Mathematical models in immunology, epidemiology and economy based on mass balance low are described by systems of nonlinear ordinary differential equations (ODE) or stochastic differential equations (SDE). Considered mathematical models are driven by a lot of parameters such as coefficients of ODE/SDE, initial conditions, source, etc., that play a key role in prediction properties of models. The most of parameters is unknown or can be rough estimated. The inverse problem consists in identification of parameters of mathematical models using additional measurements of some direct problem statements in fixed times. Considered inverse problems are ill-posed, i.e. its solutions could be non-unique and unstable to data errors. The identifiability analysis is used to construct the regularization method for solving of inverse problems.

      Inverse problems are formulated as minimization problems of loss function. To find the global minima of minimization problems the combination of machine learning (ML), heuristic and deterministic approaches are implemented. The ML methods such as artificial neural network, support vector machine, stochastic algorithms, etc., identify the global minima domain, could be easily paralleled and do not use the loss function features. Then the gradient deterministic methods identify the global minima in its area with guaranteed accuracy. On the other hand, the loss function can be represent as a multi-scale tensor to which the tensor train (TT) decomposition can be applied. TT method is easily paralleled and uses the structure of the loss function. The confidence intervals for control an accuracy of approximate inverse problem solution are constructed and analyzed. The numerical results for solving of inverse problems for mathematical models of immunology, epidemiology and economy are presented and discussed.