We live in a world full of complex systems which we need to improve our understanding of. To accomplish this, purely probabilistic investigations are often not enough. They are only the first step and must be followed by learning the system's underlying mechanisms. This is what the discipline of causality is concerned with. Many of those complex systems contain feedback loops which means that our methods have to allow for cyclic causal relations. Furthermore, systems are rarely sufficiently isolated, which means that there are usually hidden confounders, i.e., unmeasured variables that each causally affects more than one measured variable. Finally, data is often distorted by contaminating processes, and we need to apply methods that are robust against such distortions. That's why we consider the robustness of LLC, see \cite{llc}, one of the few causal analysis methods that can deal with cyclic models with hidden confounders. Following a theoretical analysis of LLC's robustness properties, we also provide robust extensions of LLC. To facilitate reproducibility and further research in this field, we make the source code publicly available.

Recent advances in MCMC use normalizing flows to precondition target distributions and enable jumps to distant regions. However, there is currently no systematic comparison of different normalizing flow architectures for MCMC. As such, many works choose simple flow architectures that are readily available and do not consider other models. Guidelines for choosing an appropriate architecture would reduce analysis time for practitioners and motivate researchers to take the recommended models as foundations to be improved. We provide the first such guideline by extensively evaluating many normalizing flow architectures on various flow-based MCMC methods and target distributions. When the target density gradient is available, we show that flow-based MCMC outperforms classic MCMC for suitable NF architecture choices with minor hyperparameter tuning. When the gradient is unavailable, flow-based MCMC wins with off-the-shelf architectures. We find contractive residual flows to be the best general-purpose models with relatively low sensitivity to hyperparameter choice. We also provide various insights into normalizing flow behavior within MCMC when varying their hyperparameters, properties of target distributions, and the overall computational budget.

We present the design for a thermodynamic computer that can perform arbitrary nonlinear calculations in or out of equilibrium. Simple thermodynamic circuits, fluctuating degrees of freedom in contact with a thermal bath and confined by a quartic potential, display an activity that is a nonlinear function of their input. Such circuits can therefore be regarded as thermodynamic neurons, and can serve as the building blocks of networked structures that act as thermodynamic neural networks, universal function approximators whose operation is powered by thermal fluctuations. We simulate a digital model of a thermodynamic neural network, and show that its parameters can be adjusted by genetic algorithm to perform nonlinear calculations at specified observation times, regardless of whether the system has attained thermal equilibrium. This work expands the field of thermodynamic computing beyond the regime of thermal equilibrium, enabling fully nonlinear computations, analogous to those performed by classical neural networks, at specified observation times.

We show that the Lorentz-Equivariant Geometric Algebra Transformer (L-GATr) yields state-of-the-art performance for a wide range of machine learning tasks at the Large Hadron Collider. L-GATr represents data in a geometric algebra over space-time and is equivariant under Lorentz transformations. The underlying architecture is a versatile and scalable transformer, which is able to break symmetries if needed. We demonstrate the power of L-GATr for amplitude regression and jet classification, and then benchmark it as the first Lorentz-equivariant generative network. For all three LHC tasks, we find significant improvements over previous architectures.

As next generation cellular networks become denser, associating users with the optimal base stations at each time while ensuring no base station is overloaded becomes critical for achieving stable and high network performance. We propose multi-agent online Q-learning (QL) algorithms for performing real-time load balancing user association and handover in dense cellular networks. The load balancing constraints at all base stations couple the actions of user agents, and we propose two multi-agent action selection policies, one centralized and one distributed, to satisfy load balancing at every learning step. In the centralized policy, the actions of UEs are determined by a central load balancer (CLB) running an algorithm based on swapping the worst connection to maximize the total learning reward. In the distributed policy, each UE takes an action based on its local information by participating in a distributed matching game with the BSs to maximize the local reward. We then integrate these action selection policies into an online QL algorithm that adapts in real-time to network dynamics including channel variations and user mobility, using a reward function that considers a handover cost to reduce handover frequency. The proposed multi-agent QL algorithm features low-complexity and fast convergence, outperforming 3GPP max-SINR association. Both policies adapt well to network dynamics at various UE speed profiles from walking, running, to biking and suburban driving, illustrating their robustness and real-time adaptability.

The reliability of substation equipment is crucial to the stability of power systems, but traditional fault analysis methods heavily rely on manual expertise, limiting their effectiveness in handling complex and large-scale data. This paper proposes a substation equipment fault analysis method based on a multimodal large language model (MLLM). We developed a database containing 40,000 entries, including images, defect labels, and analysis reports, and used an image-to-video generation model for data augmentation. Detailed fault analysis reports were generated using GPT-4. Based on this database, we developed SubstationAI, the first model dedicated to substation fault analysis, and designed a fault diagnosis knowledge base along with knowledge enhancement methods. Experimental results show that SubstationAI significantly outperforms existing models, such as GPT-4, across various evaluation metrics, demonstrating higher accuracy and practicality in fault cause analysis, repair suggestions, and preventive measures, providing a more advanced solution for substation equipment fault analysis.

We introduce a multi-modal autonomous delivery optimization framework as a coalition game for a fleet of UAVs and ADRs operating in two overlaying networks to address last-mile delivery in urban environments, including high-density areas, road-based routing, and real-world operational challenges. The problem is defined as multiple depot pickup and delivery with time windows constrained over operational restrictions, such as vehicle battery limitation, precedence time window, and building obstruction. Subsequently, the coalition game theory is applied to investigate cooperation structures among the modes to capture how strategic collaboration among vehicles can improve overall routing efficiency. To do so, a generalized reinforcement learning model is designed to evaluate the cost-sharing and allocation to different coalitions for which sub-additive property and non-empty core exist. Our methodology leverages an end-to-end deep multi-agent policy gradient method augmented by a novel spatio-temporal adjacency neighbourhood graph attention network and transformer architecture using a heterogeneous edge-enhanced attention model. Conducting several numerical experiments on last-mile delivery applications, the result from the case study in the city of Mississauga shows that despite the incorporation of an extensive network in the graph for two modes and a complex training structure, the model addresses realistic operational constraints and achieves high-quality solutions compared with the existing transformer-based and heuristics methods and can perform well on non-homogeneous data distribution, generalizes well on the different scale and configuration, and demonstrate a robust performance under stochastic scenarios subject to wind speed and direction.

Time series forecasting is crucial for various applications, such as weather forecasting, power load forecasting, and financial analysis. In recent studies, MLP-mixer models for time series forecasting have been shown as a promising alternative to transformer-based models. However, the performance of these models is still yet to reach its potential. In this paper, we propose Wavelet Patch Mixer (WPMixer), a novel MLP-based model, for long-term time series forecasting, which leverages the benefits of patching, multi-resolution wavelet decomposition, and mixing. Our model is based on three key components: (i) multi-resolution wavelet decomposition, (ii) patching and embedding, and (iii) MLP mixing. Multi-resolution wavelet decomposition efficiently extracts information in both the frequency and time domains. Patching allows the model to capture an extended history with a look-back window and enhances capturing local information while MLP mixing incorporates global information. Our model significantly outperforms state-of-the-art MLP-based and transformer-based models for long-term time series forecasting in a computationally efficient way, demonstrating its efficacy and potential for practical applications.

Nonlinear differential equations and systems play a crucial role in modeling systems where time-dependent factors exhibit nonlinear characteristics. Due to their nonlinear nature, solving such systems often presents significant difficulties and challenges. In this study, we propose a method utilizing Physics-Informed Neural Networks (PINNs) to solve the nonlinear energy supply-demand (ESD) system. We design a neural network with four outputs, where each output approximates a function that corresponds to one of the unknown functions in the nonlinear system of differential equations describing the four-dimensional ESD problem. The neural network model is then trained and the parameters are identified, optimized to achieve a more accurate solution. The solutions obtained from the neural network for this problem are equivalent when we compare and evaluate them against the Runge-Kutta numerical method of order 4/5 (RK45). However, the method utilizing neural networks is considered a modern and promising approach, as it effectively exploits the superior computational power of advanced computer systems, especially in solving complex problems. Another advantage is that the neural network model, after being trained, can solve the nonlinear system of differential equations across a continuous domain. In other words, neural networks are not only trained to approximate the solution functions for the nonlinear ESD system but can also represent the complex dynamic relationships between the system's components. However, this approach requires significant time and computational power due to the need for model training.

Smart grid, through networked smart meters employing the non-intrusive load monitoring (NILM) technique, can considerably discern the usage patterns of residential appliances. However, this technique also incurs privacy leakage. To address this issue, we propose an innovative scheme based on adversarial attack in this paper. The scheme effectively prevents NILM models from violating appliance-level privacy, while also ensuring accurate billing calculation for users. To achieve this objective, we overcome two primary challenges. First, as NILM models fall under the category of time-series regression models, direct application of traditional adversarial attacks designed for classification tasks is not feasible. To tackle this issue, we formulate a novel adversarial attack problem tailored specifically for NILM and providing a theoretical foundation for utilizing the Jacobian of the NILM model to generate imperceptible perturbations. Leveraging the Jacobian, our scheme can produce perturbations, which effectively misleads the signal prediction of NILM models to safeguard users' appliance-level privacy. The second challenge pertains to fundamental utility requirements, where existing adversarial attack schemes struggle to achieve accurate billing calculation for users. To handle this problem, we introduce an additional constraint, mandating that the sum of added perturbations within a billing period must be precisely zero. Experimental validation on real-world power datasets REDD and UK-DALE demonstrates the efficacy of our proposed solutions, which can significantly amplify the discrepancy between the output of the targeted NILM model and the actual power signal of appliances, and enable accurate billing at the same time. Additionally, our solutions exhibit transferability, making the generated perturbation signal from one target model applicable to other diverse NILM models.