## 6 Conclusions  
There are two common ways of coupling FPM and ML. In one case, data are transferred from the ML algorithm to the FPM; in the other, from the FPM to the ML algorithm. In both cases, the coupling is in series: the two components remain distinct, and data generated by one model are subsequently fed into the other. This study introduces deep multiphysics; a computational framework that couples FPM and ML in parallel rather than in series. Deep multiphysics is based upon the concept of particle-neuron duality and only works with a particle-based FPM (discrete multiphysics) and a specific ML algorithm (ANNs) and, as a case study, it is applied here to the design of a microfluidic device for separating cell populations with different levels of stiffness.  
A computational framework that couples FPM and ML in parallel can lead to computational methods that are well-grounded on the physics/chemistry/biology of the system under investigation but, at the same time, have the ability to 'learn' and 'adapt' during the simulation. In [PERSON] [5], a similar idea was applied to in-silico modelling of human physiology: DMP provided the physics of the system, while AI learned to replicate the regulatory intervention of the autonomic nervous system. This study generalizes that study by clearly defining the deep multiphysics framework and the particle-neuron duality.  
This framework can lead to new ways of coupling first-principle modelling with AI. An idea, for instance, could be fluid neural networks: ANNs that are not organized within a fixed layered structure, but, similar to a fluid, change their local structure and connectivity with time. Additionally, the particle-neuron duality could also find application in swarm-intelligence, where agents, akin to  
Figure 12: The final deep multiphysics model in action (**a**): rigid cell; (**b**): soft cell.  
Figure 13: (**a**): soft cell; (**b**): rigid cell in case 3.  
particle-neuron hybrids, interact with each other following rules determined by (i) the (multi)physics of the environment and (ii) the information they exchange with each other.  
Besides the applications mentioned above, there is an aspect of deep multiphysics that has deep theoretical implications. As discussed above, DMP combines particle methods such as SPH, LSM or DEM. The particle-neuron duality shows that, if we look at physical interactions as a form of information exchanged between particles, the mathematics behind these particle-methods and ANNs can be unified under the same computational paradigm. Within this paradigm, particle-based FPM (such SPH, LSM or DEM) and ANN-based ML algorithms are just two faces of the same coin: the AI algorithm does not need to be linked to the physical model anymore because the AI algorithm and the physical model are the same algorithm. One of the main conclusions of this work, therefore, is that, thanks to the particle-neuron duality, the coupling between ANNs and particle methods is more promising than the coupling of ANNs with mesh-based models. This study only scratches the surface of the possible implications of deep multiphysics, but, considering the recent upsurge of research activity dedicated to the coupling of FPM with ML, I believe it can have a far-reaching impact in the field.  
The following are available online at [[http://www.mdpi.com/2076-3417/9/24/5369/s1](http://www.mdpi.com/2076-3417/9/24/5369/s1)]([http://www.mdpi.com/2076-3417/9/24/5369/s1](http://www.mdpi.com/2076-3417/9/24/5369/s1)), video 1: rigid_cell.avi, video 2: soft_cell.avi.  
This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) grant number: EP/S019227/1.  
The author declares no conflict of interest.