzi A.L. et al. The challenges of modeling and forecasting the spread of COVID-19. PNAS, 2020.
[4] Stuart T. et al. Comprehensive Integration of Single-Cell Data. Cell, 2019.
[5] Litjens G. et al. A survey on deep learning in medical image analysis. Medical Image Analysis, 2017.
[6] Altrock P.M., Liu L., Michor F. The mathematics of cancer. Nature Reviews Cancer, 2015.
[7] Vamathevan J. et al. Applications of machine learning in drug discovery. Nature Reviews Drug Discovery, 2019.
[8] Samek W., Müller K.-R. Explainable Artificial Intelligence. Springer, 2019.
[9] A Bouchnita, K Yadav, JP Llored, A Gurovich, V Volpert. Thrombin generation thresholds for coagulation initiation under flow. Axioms 12 (9), 873, 2023.
[10] A Bouchnita, A Mozokhina, P Nony, JP Llored, V Volpert. Combining computational modelling and machine learning to identify COVID-19 patients with a high thromboembolism risk. Mathematics 11 (2), 289, 2023.
[11] A Bouchnita, P Nony, JP Llored, V Volpert. Combining mathematical modeling and deep learning to make rapid and explainable predictions of the patient-specific response to anticoagulant therapy under venous flow. Mathematical Biosciences 349, 108830, 2022.