One of the main challenges in using deep learning-based methods for simulating physical systems and solving partial differential equations (PDEs) is formulating physics-based data in the desired structure for neural networks. Graph neural networks (GNNs) have gained popularity in this area since graphs offer a natural way of modeling particle interactions and provide a clear way of discretizing the continuum models. However, the graphs constructed for approximating such tasks usually ignore long-range interactions due to unfavorable scaling of the computational complexity with respect to the number of nodes. The errors due to these approximations scale with the discretization of the system, thereby not allowing for generalization under mesh-refinement. Inspired by the classical multipole methods, we propose a novel multi-level graph neural network framework that captures interaction at all ranges with only linear complexity. Our multi-level formulation is equivalent to recursively adding inducing points to the kernel matrix, unifying GNNs with multi-resolution matrix factorization of the kernel. Experiments confirm our multi-graph network learns discretization-invariant solution operators to PDEs and can be evaluated in linear time.

Nonparametric two-sample tests for equality of distributions are widely studied in statistics, driven by applications in goodness-of-fit tests, anomaly and change-point detection and clustering. Classical examples of such tests include the Kolmogorov-Smirnov test [41, 69, 62] and Wald-Wolfowitz runs test [84] with subsequent multivariate extensions [25]. Due to advances in the ability to collect large amounts of real time or spatially distributed data there is a need to develop statistical methods appropriate for functional data, where each data sample is a discretised function. Such data has been studied for decades in the Functional Data Analysis (FDA) literature [32, 35] particularly in the context of analysing populations of time series, or in statistical shape analysis [45]. More recently, due to this modern abundance of functional data, increased study has been made in the machine learning literature for algorithms suited to such data [7, 15, 37, 12, 88].

Health-aware control (HAC) has emerged as one of the domains where control synthesis is sought based upon the failure prognostics of system/component or the Remaining Useful Life (RUL) predictions of critical components. The fact that mathematical dynamic (transition) models of RUL are rarely available, makes it difficult for RUL information to be incorporated into the control paradigm. A novel framework for health aware control is presented in this paper where reinforcement learning based approach is used to learn an optimal control policy in face of component degradation by integrating global system transition data (generated by an analytical model that mimics the real system) and RUL predictions. The RUL predictions generated at each step, is tracked to a desired value of RUL. The latter is integrated within a cost function which is maximized to learn the optimal control. The proposed method is studied using simulation of a DC motor and shaft wear.

Central to the design of many robot systems and their controllers is solving a constrained blackbox optimization problem. This paper presents CNMA, a new method of solving this problem that is conservative in the number of potentially expensive blackbox function evaluations; allows specifying complex, even recursive constraints directly rather than as hard-to-design penalty or barrier functions; and is resilient to the non-termination of function evaluations. CNMA leverages the ability of neural networks to approximate any continuous function, their transformation into equivalent mixed integer linear programs (MILPs) and their optimization subject to constraints with industrial strength MILP solvers. A new learning-from-failure step guides the learning to be relevant to solving the constrained optimization problem. Thus, the amount of learning is orders of magnitude smaller than that needed to learn functions over their entire domains. CNMA is illustrated with the design of several robotic systems: wave-energy propelled boat, lunar lander, hexapod, cartpole, acrobot and parallel parking. These range from 6 real-valued dimensions to 36. We show that CNMA surpasses the Nelder-Mead, Gaussian and Random Search optimization methods against the metric of number of function evaluations.

Cross-modal retrieval relies on accurate models to retrieve relevant results for queries across modalities such as image, text, and video. In this paper, we build upon previous work by tackling the difficulty of evaluating models both quantitatively and qualitatively quickly. We present DIME (Dataset, Index, Model, Embedding), a modality-agnostic tool that handles multimodal datasets, trained models, and data preprocessors to support straightforward model comparison with a web browser graphical user interface. DIME inherently supports building modality-agnostic queryable indexes and extraction of relevant feature embeddings, and thus effectively doubles as an efficient cross-modal tool to explore and search through datasets.

Due to the advancements in cellular technologies and the dense deployment of cellular infrastructure, integrating unmanned aerial vehicles (UAVs) into the fifth-generation (5G) and beyond cellular networks is a promising solution to achieve safe UAV operation as well as enabling diversified applications with mission-specific payload data delivery. In particular, 5G networks need to support three typical usage scenarios, namely, enhanced mobile broadband (eMBB), ultra-reliable low-latency communications (URLLC), and massive machine-type communications (mMTC). On the one hand, UAVs can be leveraged as cost-effective aerial platforms to provide ground users with enhanced communication services by exploiting their high cruising altitude and controllable maneuverability in three-dimensional (3D) space. On the other hand, providing such communication services simultaneously for both UAV and ground users poses new challenges due to the need for ubiquitous 3D signal coverage as well as the strong air-ground network interference. Besides the requirement of high-performance wireless communications, the ability to support effective and efficient sensing as well as network intelligence is also essential for 5G-and-beyond 3D heterogeneous wireless networks with coexisting aerial and ground users. In this paper, we provide a comprehensive overview of the latest research efforts on integrating UAVs into cellular networks, with an emphasis on how to exploit advanced techniques (e.g., intelligent reflecting surface, short packet transmission, energy harvesting, joint communication and radar sensing, and edge intelligence) to meet the diversified service requirements of next-generation wireless systems. Moreover, we highlight important directions for further investigation in future work.

This letter addresses the 3D coverage path planning (CPP) problem for terrain reconstruction of unknown obstacle rich environments. Due to sensing limitations, the proposed method, called CT-CPP, performs layered scanning of the 3D region to collect terrain data, where the traveling sequence is optimized using the concept of a coverage tree (CT). A modified TSP-based tree traversal strategy is proposed, and compared with breadth-first search (BFS) and depth-first search (DFS) methods, with TSP providing the shortest trajectory lengths. The CT-CPP method is validated on a high-fidelity underwater simulator and the results are evaluated in comparison to an existing terrain following CPP method (TF-CPP). The CT-CPP with TSP optimizer yields significant improvements in trajectory length, energy consumption, and reconstruction error.

Confucius once said, "Fish forget they live in water; people forget they live in the Tao" (Lin, 2007). Analogously, it may be easy for data scientists to forget they live in a world defined and permeated by mathematics. The two pieces, "Ten Research Challenge Areas in Data Science" by Jeannette M. Wing and "Challenges and Opportunities in Statistics and Data Science: Ten Research Areas" by Xuming He and Xihong Lin, provide an impressively complete list of data science challenges from luminaries in the field of data science. They have done an extraordinary job, so this response offers a complementary viewpoint from a mathematical perspective and evangelizes advanced mathematics as a key tool for meeting the challenges they have laid out. Notably, we pick up the themes of scientific understanding of machine learning and deep learning, computational considerations such as cloud computing and scalability, balancing computational and statistical considerations, and inference with limited data.

Facebook and Carnegie Mellon University have announced they are trying to use artificial intelligence (AI) to find new "electrocatalysts" that can help to store electricity generated by renewable energy sources. Electrocatalysts can be used to convert excess solar and wind power into other fuels, such as hydrogen and ethanol, that are easier to store. However, today's electrocatalysts are rare and expensive, with platinum being a good example, and finding new ones hasn't been easy as there are billions of ways that elements can be combined to make them. Researchers in the catalysis community can currently test tens of thousands of potential catalysts a year but Facebook and Carniegie Mellon believe they can increase the number to millions, or even billions, of catalysts with the help of AI. The social media giant and the university on Wednesday released some of their own AI software "models" that can help to find new catalysts but they want other scientists to have a go as well.

Learning to optimize (L2O) has gained increasing attention since classical optimizers require laborious problem-specific design and hyperparameter tuning. However, there is a gap between the practical demand and the achievable performance of existing L2O models. Specifically, those learned optimizers are applicable to only a limited class of problems, and often exhibit instability. With many efforts devoted to designing more sophisticated L2O models, we argue for another orthogonal, under-explored theme: the training techniques for those L2O models. We show that even the simplest L2O model could have been trained much better. We first present a progressive training scheme to gradually increase the optimizer unroll length, to mitigate a well-known L2O dilemma of truncation bias (shorter unrolling) versus gradient explosion (longer unrolling). We further leverage off-policy imitation learning to guide the L2O learning, by taking reference to the behavior of analytical optimizers. Our improved training techniques are plugged into a variety of state-of-the-art L2O models, and immediately boost their performance, without making any change to their model structures. Especially, by our proposed techniques, an earliest and simplest L2O model can be trained to outperform the latest complicated L2O models on a number of tasks. Our results demonstrate a greater potential of L2O yet to be unleashed, and urge to rethink the recent progress. Our codes are publicly available at: https://github.com/VITA-Group/L2O-Training-Techniques.