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We develop a method to describe the temporal evolution of an interactingsystem of bosons, for which the field operator expansion is truncated after afinite number $M$ of modes, in a rigorously controlled manner. UsingMcLachlan's principle of least error, we find a self-consistent set ofequations for the many-body state. As a particular benefit, and in distinctionto previously proposed approaches, the presently introduced method facilitatesthe dynamical increase of the number of orbitals during the temporal evolution,due to the fact that we can rigorously monitor the error made by increasing thetruncation dimension $M$. The additional orbitals, determined by the conditionof least error of the truncated evolution relative to the exact one, areobtained from an initial trial state by steepest $constrained$ descent.

Truncated many-body dynamics of interacting bosons: A variational principle with error monitoring