The steep price of high-resolution computation and the remoteness from high-level cognition can be levitated by replacing the detailed dynamics of single neurons with the collective equations of the population. This dimensionality-reduction strategy is the essence of the neural mass models ( David and Friston, 2003), spiking neural network ( Vreeken, 2003), and dynamical causal modeling ( Friston et al., 2003). 1.3.1. Neural Mass Models Hjorth, J. J. J. et al. The microcircuits of striatum in silico. Proc. Natl. Acad. Sci. U S A 117(17), 9554–9565. https://doi.org/10.1073/pnas.2000671117 (2020). In statistical physics, the mean-field approximation is a conventional way of lessening the dimensions of a many-body problem by averaging over the degrees of freedom. A well-known classic example is the problem of finding collective parameters (such as pressure or temperature) of a bulk of gas with known microscopic parameters (such as velocity or mass of the particles) by the Boltzmann distribution. The analogy of the classic gas shows the gist of the neural mass model: the temperature is an emergent phenomenon of the gas ensemble. Although higher temperatures correspond to higher average velocity of the particles, one needs a computational bridge to map microscopic parameters to the macroscopic one(s). To be clear, remember that each particle has many relevant attributes (e.g., velocity, mass, and the interaction force relative to other particles). Each attribute denotes one dimension in the phase space. One can immediately see how this problem can become computationally impossible even for 1 cm 3 of gas with ~10 19 molecules. An insightful interplay of function vs. structure is observed along the biologically plausible line of work by Deco and Jirsa (2012). They reconstructed the emergence of equilibrium states around multistable attractors and characteristic critical behavior like scaling-law distribution of inter-brain pair correlations as a function of global coupling parameters. Furthermore, new studies show that synchrony not only depends on the topology of the graph but also on its hysteresis ( Qian et al., 2020). Allen Brain Atlas: genome-wide map of gene expression for the human adult and mouse brain ( Jones et al., 2009).

Put simply: the goal of science is to leverage prior knowledge, not merely to forecast the future (a task well suited to engineering problems), but to answer “why,” questions, and to facilitate the discovery of mechanisms and principles of operation. Bzdok and Ioannidis (2019) discuss why inference should be prioritized over prediction for building a reproducible and expandable body of knowledge. We argue that this priority should be especially respected for clinical neuroscience. Acimovic, J., Mäki-Marttunen, T. & Linne, M. L. The effects of neuron morphology on graph theoretic measures of network connectivity: The analysis of a two-level statistical model. Fr. Neuroanat. 9, 76. https://doi.org/10.3389/fnana.2015.00076 (2015). Izhikevich, E. M. Resonate-and-fire neurons. Neural Netw. 14(6–7), 883–894. https://doi.org/10.1016/s0893-6080(01)00078-8 (2001). van Pelt, J. & van Ooyen, A. Estimating neuronal connectivity from axonal and dendritic density fields. Fr. Comput. Neurosci. 7, 160 (2013).A dynamic model such as the Neural ODE can be incorporated in an encoder-decoder framework, resembling a Variational Auto-Encoder, as mentioned in Chen et al. (2018). Such models assume that latent variables can capture the dynamics of the observed data. Previous works ( Chen et al., 2018; Kanaa et al., 2019; Rubanova et al., 2019; Yildiz et al., 2019) have successfully used this framework to define and train a generative model on time series data. 3.2.2.3. Stochastic Neural ODEs Reimann, M. W., King, J. G., Muller, E. B., Ramaswamy, S. & Markram, H. An algorithm to predict the connectome of neural microcircuits. Front Comput. Neurosci. 9, 120. https://doi.org/10.3389/fncom.2015.00120 (2015).

Casali, S., Marenzi, E., Medini, C., Casellato, C. & D’Angelo, E. Reconstruction and simulation of a scaffold model of the cerebellar network. Front Neuroinform. 13, 37. https://doi.org/10.3389/fninf.2019.00037 (2019). In the last decade, increasing attention has been devoted to elucidating the connectivity matrices of neuronal circuits (connectomics). The development of advanced imaging methods has allowed this issue to be approached experimentally 68, but a detailed description of the architecture of extended circuits is not yet possible. With the method proposed here, the resulting in-degree and out-degree distributions are consistent with those expected from theoretical and experimental analysis 20, 57. Notably, this result has been obtained without any constraints on the degree distributions, which would be required for the generation of connections through randomized processes. The independence from prior knowledge sounds interesting as it frees the methodology from inductive biases and makes the models more generalizable by definition. However, this virtue comes at the cost of a need for large training sets. In other words, the trade-off of bias and computation should be considered: Applying lots of prior knowledge and inductive biases result in a lesser need for data and computation. In contrast, little to no inductive bias calls for a great need for big and curated data. It is true that with the advancement of recording techniques, the scarcity of data is less of a problem than it was before, but even with all these advances, having clean and sufficiently large medical dataset that helps with the problem in hand is not guaranteed.

Like many biophysical systems, it is highly dissipative and functions in non-equilibrium regimes (at least while working as a living organ). The significance of phenomenological models in the reconstruction of brain dynamics is also because of their intuitiveness and reproducibility. They may demonstrate critical properties of the neuronal population. An interesting example is noise-driven dynamics of the brain, which is responsible for multistability and criticality during resting state ( Deco and Jirsa, 2012; Deco et al., 2017). 2.1. Problem Formulation, Data, and Tools Udvary, D. et al. The impact of neuron morphology on cortical network architecture. Cell Rep. 39, 110677. https://doi.org/10.1016/j.celrep.2022.110677 (2022). Sloviter, R. S. & Lømo, T. Updating the lamellar hypothesis of hippocampal organization. Fr. Neural Circuits 6, 102. https://doi.org/10.3389/fncir.2012.00102 (2012).