Building a working brain model has a scaffolding problem. There are three types of data available: structural data from connectomics (which neurons are wired to which, with what geometry), electrophysiological data from single-cell recordings (how individual neurons respond to input), and functional data from population recordings (how groups of neurons behave during behavior or stimulus presentation). Each data type provides partial constraints on what the circuit is doing. None alone is sufficient to build a model that accurately reproduces all three.

The usual approach has been to optimize against one data type at a time: fit a model to match connectivity, or to match single-cell responses, or to match population dynamics. The resulting models match their training target reasonably well and tend to fail on the others. A connectivity-accurate model may fire incorrectly. A dynamically accurate model may have the wrong wiring.

A preprint posted to bioRxiv on March 13, 2026 introduces a different approach. The team built a differentiable simulator — a neural circuit simulator in which all parameters are differentiable with respect to a loss function — and trained it simultaneously against structural constraints from electron microscopy, electrophysiological constraints from multipatch recordings, and functional constraints from Neuropixels population recordings. The circuit modeled is the mouse visual cortex, with approximately 67,000 neurons. Training completes on a single GPU in roughly ten hours.

The Three-Constraint Problem

To understand what this work achieves, it is useful to describe what previous models could not do.

The Allen Institute mouse cortex simulation modeled 9 million neurons — two orders of magnitude more than the new model — but was built from reconstructed connectivity data and electrophysiological parameterization separately, without joint optimization. The functional outputs of the model were validated against population recording data after the fact, not used to constrain the model during training. This is the standard approach, and it works well for reproducing gross statistics of population dynamics, but it does not guarantee that the model’s detailed firing patterns or circuit-level computations match biological recordings at fine resolution.

The Eon Systems fruit fly brain simulation used the full Drosophila connectome as structural scaffolding and then tuned parameters to achieve behavior. Again, the structural and functional constraints were treated sequentially rather than jointly.

Joint optimization — simultaneously satisfying structural, cellular, and functional constraints — is harder because the three data types often conflict. A structural constraint that says “neuron A connects to neuron B with 15 synapses” may be difficult to reconcile with a functional constraint that says “the population containing neuron A should exhibit a specific firing rate pattern in response to stimulus X.” The parameters that satisfy one constraint may violate the other. A differentiable simulator resolves this by computing gradients of the total loss across all three constraint types simultaneously, allowing the optimizer to find parameters that represent the best joint compromise.

Architecture of the Differentiable Simulator

The simulator represents each neuron as a conductance-based compartmental model. The dendritic morphology of each neuron is simplified relative to full biophysical reconstruction — a full multi-compartment model for 67,000 neurons would be computationally intractable — but the simplification preserves the key electrophysiological properties that determine how each neuron integrates synaptic input and generates spikes.

Synaptic connections are specified by the EM connectomics data, which provides the number of synapses between each connected pair of neurons. The synaptic weight for each connection — the amplitude of the postsynaptic conductance change per presynaptic spike — is a learnable parameter. The structural constraint specifies which connections exist; the functional and electrophysiological constraints determine the appropriate weight values.

The training loss has three terms. The first term penalizes deviation from multipatch electrophysiology data: recordings from pairs or small groups of neurons stimulated in controlled conditions, measuring how one neuron’s activity influences another. This constrains the individual synaptic weight values. The second term penalizes deviation from Neuropixels population recordings: the firing rate statistics, cross-correlations, and stimulus-response curves of the population during visual stimulus presentation. This constrains the collective dynamics. The third term penalizes violations of connectivity structure derived from the EM data.

Differentiating through all three terms simultaneously and computing gradients with respect to all learnable parameters (synaptic weights, cellular parameters, and connectivity scaling factors) produces a single optimization that finds parameters satisfying all constraints as well as the model’s expressivity allows.

Why Single-GPU Tractability Matters

Previous large-scale cortical simulations have required supercomputing infrastructure. The Allen Institute simulation ran on the Fugaku supercomputer, one of the world’s largest. The computational cost of simulating biophysically realistic neurons at scale has been a fundamental bottleneck: more neurons, more synapses, more biological detail all increase compute requirements.

The March 2026 model achieves single-GPU tractability through two design choices. First, the neuron model is simplified relative to full biophysical detail but calibrated against electrophysiological data to preserve the functionally relevant dynamics. Second, the differentiable simulator is implemented in a framework that allows efficient automatic differentiation — the same infrastructure underlying large-scale deep learning training — rather than requiring custom numerical simulation code.

The practical implication is significant. A model that requires Fugaku for training is, practically speaking, a model that can be iterated on by a small number of teams with supercomputing access. A model that trains on a single GPU in ten hours can be iterated on by any computational neuroscience laboratory. This changes the pace of scientific development: hypotheses can be tested, parameters adjusted, and new constraint datasets incorporated on a weekly rather than quarterly basis.

What the Model Reproduces

The validation in the preprint includes several benchmarks. The model reproduces the firing rate statistics of distinct cell types in the mouse visual cortex: excitatory pyramidal neurons fire at rates consistent with in vivo recordings, while fast-spiking parvalbumin-positive interneurons and slower-spiking somatostatin-positive interneurons fire at rates consistent with their respective in vivo profiles.

At the population level, the model reproduces the orientation selectivity curves of visual cortex neurons — the tuning of individual neurons to specific angles of visual edges — with accuracy comparable to the best previous models fit exclusively to functional data, despite also satisfying the structural and electrophysiological constraints.

The joint-constraint model specifically outperforms connectivity-only or dynamics-only models on the held-out test: when validated against Neuropixels recordings from sessions not included in training, the jointly optimized model produces smaller prediction errors than models fit to a single data type.

Scale Gap to Human Brain Emulation

The mouse visual cortex contains roughly 2 million neurons. The full mouse brain contains approximately 70 million. The human brain contains 86 billion. The 67,000-neuron model represents about 3% of the mouse visual cortex alone.

Scale is not the only challenge. The mouse visual cortex is among the most studied and well-characterized neural circuits in mammalian neuroscience. The EM connectome data, the Neuropixels datasets, and the multipatch physiology used in this work exist because the community has invested heavily in this particular system. Similar multi-constraint datasets do not exist for most other brain regions, and do not yet exist at any scale for human tissue.

The LICONN light microscopy advance and connectome-seq may reduce the cost of generating structural connectivity data for other regions and species. But the electrophysiology and functional recording data that provide the other two constraint types in the March 2026 model are themselves expensive to collect and do not scale trivially to whole-brain volumes.

The path from a 67,000-neuron model of mouse visual cortex to a whole-brain human model requires several independent advances: more complete structural data, large-scale electrophysiology across brain regions, functional recording datasets with matching resolution, and computational infrastructure to run models at three to four orders of magnitude greater scale. None of these is impossible in principle, but each represents years of work.

Relationship to Emulation Feasibility

The March 2026 model is directly relevant to the requirements framework for building brains on a computer: the three non-negotiable capabilities identified there are structural fidelity, functional replication, and dynamic adaptability. The differentiable simulator approach is specifically designed to achieve the first two jointly rather than sequentially. Dynamic adaptability, the capacity to update the model as the biological circuit changes over time, is not addressed in this work but is a clear extension for future versions.

The cross-species connectome transfer work demonstrated behavioral control from connectivity data transferred between species. That work operated with simpler connectivity models. A multi-constraint model like the March 2026 approach, if extended to the target species, would provide a higher-fidelity functional substrate for such transfers.

For the whole brain emulation timeline, the most important implication of this work is methodological. It demonstrates that the joint-constraint optimization approach is feasible at the ~10K–100K neuron scale. Whether it generalizes to the million-neuron scale within the next five years will depend on how efficiently the method can be parallelized and whether the training data bottleneck (collecting multi-constraint datasets for each target region) can be addressed by complementary advances in data collection.

TRL Assessment: TRL 3–4. The method is demonstrated and validated in a specific well-characterized circuit. Generalization to other brain regions and to human tissue requires further work.

Official Sources

• bioRxiv (March 13, 2026) — Differentiable simulation of biologically constrained cortical circuits. DOI: 10.64898/2026.03.13.711751. https://www.biorxiv.org/content/10.64898/2026.03.13.711751v1.full
• MICrONS Consortium (2021) — Functional connectomics spanning multiple areas of mouse visual cortex. bioRxiv. DOI: 10.1101/2021.07.28.454025
• Markram, H. et al. (2015) — Reconstruction and simulation of neocortical microcircuitry. Cell, 163(2):456–492. DOI: 10.1016/j.cell.2015.09.029
• Jun, J.J. et al. (2017) — Fully integrated silicon probes for high-density recording of neural activity. Nature, 551(7679):232–236. DOI: 10.1038/nature24636
• Turaga, S.C. et al. (2022) — Reverse engineering neural circuits with deep learning. Annual Review of Neuroscience, 45:25–44. DOI: 10.1146/annurev-neuro-110220-013937