## 2 Methods
### Simulation Example  
For our numerical exploration, we use a simulation example. As shown in Figure 1, we use a simple pendulum to represent the dynamics of the task and a Proportional Integral Derivative (PID) as a controller, along with a delay and saturation in a unity feedback configuration. The simple pendulum has length \(L\), mass \(M\), and a damping coefficient \(C\). For our simulation, we use \(L=0.65\) m, \(M=3.5\) Kg, \(C=3.375\) Kgm/s, and a PID controller with the proportional gain \(k_{p}=15\), integral gain \(k_{i}=4\) Hz, and derivative gain \(k_{d}=0.5\) s. All simulations were carried out using MATLAB & Simulink of MathWorks (Natick, MA, USA).  
This simulation example is similar to a movement control task in a clinic and has the same structure as shown in Figure 1, which is similar to other examples in the literature [36; 42; 47; 49; 57]. To simulate the degradation of stability, we first consider a small and constant delay as a representation of the human sensorimotor system of a healthy individual, and a gradually increasing delay as a representation of the human sensorimotor system of an individual with PPD. Note that this gradual increase in the delay is still below the delay threshold; that is, the delay has increased but not to the extent that it destabilizes the human sensorimotor system leading to visible motor control symptoms. Similar to delay analysis, to demonstrate that the method works equally well for other mechanisms of instability, we subsequently also consider a constant gain as a representation of the human sensorimotor system of a healthy individual and a gradual increment in gain as a representation of the human sensorimotor system for an individual with PPD. Analogous to delay, the gain is increased but not to the extent that it destabilizes the human sensorimotor system.  
**Procedure for generating a synthetic data set:** As explained in Section 2.2, a subject needs to repeat the same clinical task on several occasions over a period of time. To mimic within-subject variability in the sensorimotor delay (or gain) values over a period of time due to various physiological factors, we consider additional stochasticity around the constant value of the delay (or gain) representing healthy individuals and a gradual increasing delay (or gain) value representing PPD individuals. This stochasticity is assumed to follow a Gaussian distribution. Further, to represent noise in the human sensorimotor system, we introduce system and measurement noise with zero mean and Gaussian distribution. Next, we use these sensorimotor delay (or gain) values in the simulation example to generate simulated responses (similar to data from a clinical task) and generate several instances of the same task repeated over a period of time. As an example, Figure 2 shows the simulated data of a single clinical task. Following this procedure, we generate a synthetic data set simulating 500 instances of a sensorimotor loop system with a constant gain and delay for healthy individuals and 500 instances of sensorimotor loop system with a gradual increment in gain and delay representing PPD. These synthetic data represent the 1000 individuals for training and validation needed for the machine learning algorithm. We used 600 individuals (synthetic data set) for training (60%) and 400 individuals (40%) to validate the machine learning algorithm. The numerical values of delays and gains for the generated synthetic data set are given in Appendix A.1. The training data set was used to train the model, and the validation data set was used to test the performance of the trained model.