Inverse Modeling of Neural Recordings via Differentiable Biophysical Simulation

Inferring the latent processes that generate observable neural activity is a central challenge in neuroscience, with direct implications for brain-machine interfaces and neural engineering. Existing inverse approaches typically summarize the recording into low-dimensional features or learn black-box latents that lack a direct biophysical interpretation. A promising alternative is to fit a differentiable biophysical simulator end-to-end against the full extracellular signal, using direct and scalable gradient optimization. In practice, however, recovering a per-neuron input via backpropagation through neuronal dynamics is difficult because the loss landscape is nearly flat in the subthreshold regime and jumps sharply at spike threshold, leaving gradient descent without a useful signal. We observe that per-neuron spike times, routinely available from spike sorting, expose discrete millisecond-scale anchors at which the loss does carry information. Gradients from these anchors flow back in time through the differentiable simulator and shape the subthreshold drive that produced each spike. Building on this, we present a fully differentiable pipeline coupling biophysical membrane dynamics to a volume conductor model of the multi-electrode array. For each neuron in a recorded population, the method jointly recovers a time-varying latent input current and a probe-relative position consistent with both the extracellular trace and the observed spike times. No explicit likelihood or posterior estimation is required, and every fitted latent corresponds to a named biophysical quantity. On paired patch-clamp / Neuropixels SPE-1 data, the model localizes the patched neuron to within $40 \mu m$ on average across cells, while reproducing observed spatio-temporal activity patterns under realistic noise. These results position scalable differentiable biophysical simulation as a practical route to mechanistic, gradient-based analysis of high-density neural recordings.