We propose a novel finite element-based physics-informed operator learning framework that allows for predicting spatiotemporal dynamics governed by partial differential equations (PDEs). The proposed framework employs a loss function inspired by the finite element method (FEM) with the implicit Euler time integration scheme. A transient thermal conduction problem is considered to benchmark the performance. The proposed operator learning framework takes a temperature field at the current time step as input and predicts a temperature field at the next time step. The Galerkin discretized weak formulation of the heat equation is employed to incorporate physics into the loss function, which is coined finite operator learning (FOL). Upon training, the networks successfully predict the temperature evolution over time for any initial temperature field at high accuracy compared to the FEM solution. The framework is also confirmed to be applicable to a heterogeneous thermal conductivity and arbitrary geometry. The advantages of FOL can be summarized as follows: First, the training is performed in an unsupervised manner, avoiding the need for a large data set prepared from costly simulations or experiments. Instead, random temperature patterns generated by the Gaussian random process and the Fourier series, combined with constant temperature fields, are used as training data to cover possible temperature cases. Second, shape functions and backward difference approximation are exploited for the domain discretization, resulting in a purely algebraic equation. This enhances training efficiency, as one avoids time-consuming automatic differentiation when optimizing weights and biases while accepting possible discretization errors. Finally, thanks to the interpolation power of FEM, any arbitrary geometry can be handled with FOL, which is crucial to addressing various engineering application scenarios.

Thermal management of power electronics and Electronic Control Units is crucial in times of increasing power densities and limited assembly space. Electric and autonomous vehicles are a prominent application field. Thermal Interface Materials are used to transfer heat from a semiconductor to a heatsink. They are applied along a dispense path onto the semiconductor and spread over its entire surface once the heatsink is joined. To plan this application path, design engineers typically perform an iterative trial-and-error procedure of elaborate simulations and manual experiments. We propose a fully automated optimization approach, which clearly outperforms the current manual path planning and respects all relevant manufacturing constraints. An optimum dispense path increases the reliability of the thermal interface and makes the manufacturing more sustainable by reducing material waste. We show results on multiple real products from automotive series production, including an experimental validation on actual series manufacturing equipment.

Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability. Although this problem is well studied for ordinary differential equations (ODEs), few studies have focused on the more general class of systems described by differential-algebraic equations (DAEs). Examples of DAEs include dynamical systems with algebraic equations representing conservation laws or approximating fast dynamics. This work introduces a novel identifiability test for models characterized by nonlinear DAEs. Unlike previous approaches, our test only requires prior knowledge of the system equations and does not need nonlinear transformation, index reduction, or numerical integration of the DAEs. We employed our identifiability analysis across a diverse range of DAE models, illustrating how system identifiability depends on the choices of sensors, experimental conditions, and model structures. Given the added challenges involved in identifying DAEs when compared to ODEs, we anticipate that our findings will have broad applicability and contribute significantly to the development and validation of data-driven methods for DAEs and other structure-preserving models.

Deep reinforcement learning (DRL) is a powerful machine learning paradigm for generating agents that control autonomous systems. However, the "black box" nature of DRL agents limits their deployment in real-world safety-critical applications. A promising approach for providing strong guarantees on an agent's behavior is to use Neural Lyapunov Barrier (NLB) certificates, which are learned functions over the system whose properties indirectly imply that an agent behaves as desired. However, NLB-based certificates are typically difficult to learn and even more difficult to verify, especially for complex systems. In this work, we present a novel method for training and verifying NLB-based certificates for discrete-time systems. Specifically, we introduce a technique for certificate composition, which simplifies the verification of highly-complex systems by strategically designing a sequence of certificates. When jointly verified with neural network verification engines, these certificates provide a formal guarantee that a DRL agent both achieves its goals and avoids unsafe behavior. Furthermore, we introduce a technique for certificate filtering, which significantly simplifies the process of producing formally verified certificates. We demonstrate the merits of our approach with a case study on providing safety and liveness guarantees for a DRL-controlled spacecraft.

Learning effective geospatial embeddings is crucial for a series of geospatial applications such as city analytics and earth monitoring. However, learning comprehensive region representations presents two significant challenges: first, the deficiency of effective intra-region feature representation; and second, the difficulty of learning from intricate inter-region dependencies. In this paper, we present GeoHG, an effective heterogeneous graph structure for learning comprehensive region embeddings for various downstream tasks. Specifically, we tailor satellite image representation learning through geo-entity segmentation and point-of-interest (POI) integration for expressive intra-regional features. Furthermore, GeoHG unifies informative spatial interdependencies and socio-environmental attributes into a powerful heterogeneous graph to encourage explicit modeling of higher-order inter-regional relationships. The intra-regional features and inter-regional correlations are seamlessly integrated by a model-agnostic graph learning framework for diverse downstream tasks. Extensive experiments demonstrate the effectiveness of GeoHG in geo-prediction tasks compared to existing methods, even under extreme data scarcity (with just 5% of training data). With interpretable region representations, GeoHG exhibits strong generalization capabilities across regions. We will release code and data upon paper notification.

Modern power grids are undergoing significant changes driven by information and communication technologies (ICTs), and evolving into smart grids with higher efficiency and lower operation cost. Using ICTs, however, comes with an inevitable side effect that makes the power system more vulnerable to cyber attacks. In this paper, we propose a self-supervised learning-based framework to detect and identify various types of cyber attacks. Different from existing approaches, the proposed framework does not rely on large amounts of well-curated labeled data but makes use of the massive unlabeled data in the wild which are easily accessible. Specifically, the proposed framework adopts the BERT model from the natural language processing domain and learns generalizable and effective representations from the unlabeled sensing data, which capture the distinctive patterns of different attacks. Using the learned representations, together with a very small amount of labeled data, we can train a task-specific classifier to detect various types of cyber attacks. Meanwhile, real-world training datasets are usually imbalanced, i.e., there are only a limited number of data samples containing attacks. In order to cope with such data imbalance, we propose a new loss function, separate mean error (SME), which pays equal attention to the large and small categories to better train the model. Experiment results in a 5-area power grid system with 37 buses demonstrate the superior performance of our framework over existing approaches, especially when a very limited portion of labeled data are available, e.g., as low as 0.002\%. We believe such a framework can be easily adopted to detect a variety of cyber attacks in other power grid scenarios.

The advent of Large Language Models (LLMs) has revolutionized language understanding and human-like text generation, drawing interest from many other fields with this question in mind: What else are the LLMs capable of? Despite their widespread adoption, ongoing research continues to explore new ways to integrate LLMs into diverse systems. This paper explores new techniques to harness the power of LLMs for 6G (6th Generation) wireless communication technologies, a domain where automation and intelligent systems are pivotal. The inherent adaptability of LLMs to domain-specific tasks positions them as prime candidates for enhancing wireless systems in the 6G landscape. We introduce a novel Reinforcement Learning (RL) based framework that leverages LLMs for network deployment in wireless communications. Our approach involves training an RL agent, utilizing LLMs as its core, in an urban setting to maximize coverage. The agent's objective is to navigate the complexities of urban environments and identify the network parameters for optimal area coverage. Additionally, we integrate LLMs with Convolutional Neural Networks (CNNs) to capitalize on their strengths while mitigating their limitations. The Deep Deterministic Policy Gradient (DDPG) algorithm is employed for training purposes. The results suggest that LLM-assisted models can outperform CNN-based models in some cases while performing at least as well in others.

Time series prediction is crucial for understanding and forecasting complex dynamics in various domains, ranging from finance and economics to climate and healthcare. Based on Transformer architecture, one approach involves encoding multiple variables from the same timestamp into a single temporal token to model global dependencies. In contrast, another approach embeds the time points of individual series into separate variate tokens. The former method faces challenges in learning variate-centric representations, while the latter risks missing essential temporal information critical for accurate forecasting. In our work, we introduce GridTST, a model that combines the benefits of two approaches using innovative multi-directional attentions based on a vanilla Transformer. We regard the input time series data as a grid, where the $x$-axis represents the time steps and the $y$-axis represents the variates. A vertical slicing of this grid combines the variates at each time step into a \textit{time token}, while a horizontal slicing embeds the individual series across all time steps into a \textit{variate token}. Correspondingly, a \textit{horizontal attention mechanism} focuses on time tokens to comprehend the correlations between data at various time steps, while a \textit{vertical}, variate-aware \textit{attention} is employed to grasp multivariate correlations. This combination enables efficient processing of information across both time and variate dimensions, thereby enhancing the model's analytical strength. % We also integrate the patch technique, segmenting time tokens into subseries-level patches, ensuring that local semantic information is retained in the embedding. The GridTST model consistently delivers state-of-the-art performance across various real-world datasets.

Parameter-efficient finetuning (PEFT) methods seek to adapt large neural models via updates to a small number of weights. However, much prior interpretability work has shown that representations encode rich semantic information, suggesting that editing representations might be a more powerful alternative. We pursue this hypothesis by developing a family of Representation Finetuning (ReFT) methods. ReFT methods operate on a frozen base model and learn task-specific interventions on hidden representations. We define a strong instance of the ReFT family, Low-rank Linear Subspace ReFT (LoReFT), and we identify an ablation of this method that trades some performance for increased efficiency. Both are drop-in replacements for existing PEFTs and learn interventions that are 15x--65x more parameter-efficient than LoRA. We showcase LoReFT on eight commonsense reasoning tasks, four arithmetic reasoning tasks, instruction-tuning, and GLUE. In all these evaluations, our ReFTs deliver the best balance of efficiency and performance, and almost always outperform state-of-the-art PEFTs. We release a generic ReFT training library publicly at https://github.com/stanfordnlp/pyreft.

We study reinforcement learning for global decision-making in the presence of many local agents, where the global decision-maker makes decisions affecting all local agents, and the objective is to learn a policy that maximizes the rewards of both the global and the local agents. Such problems find many applications, e.g. demand response, EV charging, queueing, etc. In this setting, scalability has been a long-standing challenge due to the size of the state/action space which can be exponential in the number of agents. This work proposes the $\texttt{SUB-SAMPLE-Q}$ algorithm where the global agent subsamples $k\leq n$ local agents to compute an optimal policy in time that is only exponential in $k$, providing an exponential speedup from standard methods that are exponential in $n$. We show that the learned policy converges to the optimal policy in the order of $\tilde{O}(1/\sqrt{k}+\epsilon_{k,m})$ as the number of sub-sampled agents $k$ increases, where $\epsilon_{k,m}$ is the Bellman noise, by proving a novel generalization of the Dvoretzky-Kiefer-Wolfowitz inequality to the regime of sampling without replacement. We also conduct numerical simulations in a demand-response setting and a queueing setting.