Many natural processes are described by differential equations, but scientists often have only fragmentary data — a sort of torn map. The new computational method works like a cartographer who reconstructs a complete map of the terrain from a few landmarks. Known physical laws provide a reliable Standard Model framework (for instance, the Standard Model of particle physics) like a coastline on a map, while the neural network fills in the hidden dynamics by analyzing incoming experimental data. The algorithm operates iteratively: in each cycle, it first reconstructs the full history of the system using the current approximation, then corrects the unknown parts of the model by minimizing the discrepancy with observations. This procedure resembles how astronomers map invisible dark matter, a hypothetical form of matter that does not participate in electromagnetic interactions, in galaxies by its gravitational influence on visible matter.

Experimental tests have shown that the method can accurately predict system behavior even when only 5% of all significant factors are observable in the data. The key difference from 'black box' models is that it preserves physical interpretability: each reconstructed component has meaning in terms of the original laws, which is critical for building reliable predictive models in fields such as medicine and ecology.