In neural networks, task-relevant information is represented jointly by groups of neurons. However, the specific way in which this mutual information about the classification label is distributed among the individual neurons is not well understood: While parts of it may only be obtainable from specific single neurons, other parts are carried redundantly or synergistically by multiple neurons. We show how Partial Information Decomposition (PID), a recent extension of information theory, can disentangle these different contributions. From this, we introduce the measure of "Representational Complexity", which quantifies the difficulty of accessing information spread across multiple neurons. We show how this complexity is directly computable for smaller layers. For larger layers, we propose subsampling and coarse-graining procedures and prove corresponding bounds on the latter. Empirically, for quantized deep neural networks solving the MNIST and CIFAR10 tasks, we observe that representational complexity decreases both through successive hidden layers and over training, and compare the results to related measures. Overall, we propose representational complexity as a principled and interpretable summary statistic for analyzing the structure and evolution of neural representations and complex systems in general. These authors contributed equally to this work.

We propose conditioning field initialization for neural network based topology optimization. In this work, we focus on (1) improving upon existing neural network based topology optimization, (2) demonstrating that by using a prior initial field on the unoptimized domain, the efficiency of neural network based topology optimization can be further improved. Our approach consists of a topology neural network that is trained on a case by case basis to represent the geometry for a single topology optimization problem. It takes in domain coordinates as input to represent the density at each coordinate where the topology is represented by a continuous density field. The displacement is solved through a finite element solver. We employ the strain energy field calculated on the initial design domain as an additional conditioning field input to the neural network throughout the optimization. The addition of the strain energy field input improves the convergence speed compared to standalone neural network based topology optimization.

Lithium-ion batteries are widely used in various applications, including portable electronic devices, electric vehicles, and renewable energy storage systems. Accurately estimating the remaining useful life of these batteries is crucial for ensuring their optimal performance, preventing unexpected failures, and reducing maintenance costs. In this paper, we present a comprehensive review of the existing approaches for estimating the remaining useful life of lithium-ion batteries, including data-driven methods, physics-based models, and hybrid approaches. We also propose a novel approach based on machine learning techniques for accurately predicting the remaining useful life of lithium-ion batteries. Our approach utilizes various battery performance parameters, including voltage, current, and temperature, to train a predictive model that can accurately estimate the remaining useful life of the battery. We evaluate the performance of our approach on a dataset of lithium-ion battery cycles and compare it with other state-of-the-art methods. The results demonstrate the effectiveness of our proposed approach in accurately estimating the remaining useful life of lithium-ion batteries.

Ensuring solution feasibility is a key challenge in developing Deep Neural Network (DNN) schemes for solving constrained optimization problems, due to inherent DNN prediction errors. In this paper, we propose a ``preventive learning'' framework to guarantee DNN solution feasibility for problems with convex constraints and general objective functions without post-processing, upon satisfying a mild condition on constraint calibration. Without loss of generality, we focus on problems with only inequality constraints. We systematically calibrate inequality constraints used in DNN training, thereby anticipating prediction errors and ensuring the resulting solutions remain feasible. We characterize the calibration magnitudes and the DNN size sufficient for ensuring universal feasibility. We propose a new Adversarial-Sample Aware training algorithm to improve DNN's optimality performance without sacrificing feasibility guarantee. Overall, the framework provides two DNNs. The first one from characterizing the sufficient DNN size can guarantee universal feasibility while the other from the proposed training algorithm further improves optimality and maintains DNN's universal feasibility simultaneously. We apply the framework to develop DeepOPF+ for solving essential DC optimal power flow problems in grid operation. Simulation results over IEEE test cases show that it outperforms existing strong DNN baselines in ensuring 100% feasibility and attaining consistent optimality loss ($<$0.19%) and speedup (up to $\times$228) in both light-load and heavy-load regimes, as compared to a state-of-the-art solver. We also apply our framework to a non-convex problem and show its performance advantage over existing schemes.

Interest in reinforcement learning (RL) has recently surged due to the application of deep learning techniques, but these connectionist approaches are opaque compared with symbolic systems. Learning Classifier Systems (LCSs) are evolutionary machine learning systems that can be categorised as eXplainable AI (XAI) due to their rule-based nature. Michigan LCSs are commonly used in RL domains as the alternative Pittsburgh systems (e.g. SAMUEL) suffer from complex algorithmic design and high computational requirements; however they can produce more compact/interpretable solutions than Michigan systems. We aim to develop two novel Pittsburgh LCSs to address RL domains: PPL-DL and PPL-ST. The former acts as a "zeroth-level" system, and the latter revisits SAMUEL's core Monte Carlo learning mechanism for estimating rule strength. We compare our two Pittsburgh systems to the Michigan system XCS across deterministic and stochastic FrozenLake environments. Results show that PPL-ST performs on-par or better than PPL-DL and outperforms XCS in the presence of high levels of environmental uncertainty. Rulesets evolved by PPL-ST can achieve higher performance than those evolved by XCS, but in a more parsimonious and therefore more interpretable fashion, albeit with higher computational cost. This indicates that PPL-ST is an LCS well-suited to producing explainable policies in RL domains.

The quest for low-cost fusion power has led to the construction of experimental devices such as the DIII-D[8], an operational device for conducting magnetic fusion research, and ITER [16], an international project to help make the transition from studies of plasma physics to electricity-generating fusion power plants. These devices, called tokamaks, use magnetic fields to confine the fusion fuel in the form of a plasma, enabling physicists to perform experiments to determine the best shape for the hot reacting plasma and the magnetic fields necessary to hold it in place. To complement the experiments, computer simulations are used to gain an understanding of the complex physics of the plasmas, design new reactors, and select the parameters to be used in experiments. Data from both the experiments and the simulations are analyzed to provide the insights that will contribute to achieving the goal of fusion power. In this paper, we focus on a specific analysis problem that arises in both simulation and experimental data, namely, the classification of orbits in a Poincaré map, also called a Poincaré plot. These two-dimensional plots are obtained for planes, called poloidal planes, which intersect the torus-shaped tokamak perpendicular to the magnetic axis, as shown in Figure 1(a). A plot consists of several orbits, each composed of a number of points (Figure 1(b)). For a given orbit, these points are the intersections of a field line (the solid lines in Figure 1(a)) with a poloidal plane, as the field line is followed around the torus. There are four distinct shapes traced out by these points, leading to four classes of orbits: quasi-periodic, separatrix, island chain, and stochastic, as shown in Figure 2. In some cases, the orbit shows its distinctive shape with just a few points, corresponding to the first few intersections of the field line with the poloidal plane.

Coronal Mass Ejections (CMEs) correspond to dramatic expulsions of plasma and magnetic field from the solar corona into the heliosphere. CMEs are scientifically relevant because they are involved in the physical mechanisms characterizing the active Sun. However, more recently CMEs have attracted attention for their impact on space weather, as they are correlated to geomagnetic storms and may induce the generation of Solar Energetic Particles streams. In this space weather framework, the present paper introduces a physics-driven artificial intelligence (AI) approach to the prediction of CMEs travel time, in which the deterministic drag-based model is exploited to improve the training phase of a cascade of two neural networks fed with both remote sensing and in-situ data. This study shows that the use of physical information in the AI architecture significantly improves both the accuracy and the robustness of the travel time prediction.

Deep learning models form one of the most powerful machine learning models for the extraction of important features. Most of the designs of deep neural models, i.e., the initialization of parameters, are still manually tuned. Hence, obtaining a model with high performance is exceedingly time-consuming and occasionally impossible. Optimizing the parameters of the deep networks, therefore, requires improved optimization algorithms with high convergence rates. The single objective-based optimization methods generally used are mostly time-consuming and do not guarantee optimum performance in all cases. Mathematical optimization problems containing multiple objective functions that must be optimized simultaneously fall under the category of multi-objective optimization sometimes referred to as Pareto optimization. Multi-objective optimization problems form one of the alternatives yet useful options for parameter optimization. However, this domain is a bit less explored. In this survey, we focus on exploring the effectiveness of multi-objective optimization strategies for parameter optimization in conjunction with deep neural networks. The case studies used in this study focus on how the two methods are combined to provide valuable insights into the generation of predictions and analysis in multiple applications.

This paper reconsiders end-to-end learning approaches to the Optimal Power Flow (OPF). Existing methods, which learn the input/output mapping of the OPF, suffer from scalability issues due to the high dimensionality of the output space. This paper first shows that the space of optimal solutions can be significantly compressed using principal component analysis (PCA). It then proposes Compact Learning, a new method that learns in a subspace of the principal components before translating the vectors into the original output space. This compression reduces the number of trainable parameters substantially, improving scalability and effectiveness. Compact Learning is evaluated on a variety of test cases from the PGLib with up to 30,000 buses. The paper also shows that the output of Compact Learning can be used to warm-start an exact AC solver to restore feasibility, while bringing significant speed-ups.

Wind power is becoming an increasingly important source of renewable energy worldwide. However, wind farm power control faces significant challenges due to the high system complexity inherent in these farms. A novel communication-based multi-agent deep reinforcement learning large-scale wind farm multivariate control is proposed to handle this challenge and maximize power output. A wind farm multivariate power model is proposed to study the influence of wind turbines (WTs) wake on power. The multivariate model includes axial induction factor, yaw angle, and tilt angle controllable variables. The hierarchical communication multi-agent proximal policy optimization (HCMAPPO) algorithm is proposed to coordinate the multivariate large-scale wind farm continuous controls. The large-scale wind farm is divided into multiple wind turbine aggregators (WTAs), and neighboring WTAs can exchange information through hierarchical communication to maximize the wind farm power output. Simulation results demonstrate that the proposed multivariate HCMAPPO can significantly increase wind farm power output compared to the traditional PID control, coordinated model-based predictive control, and multi-agent deep deterministic policy gradient algorithm. Particularly, the HCMAPPO algorithm can be trained with the environment based on the thirteen-turbine wind farm and effectively applied to larger wind farms. At the same time, there is no significant increase in the fatigue damage of the wind turbine blade from the wake control as the wind farm scale increases. The multivariate HCMAPPO control can realize the collective large-scale wind farm maximum power output.