1 Physics-Based Neural Network Models for Prediction of Cam-Follower Dynamics Beyond Nominal Operations Wannes De Groote, Sofie Van Hoecke, Guillaume Crevecoeur Abstract—Cam-follower mechanisms are key in various mecha- tronic applications to convert rotary to linear reciprocating motions. The dynamic behavior of these systems relies on the design parameters such as the cam shape and follower mass. It appears that for some combinations of system parameters, con- tinuous contact between the cam and follower cannot be assured, leading to harmful periodic impacts. This research presents a data-driven approach to predict the influence of parameter settings on the system dynamics by learning from a limited data set of nominal operating conditions. More specifically, we present a hybrid model architecture encompassing an ordinary differential equation, consisting of a close interconnection of neural and physics-based network layers. Due to an increased generalization established by the physical laws, these physics- based neural network models exhibit enhanced extrapolation capabilities compared to their black-box counterparts. Conse- quently, the presented models can accurately simulate the system behavior for parameter settings far beyond the nominal values included in the training data. This way, starting from a limited set of nominal time-series data, we could accurately estimate the set of critical system parameters that lead to hazardous jump phenomena in cam-follower systems. Index Terms—Nonlinear Dynamic Systems Modeling, Cam- Follower Mechanism, Neural Networks, Physics-Informed AI, Parameter Exploration I. I NTRODUCTION Cam-follower mechanisms are mechanical subsystems that translate a rotational displacement of a drivetrain shaft into a reciprocating motion [1]. These mechanisms are typically implemented in combustion engines to regulate the cylinder intake and exhaust valves [2]. Mechatronic implementations of cam-follower mechanisms can be found in, among others, actuators [3] and robotics [4]. They can also be found in high-precision pumps with applications in avionics [5] and biomedical applications [6], [7]. The cam shape is typically designed so that it provides the desired displacement path to the follower while limiting the dynamics induced to the overall system [8]. By controlling the rotational speed of the camshaft, the motion dynamics can be W. De Groote holds a doctoral grant in strategic basic research (3S07219) from the Fund for Scientific research Flanders (FWO). This research received funding from the Flemish Government (AI Research Program) W. De Groote and G. Crevecoeur are with the Department of Electrome- chanical, Systems and Metal Engineering, Ghent University, 9000 Ghent, Belgium, and also with EEDT-DC, Flanders Make, 3920 Lommel, Belgium (e-mail: wannes.degroote@ugent.be; guillaume.crevecoeur@ugent.be). S. Van Hoecke is with the Internet Technology and Data Science Lab (IDLab) of Ghent University and imec, 9000 Ghent, Belgium (e-mail: sofie.vanhoecke@ugent.be). further optimized [9]. It is generally assumed that the follower perfectly and continuously tracks the cam perimeter. However, for increased rotational speed, the follower can detach from the cam, resulting in hazardous bouncing behavior [10], [11]. This unwanted phenomenon can inflict damage to the system due to the large periodic impacts caused by the follower jumps [12]. Although this behavior is desired for some dedicated machines, such as cutting tools [13], most system designs need to avoid this harmful behavior. In this research, we endeavor to predict the occurrence of follower jumps for unseen system parameter settings. Recent advances in machine learning have shown the ability to discover complex relations in machine data, enabling a data- driven assessment of the system behavior [14]. However, these algorithms become typically less useful when labeled data of the failure events are scarce or not available at all. A possible approach to overcome this burden is to augment the data set with synthetic data obtained by emulating erroneous situations on high-fidelity physics models [15]. The construction of physics-inspired simulation models typically comprises the definition of a simplified model structure, followed by the identification of the introduced system parameters such as inertia and friction coefficients [16], [17]. Unfortunately, the ingrained system behavior of many mechatronic systems is often too complex, making it very challenging to deduce the physical relations of all interactions at play. Alternatively, black-box system identification methods can learn the system dynamics directly from the measured time series [18]. In particular, deep learning methods have shown the ability to replace the traditional physics-inspired relations defined in state-space [19], Lagrangian [20] and Hamilto- nian [21] representations. Although the high flexibility of these modeling formalisms enables enhanced predictive per- formances, they typically become unreliable when evaluated on regions for which they have not seen training data. Re- cent research on combining black-box models with physics- inspired methods showed promise in accommodating this bur- den. For instance, enhanced generalization can be obtained by enforcing physical consistency (i.e., conservation of energy) in the loss function [22]. Alternatively, the influence of the neural networks can be attenuated by using them as mappings that compensate for prediction discrepancies of simplified physics- based models [23], [24]. Furthermore, neural networks have been used to accommodate specific unknown interactions in incomplete yet accurate physics models [25], [26]. Inspired by the benefits of combining machine learning