§3.17 现状与展望

Even nowadays, the cosmological simulations used as theoretical counterparts for very large surveys (like EUCLID, DESI, LSST), for which extremely large volumes need to be sampled, are based on pure gravitational physics (e.g., ^[10] ,^[14] ). These simulations are usually complemented by running semianalytic models (SAMs) of galaxy formation (e.g., ^[314] ). While SAMs provide a realistic description of the properties of galaxy populations, they bring at best indirect information on the properties of the ISM/IGM. In fact, they do not include a self-consistent treatment of gas dynamics and loosely capture the effects of baryons on structure formation, which is highly relevant for the study of environmental effects.

In the last decades, a growing number of different, large-scale, cosmological, hydro-dynamical simulations have been performed with varying resolutions and volumes covered (see initial Fig. 1 in section §3.1). One limitation of state-of-the-art cosmological simulations is that different sub-grid models often predict very similar results in direct observable properties, and the main differences among their outcome are often hidden in properties which are not directly or easily accessible (like the IGM/CGM of galaxies), and/or in the different evolution of them (see Fig. 14). This weakens the predictive power of individual simulations, and undermines the possibility to ascribe discrepancies among simulations to different numerical prescriptions adopted or to physical processes included. Comparing predictions from simulations with observations can help to constrain the theoretical modelling: however, evaluating differences fairly is not trivial. In fact, the comparison process often involves sophisticated techniques to create meaningfully mock observations (e.g., ^[315] ,^[211] ), and also has to cover multi-wavelength regimes and different components (e.g., stars, gas, dust, ...) simultaneously.

Several lines of refinement have been under development during the last years. They include, for instance, hyper-refinement in the innermost regions of simulated structures ^[316] ,^[317] ,^[318] , to increase the resolution in those regions which are crucial to better resolve to capture additional physics. Not only is higher resolution needed in the densest regions or around SMBHs, but it is fundamental also increase the spatial refinement within the virial radius, to capture CGM physics and evolution more accurately (e.g., ^[319] ). Also, a number of works have included a detailed modelling of sub-resolution accretion discs and BH spin modelling ^[305] ,^[320] ,^[321] ,^[322] ,^[291] , and have progressed in linking the accretion process onto SMBHs with the launch of AGN-triggered jets ^[323] . Furthermore, the modelling of SMBH outflows and jets has been enhanced ^[301] ,^[324] , and interests experiments involve the inclusion of spin-driven (Blandford-Znajek) AGN jets ^[325] ,^[326] . So far, these improvements have been validated mainly with dedicated and somehow ad-hoc setups, or included in cosmological simulations of smaller haloes or volumes. As the numerical advancement of the aforementioned improvements has been included in state-of-the-art codes, we expect that these new modules will be featured by upcoming large-volume simulations, and improve the accuracy of the numerical prediction in the near future.

While the predictive power of modern cosmological simulations is beyond discussion, still there are several caveats that cannot be overlooked. The majority of state-of-the-art cosmological simulations, for instance, assume that all haloes above a mass threshold host BHs, and adopt massive BH seeds to promote their early growth. Also, they commonly rely on Bondi accretion -- though with modifications -- to facilitate the initial growth of BHs and to make them easily reach the Eddington limit.

In addition, the implementation of feedback processes is still far from reaching an adequate degree of complexity, and it is often driven by numerical effectiveness. Besides, several feedback processes (e.g., early feedback, radiation from stars, stellar and AGN winds, radiation pressure on dust) which could hamper BH growth and reduce the SFR are often neglected. A number of relevant physics modules are still not included in the reference runs of the majority of cosmological simulations of large volumes, as their integration in the existing framework is not straightforward. As an example, it is worth mentioning: radiative transport, cosmic rays, magnetic fields, scenarios for DM alternative to the standard $\Lambda$CDM, chemical diffusion, just to name a few. The need for higher spatial resolution makes it difficult to consistently account for all the relevant physics.

Finally, it is worth recalling that we have now entered the era of high-performance computing, with always growing computational power available from current and future HPC facilities. It is therefore of paramount importance to have numerical codes which are not only as complete as possible as for the inclusion of physical processes implemented, but also very efficient from the computational point of view. Codes are indeed supposed to be able to smoothly scale on state-of-the-art exascale infrastructures, and to efficiently exploit CPUs (Central Processing Units) and GPUs (Graphics Processing Units).

The aforementioned efforts, together with the improvements in numerical methods, will allow us to study the formation process of cosmological structures with unprecedented detail, and to better link the small-scale physical processes of galaxy formation to the evolution of the large-scale structure and of the cosmic web.