**6. Conclusions**

The adaptive interpolation algorithm allows simulating dynamic systems with interval parameters. In the course of the algorithm operation, a regular grid is constructed in the parameter space. The number of grid nodes depends exponentially on the number of interval parameters, which limits the scope of the algorithm. A typical situation is when the degree of influence of different parameters and their combinations on the solution can differ significantly. This can be used in adaptive interpolation. The paper presents an adaptive interpolation algorithm on sparse grids, which allows for reducing the exponential complexity when solving multidimensional problems in parameter space. The efficiency of the proposed approach has been demonstrated on representative interval problems of nonlinear dynamics and computational materials science. It is shown that, for most variants, adaptive sparse grids are more efficient than the classical adaptive interpolation algorithm in terms of computational costs. With the suggested method, it was possible to solve problems with up to 10 interval parameters in a reasonable amount of time. At the same time, the classical algorithm of adaptive interpolation failed to do so. Taking into account that an increase in the degree of the interpolation polynomial in the classical adaptive interpolation algorithm leads to higher accuracy and lower computational costs, we can outline the use of sparse grids with a nonlinear basis as a direction for further research.

**Author Contributions:** Methodology, software, investigation, A.Y.M.; investigation, software, validation, A.A.Z.; conceptualization, methodology, supervision, D.L.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the Ministry of Science and Higher Education of the Russian Federation, project No 075-15-2020-799.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sharing not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

