Learning Equations for Extrapolation and Control

We present an approach to identify concise equations from data using a shallow neural network approach. In contrast to ordinary black-box regression, this approach allows understanding functional relations and generalizing them from observed data to unseen parts of the parameter space. We show how to extend the class of learnable equations for a recently proposed equation learning network to include divisions, and we improve the learning and model selection strategy to be useful for challenging real-world data. For systems governed by analytical expressions, our method can in many cases identify the true underlying equation and extrapolate to unseen domains. We demonstrate its effectiveness by experiments on a cart-pendulum system, where only 2 random rollouts are required to learn the forward dynamics and successfully achieve the swing-up task.Comment: 9 pages, 9 figures, ICML 201

Training Neural Networks using SAT solvers

We propose an algorithm to explore the global optimization method, using SAT solvers, for training a neural net. Deep Neural Networks have achieved great feats in tasks like-image recognition, speech recognition, etc. Much of their success can be attributed to the gradient-based optimisation methods, which scale well to huge datasets while still giving solutions, better than any other existing methods. However, there exist learning problems like the parity function and the Fast Fourier Transform, where a neural network using gradient-based optimisation algorithm can not capture the underlying structure of the learning task properly. Thus, exploring global optimisation methods is of utmost interest as the gradient-based methods get stuck in local optima. In the experiments, we demonstrate the effectiveness of our algorithm against the ADAM optimiser in certain tasks like parity learning. However, in the case of image classification on the MNIST Dataset, the performance of our algorithm was less than satisfactory. We further discuss the role of the size of the training dataset and the hyper-parameter settings in keeping things scalable for a SAT solver

Learning equations for extrapolation and control

We present an approach to identify concise equations from data using a shallow neural network approach. In contrast to ordinary black-box regression, this approach allows understanding functional relations and generalizing them from observed data to unseen parts of the parameter space. We show how to extend the class of learnable equations for a recently proposed equation learning network to include divisions, and we improve the learning and model selection strategy to be useful for challenging real-world data. For systems governed by analytical expressions, our method can in many cases identify the true underlying equation and extrapolate to unseen domains. We demonstrate its effectiveness by experiments on a cart-pendulum system, where only 2 random rollouts are required to learn the forward dynamics and successfully achieve the swing-up task

Resilient Cooperative Secondary Control of Islanded AC Microgrids Utilizing Inverter-Based Resources Against State-Dependent False Data Injection Attacks

This paper investigates the impact of potential state-dependent false data injection cyber-attacks on frequency synchronization and active power management in islanded ac microgrids. One potential way of affecting microgrid reliability is by forcing a generation outage. Thus, the attacker could potentially aim to desynchronize inverter-based resources in microgrids by manipulating their frequency with malicious injections. The attack signals are injected to manipulate control input channels, sensor nodes, reference values, and the information exchanged through communication networks. In order to mitigate the adverse impacts of such cyber-attacks, firstly, the conventional distributed consensus-based secondary control approach is modified and complemented in the presence of cyber-attacks. Secondly, a resilient cooperative distributed secondary control scheme is proposed by utilizing the concept of a virtual layer interconnected with the main network layer. Thirdly, theoretical stability, resilience analysis, and design considerations of interconnection matrices are also provided. Finally, simulations through MATLAB/Simulink and experimental results are presented in order to illustrate the robust performance of the proposed control scheme