Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions that exhibit heterogeneous properties, requiring multiple sensors to handle functions with minimal regularity. To address this issue, discretization-invariant neural operators have been used, allowing the sampling of diverse input functions with different sensor locations. However, existing frameworks still require an equal number of sensors for all functions. In our study, we propose a novel distributed approach to further relax the discretization requirements and solve the heterogeneous dataset challenges. Our method involves partitioning the input function space and processing individual input functions using independent and separate neural networks. A centralized neural network is used to handle shared information across all output functions. This distributed methodology reduces the number of gradient descent back-propagation steps, improving efficiency while maintaining accuracy. We demonstrate that the corresponding neural network is a universal approximator of continuous nonlinear operators and present four numerical examples to validate its performance.
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Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively expensive. In order to save computational cost, one can construct surrogate models by expressing the system in a low-dimensional basis, obtained from training data. This is referred to as model reduction. Past investigations have shown that, when performing model reduction of Hamiltonian systems, it is crucial to preserve the symplectic structure associated with the system in order to ensure long-term numerical stability. Up to this point structure-preserving reductions have largely been limited to linear transformations. We propose a new neural network architecture in the spirit of autoencoders, which are established tools for dimension reduction and feature extraction in data science, to obtain more general mappings. In order to train the network, a non-standard gradient descent approach is applied that leverages the differential-geometric structure emerging from the network design. The new architecture is shown to significantly outperform existing designs in accuracy.
Many functions characterising physical systems are additively separable. This is the case, for instance, of mechanical Hamiltonian functions in physics, population growth equations in biology, and consumer preference and utility functions in economics. We consider the scenario in which a surrogate of a function is to be tested for additive separability. The detection that the surrogate is additively separable can be leveraged to improve further learning. Hence, it is beneficial to have the ability to test for such separability in surrogates. The mathematical approach is to test if the mixed partial derivative of the surrogate is zero; or empirically, lower than a threshold. We present and comparatively and empirically evaluate the eight methods to compute the mixed partial derivative of a surrogate function.
Krylov subspace, which is generated by multiplying a given vector by the matrix of a linear transformation and its successive powers, has been extensively studied in classical optimization literature to design algorithms that converge quickly for large linear inverse problems. For example, the conjugate gradient method (CG), one of the most popular Krylov subspace methods, is based on the idea of minimizing the residual error in the Krylov subspace. However, with the recent advancement of high-performance diffusion solvers for inverse problems, it is not clear how classical wisdom can be synergistically combined with modern diffusion models. In this study, we propose a novel and efficient diffusion sampling strategy that synergistically combine the diffusion sampling and Krylov subspace methods. Specifically, we prove that if the tangent space at a denoised sample by Tweedie's formula forms a Krylov subspace, then the CG initialized with the denoised data ensures the data consistency update to remain in the tangent space. This negates the need to compute the manifold-constrained gradient (MCG), leading to a more efficient diffusion sampling method. Our method is applicable regardless of the parametrization and setting (i.e., VE, VP). Notably, we achieve state-of-the-art reconstruction quality on challenging real-world medical inverse imaging problems, including multi-coil MRI reconstruction and 3D CT reconstruction. Moreover, our proposed method achieves more than 80 times faster inference time than the previous state-of-the-art method.
The far-field channel model has historically been used in wireless communications due to the simplicity of mathematical modeling and convenience for algorithm design. With the need for high data rates, low latency, and ubiquitous connectivity in the sixth generation (6G) of communication systems, new technology enablers such as extremely large antenna arrays (ELAAs), reconfigurable intelligent surfaces (RISs), and distributed multiple-input-multiple-output (D-MIMO) systems will be adopted. These enablers not only aim to improve communication services but also have an impact on localization and sensing (L&S), which are expected to be fundamentally built-in functionalities in future wireless systems. Despite appearing in different scenarios and supporting different frequency bands, such enablers share the so-called near-field (NF) features, which will provide extra geometric information conducive to L&S. In this work, we describe the NF features, namely, the spherical wave model, spatial non-stationarity, and beam squint effect. After discussing how L&S see NF differently from communication, the opportunities and open research challenges are provided.
A robust authentication and authorization mechanism is imperative in modular system development, where modularity and modular thinking are pivotal. Traditional systems often employ identity modules responsible for authentication and token issuance. Tokens, representing user credentials, offer advantages such as reduced reliance on passwords, limited lifespan, and scoped access. Despite these benefits, the "bearer token" problem persists, leaving systems vulnerable to abuse if tokens are compromised. We propose a token-based authentication mechanism addressing modular systems' critical bearer token problem. The proposed mechanism includes a novel RAF (Recursive Augmented Fernet) token, a blacklist component, and a policy enforcer component. RAF tokens are one-time-use tokens, like tickets. They carry commands, and the receiver of an RAF token can issue new tokens using the received RAF token. The blacklist component guarantees an RAF token can not be approved more than once, and the policy enforcer checks the compatibility of commands carried by an RAF token. We introduce two variations of RAF tokens: User-tied RAF, offering simplicity and compatibility, and Fully-tied RAF, providing enhanced security through service-specific secret keys. We thoroughly discuss the security guarantees, technical definitions, and construction of RAF tokens backed by game-based proofs. We demonstrate a proof of concept in the context of OpenStack, involving modifications to Keystone and creating an RAFT library. The experimental results reveal minimal overhead in typical scenarios, establishing the practicality and effectiveness of RAF. Our experiments show that the RAF mechanism beats the idea of using short-life Fernet tokens while providing much better security.
Precise arbitrary trajectory tracking for quadrotors is challenging due to unknown nonlinear dynamics, trajectory infeasibility, and actuation limits. To tackle these challenges, we present Deep Adaptive Trajectory Tracking (DATT), a learning-based approach that can precisely track arbitrary, potentially infeasible trajectories in the presence of large disturbances in the real world. DATT builds on a novel feedforward-feedback-adaptive control structure trained in simulation using reinforcement learning. When deployed on real hardware, DATT is augmented with a disturbance estimator using L1 adaptive control in closed-loop, without any fine-tuning. DATT significantly outperforms competitive adaptive nonlinear and model predictive controllers for both feasible smooth and infeasible trajectories in unsteady wind fields, including challenging scenarios where baselines completely fail. Moreover, DATT can efficiently run online with an inference time less than 3.2 ms, less than 1/4 of the adaptive nonlinear model predictive control baseline
Graphs are used widely to model complex systems, and detecting anomalies in a graph is an important task in the analysis of complex systems. Graph anomalies are patterns in a graph that do not conform to normal patterns expected of the attributes and/or structures of the graph. In recent years, graph neural networks (GNNs) have been studied extensively and have successfully performed difficult machine learning tasks in node classification, link prediction, and graph classification thanks to the highly expressive capability via message passing in effectively learning graph representations. To solve the graph anomaly detection problem, GNN-based methods leverage information about the graph attributes (or features) and/or structures to learn to score anomalies appropriately. In this survey, we review the recent advances made in detecting graph anomalies using GNN models. Specifically, we summarize GNN-based methods according to the graph type (i.e., static and dynamic), the anomaly type (i.e., node, edge, subgraph, and whole graph), and the network architecture (e.g., graph autoencoder, graph convolutional network). To the best of our knowledge, this survey is the first comprehensive review of graph anomaly detection methods based on GNNs.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
In multi-turn dialog, utterances do not always take the full form of sentences \cite{Carbonell1983DiscoursePA}, which naturally makes understanding the dialog context more difficult. However, it is essential to fully grasp the dialog context to generate a reasonable response. Hence, in this paper, we propose to improve the response generation performance by examining the model's ability to answer a reading comprehension question, where the question is focused on the omitted information in the dialog. Enlightened by the multi-task learning scheme, we propose a joint framework that unifies these two tasks, sharing the same encoder to extract the common and task-invariant features with different decoders to learn task-specific features. To better fusing information from the question and the dialog history in the encoding part, we propose to augment the Transformer architecture with a memory updater, which is designed to selectively store and update the history dialog information so as to support downstream tasks. For the experiment, we employ human annotators to write and examine a large-scale dialog reading comprehension dataset. Extensive experiments are conducted on this dataset, and the results show that the proposed model brings substantial improvements over several strong baselines on both tasks. In this way, we demonstrate that reasoning can indeed help better response generation and vice versa. We release our large-scale dataset for further research.
Image segmentation is still an open problem especially when intensities of the interested objects are overlapped due to the presence of intensity inhomogeneity (also known as bias field). To segment images with intensity inhomogeneities, a bias correction embedded level set model is proposed where Inhomogeneities are Estimated by Orthogonal Primary Functions (IEOPF). In the proposed model, the smoothly varying bias is estimated by a linear combination of a given set of orthogonal primary functions. An inhomogeneous intensity clustering energy is then defined and membership functions of the clusters described by the level set function are introduced to rewrite the energy as a data term of the proposed model. Similar to popular level set methods, a regularization term and an arc length term are also included to regularize and smooth the level set function, respectively. The proposed model is then extended to multichannel and multiphase patterns to segment colourful images and images with multiple objects, respectively. It has been extensively tested on both synthetic and real images that are widely used in the literature and public BrainWeb and IBSR datasets. Experimental results and comparison with state-of-the-art methods demonstrate that advantages of the proposed model in terms of bias correction and segmentation accuracy.
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