The current manufacturing environment places a growing demand on autonomous control and optimization of manufacturing processes, especially for unattended machines. In grinding, operator surveillance is fundamental to cope with the strong process variability introduced by tool characteristics, machine dynamics and workpiece material. For example, progressive wheel wear decreases the quality of the machined workpiece, through different mechanisms: in cylindrical center grinding the phenomena are mainly ascribable to vibrations occurrence, while in centerless grinding the geometrical configuration plays a paramount role. In general, optimization strategies for grinding operations have been designed by many authors in literature. In their comprehensive review, Rowe et al. [1], show that most of them rely on Artificial Intelligence (AI). Among these techniques, two big families are identified: in the first one desktop systems assist tool and parameters selection, while in the second self-optimizing systems are integrated within the machine controller. AI methods often exploits black box models. In fact, black box machine learning models (typically neural networks) are currently being used for high-stakes decision making throughout many industrial sectors. This circumstance arises concerns on machine behavior predictability, from one side [2], and on the role of human experts on the other side. Creating methods for explainingthese black box models could alleviate some of the problems [3], but trying to explain black box models, rather than creating models that are interpretable in the first place, is likely to perpetuate bad practice and can potentially affect the further development of a mature technology like grinding. Additionally, is envisaged to exploit, together with pure black box models, the treasury of apriori knowledge accumulated by long-term physic- based modeling activity and technologists experience. The proposed approach is to design controllers based on models that are inherently interpretable, while integrating some Machine Learning (ML) features. According to the physical analytics paradigm, data analytics is fused with physical-model in order to improve accuracy and robustness while preserving the overall meaning and interpretability typical of explicit scientific knowledge. The above-mentioned approach is herein exemplified by presenting two different applications. Firstly, a novel chatter controller for cylindrical traverse grinding, in particular roll grinding, is presented (Fig.1) [4] . It merges the apriori knowledge on the regenerative chatter phenomenon with the adaptiveness of an evolving stability map (ML feature). The apriori knowledge, mainly concerned with frequency contents and wheel lobing effect, allows the development of an algorithm for a fast chatter detection and the identification of the proper control action. In the literature several grinding monitoring algorithms for chatter detection and control have been proposed in the last decades, as reviewed by Tönshoff et al. [5]. Anyway, data analysis showed that the monitoring methods were successful in different conditions but the overall robustness, with respect to real-time implementations on industrial control hardware, has not been tested, especially considering the computational lightness required for the deployment in an industrial control hardware. Our solution is implemented following a state machine concept (details can be found in [6]).It is characterized by an "open structure", that easily allows further development and improvements to the control logic, in adaptation to varying operating conditions. “Intelligent” synthetic indicators, embedding knowledge about the process,trigger the transitions between states. In particular, indicators must provide a quantitative estimation of the generated waviness in real-time for triggering the proper control actions. A model- based waviness observer module, based on accelerometers installed in different points of the grinder, is exploited to produce this estimation relying on a process-machine dynamic model. The control actions are also governed by an additional set of heuristic rules derived from operator expertise, to optimize the overall performance in industrial operations. Moreover, the rules driving the selection of the best wheel velocity rely upon an evolving memory structure with self-learning adaptive capabilities. This Stability Map (SM) is the knowledge base exploited by the controller to select an optimal wheel velocity and it evolves according to the results of monitoring events, being the ML kernel of the system. The SM has been designed to exploit synergistically a priori and in-process information. It is updated whenever the current wheel velocity is classified as stable or unstable (ML); but, then, the same classification is extrapolated to other velocity consistently with the well-known regenerative chatter theory ( Physical knowledge). The second example refers to the design of a process controller for centerless grinding. The controller is aimed at reducing workpiece roundness error due to the so-called geometric instability (lobing effect). Geometric lobing depends on the geometric setup of the workpiece (WP), i.e., blade angle and WP height (see Fig. 2 for a scheme of process geometry), and on the structural compliance of the machine. It represents one of the main restrictions to WP roundness accuracy: WP center oscillations produce a waved profile. Several authors have modeled the lobing phenomenon to guide set up and optimization of centerless plunge grinding processes, in order to reduce set-up time and avoid geometric instabilities as a function of WP height and blade angle, even taking into account machine-WP dynamic interaction [7-11]. In particular, a stability map can be computed relating the lobes number and growth rate to the various process parameters. Unluckily, such maps are subject to various uncertainties: a significant one is related to filtering effect and compliance entailed by wheel-WP contact, which, on its turn, depend on unpredictable characteristics of wheel and WP material. For instance, in Fig.3, the stability diagram relating geometrical parameters to the number of lobes arising around WP profile, is depicted for two different value of the wheel-WP contact length, demonstrating the great influence of this quantity on stability. The basic idea of the outlined process optimizer/controller is to carry out a continuous on-line updating of the diagram ( ML), assuming that is changes accordingly to the physical model ( Physical knowledge), e.g. because of increasing wheel dullness. Then, a more reliable geometric configuration can be selected, based on the diagram obtained from the updated process model. ML is fed both by a synthetic lobing indicator computed from monitoring data and by the operator feedback, considering also WP quality control, when available. The synthetic lobing indicator is based on a time-frequency envelope analysis of acceleration or acoustic-emission signals collected on the machine.