Physics-Informed Neural Network (PINN) is a data-driven solver for partial and ordinary differential equations (ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the objective function often leads to training failures. This issue is particularly prominent when solving high-frequency and multi-scale problems. We proposed using transfer learning to boost the robustness and convergence of training PINN, starting training from low-frequency problems and gradually approaching high-frequency problems through fine-tuning. Through two case studies, we discovered that transfer learning can effectively train PINNs to approximate solutions from low-frequency problems to high-frequency problems without increasing network parameters. Furthermore, it requires fewer data points and less training time. We compare the PINN results using direct differences and $L_2$ relative error showing the advantage of using transfer learning techniques. We describe our training strategy in detail, including optimizer selection, and suggest guidelines for using transfer learning to train neural networks to solve more complex problems.

We present a device- and network-based solution for automatic passnger counting that operates on the edge in real time. The proposed solution consists of a low-cost WiFi scanner device equipped with custom algorithms for dealing with MAC address randomization. Our low-cost scanner is able to capture and analyze 802.11 probe requests emitted by passengers’ devices such as laptops, smartphones, and tablets. The device is configured with a Python data-processing pipeline that combines data coming from different types of sensors and processes them on the fly. For the analysis task, we have devised a lightweight version of the DBSCAN algorithm. Our software artifact is designed in a modular way in order to accommodate possible extensions of the pipeline, e.g., either additional filters or data sources. Furthermore, we exploit multi-threading and multi-processing for speeding up the entire computation. The proposed solution has been tested with different types of mobile devices, obtaining promising experimental results. In this paper, we present the key ingredients of our edge computing solution.

Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the objective function often leads to training failures. This issue is particularly prominent when solving high-frequency and multi-scale problems. We proposed using transfer learning to boost the robustness and convergence of training PINN, starting training from low-frequency problems and gradually approaching high-frequency problems. Through two case studies, we discovered that transfer learning can effectively train PINN to approximate solutions from low-frequency problems to high-frequency problems without increasing network parameters. Furthermore, it requires fewer data points and less training time. We elaborately described our training strategy, including optimizer selection, and suggested guidelines for using transfer learning to train neural networks for solving more complex problems.