PDE Control Gym: A Benchmark for Data-Driven Boundary Control of Partial Differential Equations

Over the last decade, data-driven methods have surged in popularity, emerging as valuable tools for control theory. As such, neural network approximations of control feedback laws, system dynamics, and even Lyapunov functions have attracted growing attention. With the ascent of learning based control, the need for accurate, fast, and easy-to-use benchmarks has increased. In this work, we present the first learning-based environment for boundary control of PDEs. In our benchmark, we introduce three foundational PDE problems - a 1D transport PDE, a 1D reaction-diffusion PDE, and a 2D Navier-Stokes PDE - whose solvers are bundled in an user-friendly reinforcement learning gym. With this gym, we then present the first set of model-free, reinforcement learning algorithms for solving this series of benchmark problems, achieving stability, although at a higher cost compared to model-based PDE backstepping. With the set of benchmark environments and detailed examples, this work significantly lowers the barrier to entry for learning-based PDE control - a topic largely unexplored by the data-driven control community. The entire benchmark is available on Github along with detailed documentation and the presented reinforcement learning models are open sourced.

Improving Sequential Market Clearing via Value-oriented Renewable Energy Forecasting

Large penetration of renewable energy sources (RESs) brings huge uncertainty into the electricity markets. While existing deterministic market clearing fails to accommodate the uncertainty, the recently proposed stochastic market clearing struggles to achieve desirable market properties. In this work, we propose a value-oriented forecasting approach, which tactically determines the RESs generation that enters the day-ahead market. With such a forecast, the existing deterministic market clearing framework can be maintained, and the day-ahead and real-time overall operation cost is reduced. At the training phase, the forecast model parameters are estimated to minimize expected day-ahead and real-time overall operation costs, instead of minimizing forecast errors in a statistical sense. Theoretically, we derive the exact form of the loss function for training the forecast model that aligns with such a goal. For market clearing modeled by linear programs, this loss function is a piecewise linear function. Additionally, we derive the analytical gradient of the loss function with respect to the forecast, which inspires an efficient training strategy. A numerical study shows our forecasts can bring significant benefits of the overall cost reduction to deterministic market clearing, compared to quality-oriented forecasting approach.

Identifying Electrocardiogram Abnormalities Using a Handcrafted-Rule-Enhanced Neural Network

A large number of people suffer from life-threatening cardiac abnormalities, and electrocardiogram (ECG) analysis is beneficial to determining whether an individual is at risk of such abnormalities. Automatic ECG classification methods, especially the deep learning based ones, have been proposed to detect cardiac abnormalities using ECG records, showing good potential to improve clinical diagnosis and help early prevention of cardiovascular diseases. However, the predictions of the known neural networks still do not satisfactorily meet the needs of clinicians, and this phenomenon suggests that some information used in clinical diagnosis may not be well captured and utilized by these methods. In this paper, we introduce some rules into convolutional neural networks, which help present clinical knowledge to deep learning based ECG analysis, in order to improve automated ECG diagnosis performance. Specifically, we propose a Handcrafted-Rule-enhanced Neural Network (called HRNN) for ECG classification with standard 12-lead ECG input, which consists of a rule inference module and a deep learning module. Experiments on two large-scale public ECG datasets show that our new approach considerably outperforms existing state-of-the-art methods. Further, our proposed approach not only can improve the diagnosis performance, but also can assist in detecting mislabelled ECG samples. Our codes are available at https://github.com/alwaysbyx/ecg_processing.