Mechanistic understanding of the brain requires models constrained by anatomy, physiology, and functional activity. We present a differentiable simulator and a ∼67,000-neuron model of mouse primary visual cortex that integrates multimodal data, including electron-microscopy connectomics, multipatch synaptic physiology, cell-type-resolved electrophysiology, and large-scale Neuropixels recordings across diverse cell types. End-to-end training completes on a single GPU in ∼10 hours while preserving biological constraints. Networks trained only on brief drifting-grating responses reproduce cell-type-specific benchmarks and generalize to new contrasts and natural scenes. We uncover heterogeneous cell-type- and tuning-dependent synaptic organization and show that training preferentially sculpts inhibitory connectivity into distinct cohorts with strong causal influence on network activity. Targeted ablations show that removing biological priors on synaptic weight distributions can preserve functional activity yet disrupts emergent wiring rules. Our freely shared models and code facilitate differentiable simulations as a computationally practical framework for studying brain circuit function and mechanisms under biological constraints.