World is looking for clean and renewable energy sources that do not pollute the environment, in an attempt to reduce greenhouse gas emissions that contribute to global warming. Wind energy has significant potential to not only reduce greenhouse emission, but also meet the ever increasing demand for energy. To enable the effective utilization of wind energy, addressing the following three challenges in wind data analysis is crucial. Firstly, improving data resolution in various climate conditions to ensure an ample supply of information for assessing potential energy resources. Secondly, implementing dimensionality reduction techniques for data collected from sensors/simulations to efficiently manage and store large datasets. Thirdly, extrapolating wind data from one spatial specification to another, particularly in cases where data acquisition may be impractical or costly. We propose a deep learning based approach to achieve multi-modal continuous resolution wind data prediction from discontinuous wind data, along with data dimensionality reduction.

Due to non-stationarity of time series, the distribution shift problem largely hinders the performance of time series forecasting. Existing solutions either fail for the shifts beyond simple statistics or the limited compatibility with forecasting models. In this paper, we propose a general decoupled formulation for time series forecasting, with no reliance on fixed statistics and no restriction on forecasting architectures. Then, we make such a formulation formalized into a bi-level optimization problem, to enable the joint learning of the transformation (outer loop) and forecasting (inner loop). Moreover, the special requirements of expressiveness and bi-direction for the transformation motivate us to propose instance normalization flows (IN-Flow), a novel invertible network for time series transformation. Extensive experiments demonstrate our method consistently outperforms state-of-the-art baselines on both synthetic and real-world data.

In this paper, we present a novel transformer architecture tailored for learning robust power system state representations, which strives to optimize power dispatch for the power flow adjustment across different transmission sections. Specifically, our proposed approach, named Powerformer, develops a dedicated section-adaptive attention mechanism, separating itself from the self-attention used in conventional transformers. This mechanism effectively integrates power system states with transmission section information, which facilitates the development of robust state representations. Furthermore, by considering the graph topology of power system and the electrical attributes of bus nodes, we introduce two customized strategies to further enhance the expressiveness: graph neural network propagation and multi-factor attention mechanism. Extensive evaluations are conducted on three power system scenarios, including the IEEE 118-bus system, a realistic 300-bus system in China, and a large-scale European system with 9241 buses, where Powerformer demonstrates its superior performance over several baseline methods.

The use of large language models for code generation is a rapidly growing trend in software development. However, without effective methods for ensuring the correctness of generated code, this trend could lead to any number of undesirable outcomes. In this paper, we lay out a vision for addressing this challenge: the Clover paradigm, short for Closed-Loop Verifiable Code Generation, which reduces correctness checking to the more accessible problem of consistency checking. At the core of Clover lies a checker that performs consistency checks among code, docstrings, and formal annotations. The checker is implemented using a novel integration of formal verification tools and large language models. We provide a theoretical analysis to support our thesis that Clover should be effective at consistency checking. We also empirically investigate its feasibility on a hand-designed dataset (CloverBench) featuring annotated Dafny programs at a textbook level of difficulty. Experimental results show that for this dataset, (i) LLMs are reasonably successful at automatically generating formal specifications; and (ii) our consistency checker achieves a promising acceptance rate (up to 87%) for correct instances while maintaining zero tolerance for incorrect ones (no false positives).

Dynamic locomotion in legged robots is close to industrial collaboration, but a lack of standardized testing obstructs commercialization. The issues are not merely political, theoretical, or algorithmic but also physical, indicating limited studies and comprehension regarding standard testing infrastructure and equipment. For decades, the approaches we have been testing legged robots were rarely standardizable with hand-pushing, foot-kicking, rope-dragging, stick-poking, and ball-swinging. This paper aims to bridge the gap by proposing the use of the linear impactor, a well-established tool in other standardized testing disciplines, to serve as an adaptive, repeatable, and fair disturbance rejection testing equipment for legged robots. A pneumatic linear impactor is also adopted for the case study involving the humanoid robot Digit. Three locomotion controllers are examined, including a commercial one, using a walking-in-place task against frontal impacts. The statistically best controller was able to withstand the impact momentum (26.376 kg$\cdot$m/s) on par with a reported average effective momentum from straight punches by Olympic boxers (26.506 kg$\cdot$m/s). Moreover, the case study highlights other anti-intuitive observations, demonstrations, and implications that, to the best of the authors' knowledge, are first-of-its-kind revealed in real-world testing of legged robots.

Simulating turbulent flows is crucial for a wide range of applications, and machine learning-based solvers are gaining increasing relevance. However, achieving temporal stability when generalizing to longer rollout horizons remains a persistent challenge for learned PDE solvers. In this work, we analyze if fully data-driven fluid solvers that utilize an autoregressive rollout based on conditional diffusion models are a viable option to address this challenge. We investigate accuracy, posterior sampling, spectral behavior, and temporal stability, while requiring that methods generalize to flow parameters beyond the training regime. To quantitatively and qualitatively benchmark the performance of a range of flow prediction approaches, three challenging scenarios including incompressible and transonic flows, as well as isotropic turbulence are employed. We find that even simple diffusion-based approaches can outperform multiple established flow prediction methods in terms of accuracy and temporal stability, while being on par with state-of-the-art stabilization techniques like unrolling at training time. Such traditional architectures are superior in terms of inference speed, however, the probabilistic nature of diffusion approaches allows for inferring multiple predictions that align with the statistics of the underlying physics. Overall, our benchmark contains three carefully chosen data sets that are suitable for probabilistic evaluation alongside various established flow prediction architectures.

Dynamics model learning deals with the task of inferring unknown dynamics from measurement data and predicting the future behavior of the system. A typical approach to address this problem is to train recurrent models. However, predictions with these models are often not physically meaningful. Further, they suffer from deteriorated behavior over time due to accumulating errors. Often, simulators building on first principles are available being physically meaningful by design. However, modeling simplifications typically cause inaccuracies in these models. Consequently, hybrid modeling is an emerging trend that aims to combine the best of both worlds. In this paper, we propose a new approach to hybrid modeling, where we inform the latent states of a learned model via a black-box simulator. This allows to control the predictions via the simulator preventing them from accumulating errors. This is especially challenging since, in contrast to previous approaches, access to the simulator's latent states is not available. We tackle the task by leveraging observers, a well-known concept from control theory, inferring unknown latent states from observations and dynamics over time. In our learning-based setting, we jointly learn the dynamics and an observer that infers the latent states via the simulator. Thus, the simulator constantly corrects the latent states, compensating for modeling mismatch caused by learning. To maintain flexibility, we train an RNN-based residuum for the latent states that cannot be informed by the simulator.

Recent studies reveal the connection between GNNs and the diffusion process, which motivates many diffusion-based GNNs to be proposed. However, since these two mechanisms are closely related, one fundamental question naturally arises: Is there a general diffusion framework that can formally unify these GNNs? The answer to this question can not only deepen our understanding of the learning process of GNNs, but also may open a new door to design a broad new class of GNNs. In this paper, we propose a general diffusion equation framework with the fidelity term, which formally establishes the relationship between the diffusion process with more GNNs. Meanwhile, with this framework, we identify one characteristic of graph diffusion networks, i.e., the current neural diffusion process only corresponds to the first-order diffusion equation. However, by an experimental investigation, we show that the labels of high-order neighbors actually exhibit monophily property, which induces the similarity based on labels among high-order neighbors without requiring the similarity among first-order neighbors. This discovery motives to design a new high-order neighbor-aware diffusion equation, and derive a new type of graph diffusion network (HiD-Net) based on the framework. With the high-order diffusion equation, HiD-Net is more robust against attacks and works on both homophily and heterophily graphs. We not only theoretically analyze the relation between HiD-Net with high-order random walk, but also provide a theoretical convergence guarantee. Extensive experimental results well demonstrate the effectiveness of HiD-Net over state-of-the-art graph diffusion networks.

Deep neural network approximation of nonlinear operators, commonly referred to as DeepONet, has proven capable of approximating PDE backstepping designs in which a single Goursat-form PDE governs a single feedback gain function. In boundary control of coupled PDEs, coupled Goursat-form PDEs govern two or more gain kernels -- a PDE structure unaddressed thus far with DeepONet. In this note, we open the subject of approximating systems of gain kernel PDEs for hyperbolic PDE plants by considering a simple counter-convecting $2\times 2$ coupled system in whose control a $2\times 2$ kernel PDE systems in Goursat form arises. Applications include oil drilling, Saint-Venant model of shallow water waves, and Aw-Rascle-Zhang model of stop-and-go instability in congested traffic flow. In this paper we establish the continuity of the mapping from (a total of five) plant PDE functional coefficients to the kernel PDE solutions, prove the existence of an arbitrarily close DeepONet approximation to the kernel PDEs, and establish that the DeepONet-approximated gains guarantee stabilization when replacing the exact backstepping gain kernels. Taking into account anti-collocated boundary actuation and sensing, our $L^2$\emph{-Globally-exponentially} stabilizing (GES) approximate gain kernel-based output feedback design implies the deep learning of both the controller's and the observer's gains. Moreover, the encoding of the output-feedback law into DeepONet ensures \emph{semi-global practical exponential stability (SG-PES).} The DeepONet operator speeds up the computation of the controller gains by multiple orders of magnitude. Its theoretically proven stabilizing capability is demonstrated through simulations.

We investigate the applicability of machine learning technologies to the development of parsimonious, interpretable, catchment-scale hydrologic models using directed-graph architectures based on the mass-conserving perceptron (MCP) as the fundamental computational unit. Here, we focus on architectural complexity (depth) at a single location, rather than universal applicability (breadth) across large samples of catchments. The goal is to discover a minimal representation (numbers of cell-states and flow paths) that represents the dominant processes that can explain the input-state-output behaviors of a given catchment, with particular emphasis given to simulating the full range (high, medium, and low) of flow dynamics. We find that a HyMod-like architecture with three cell-states and two major flow pathways achieves such a representation at our study location, but that the additional incorporation of an input-bypass mechanism significantly improves the timing and shape of the hydrograph, while the inclusion of bi-directional groundwater mass exchanges significantly enhances the simulation of baseflow. Overall, our results demonstrate the importance of using multiple diagnostic metrics for model evaluation, while highlighting the need for designing training metrics that are better suited to extracting information across the full range of flow dynamics. Further, they set the stage for interpretable regional-scale MCP-based hydrological modeling (using large sample data) by using neural architecture search to determine appropriate minimal representations for catchments in different hydroclimatic regimes.