Alexandre Muzy

Alexandre Muzy

Brain digital twins aim to provide faithful, individualized computational representations of brains as dynamical systems, enabling mechanistic understanding and supporting prediction of clinical interventions. Yet current approaches remain fragmented across data pipelines, model classes, temporal scales, and computing platforms, which prevents the preservation of execution semantics across the end-toend workflow. This survey introduces physically constrained executability as a unifying perspective for comparing approaches at the level of execution: whether an execution state is persistent, which events are permitted to update it (simulation, measurement, actuation), and how strongly execution is temporally and causally coupled to neurobiological dynamics. Building on modeling and simulation theory, I propose a taxonomy of execution regimes ranging from isolated offline models to coordinated co-simulation, to continuously executing digital twins sustained by online data assimilation, and ultimately to neuro-neuromorphic physical systems in which biological and computational dynamics are co-executed under shared physical constraints. The executability concept clarifies why accuracy alone is insufficient, and motivates an agenda centered on semantic interoperability, hybrid-time correctness, evaluation protocols, scalable reproducible workflows, and safe closed-loop validation. This survey adopts a systems and runtime-oriented perspective, enabling comparison of heterogeneous approaches based on their execution semantics rather than on model form or application domain alone.

Alexandre Muzy

Cyber-Physical Systems (CPS) produce behavior through execution on substrates coupling computation with physical processes. However, usual engineering approaches do not treat execution semantics as first-class engineering entities. Formal verification reasons about model behaviors under fixed semantic assumptions that are not revisable and do not account for physical execution constraints. Simulation-based validation explores scenarios under execution semantics that are implicitly determined by the simulation engine. In both cases, physical constraints of the execution substrate are addressed as implementation details rather than as semantic boundary conditions. In this article, it is hypothesized that making execution semantics explicit as first-class engineering entities is necessary and sufficient to bridge the gap between verified model behaviors and validated executed behaviors in CPS. To test this hypothesis, Modeling and Simulation Based Engineering (MSBE) is proposed: a methodology grounded in the Theory of Modeling and Simulation. MSBE formalizes execution conditions as four components: execution semantics, activity (behaviorally meaningful changes), admissibility constraints (physical bounds), and specified properties (behavioral guarantees). MSBE organizes engineering around an iterative cycle alternating formal execution, experimental execution, verification, and activity-mediated validation. Executability is defined as stabilization of execution conditions and the induced admissible model space. The cycle is applied to four CPS classes (human-centric, biophysical, technological, and digital twins). These applications show that the framework generalizes beyond CPS to any system whose behavior depends on explicitly defined execution conditions. Modeling and Simulation-Based Engineering

Alban Gattepaille, Alexandre Muzy

In Deep Neural Networks (DNN) and Spiking Neural Networks (SNN), the information of a neuron is computed based on the sum of the amplitudes (weights) of the electrical potentials received in input from other neurons. We propose here a new class of neural networks, namely Delay Neural Networks (DeNN), where the information of a neuron is computed based on the sum of its input synaptic delays and on the spike times of the electrical potentials received from other neurons. This way, DeNN are designed to explicitly use exact continuous temporal information of spikes in both forward and backward passes, without approximation. (Deep) DeNN are applied here to images and event-based (audio and visual) data sets. Good performances are obtained, especially for datasets where temporal information is important, with much less parameters and less energy than other models.

Tien Cuong Phi, Alexandre Muzy, Patricia Reynaud-Bouret

Event-scheduling algorithms can compute in continuous time the next occurrence of points (as events) of a counting process based on their current conditional intensity. In particular event-scheduling algorithms can be adapted to perform the simulation of finite neuronal networks activity. These algorithms are based on Ogata's thinning strategy \cite{Oga81}, which always needs to simulate the whole network to access the behaviour of one particular neuron of the network. On the other hand, for discrete time models, theoretical algorithms based on Kalikow decomposition can pick at random influencing neurons and perform a perfect simulation (meaning without approximations) of the behaviour of one given neuron embedded in an infinite network, at every time step. These algorithms are currently not computationally tractable in continuous time. To solve this problem, an event-scheduling algorithm with Kalikow decomposition is proposed here for the sequential simulation of point processes neuronal models satisfying this decomposition. This new algorithm is applied to infinite neuronal networks whose finite time simulation is a prerequisite to realistic brain modeling.