Conference Agenda

Physics-informed neural networks (PINNs) make data-based predictions using physical laws, typically in the form of differential equations. The PINN approximates the solution, minimizing the data loss, corresponding to deviation from the data, and the residual loss, quantifying deviation from the differential equation, resulting in a biobjective optimization problem. The growing popularity of PINNs is attributed to their robustness on small, noisy datasets, which is particularly desirable for experimental applications. The application of PINNs is not limited to physical phenomena. The seamless integration of domain knowledge into data-driven approaches makes them promising candidates for a wide range of scientific, economic, and engineering applications.

The aim of this study is to design and train a PINN but also to evaluate its performance in the context of data affected by measurement errors and determining missing parameter values of the differential equation. The oscillation of a damped simple pendulum is selected as a case study, offering both evaluation aspects. To distinguish the performance of a PINN from that of a standard neural network, both were implemented as feedforward neural networks and trained using the same variant of the gradient descent method.

The results demonstrate that the systematic selection of hyperparameters enables accurate predictions with PINNs, in contrast to the significant deviation from the data observed for standard neural networks. Training parameter values of the differential equation alongside network parameters enhances accuracy. Random measurement errors are negligible due to regularization, while systematic errors affect the accuracy of the prediction and the determined parameter values.

Reinforcement Learning algorithms have garnered significant attention for their ability to learn optimal decision-making policies in uncertain and dynamic environments. However, the performance of RL algorithms can vary considerably depending on the underlying probability distributions characterizing the environment. We presents a comprehensive comparison of RL algorithms under various probability distributions, emphasizing the importance of understanding their behavior beyond the typical assumption of Gaussian or normal distributions.

Through experiments across different settings, we explore the performance of popular RL algorithms, including Q-Learning, Deep Q-Networks, and Proximal Policy Optimization, across a range of probability. We investigate how the shape, scale, and skewness of these distributions influence the convergence rate and stability of RL algorithms.

This work introduces a novel clustered sampling approach aimed at ensuring the representativeness of samples across diverse populations. The method formulates the sampling problem as an optimization problem, with the objective of selecting the best representative sample while accommodating variations in sample characteristics. Through rigorous optimization techniques, the method facilitates informed decision-making processes and supports robust statistical analyses.

Comparison of the results obtained from this method with those of other sampling methods reveals a significantly more representative sample generated by the proposed approach. Notably, the characteristics of the selected sample exhibit the same distribution as the entire network, emphasizing the method's effectiveness in accurately capturing the population's diversity.

Furthermore, this method has been successfully implemented for experimentation purposes in a meal delivery service company. The application of the approach in real-world settings underscores its effectiveness and practical utility in addressing sampling challenges across different industries.