Multivariate time series classification (MTSC) has broad applications in numerous domains. Existing MTSC methods typically focus on either temporal dynamics or variable interactions of the data, often overlooking cross-scale couplings among different variables. To bridge this gap, we propose Scale-Variable Graph Learning (SVGL), a novel framework that effectively captures data-inherent scale-variable interactions for MTSC. SVGL begins with spectral analysis to adaptively identify key periodic scales for each variable. A period-aware reservoir computing network is then incorporated to fit the variable at these scales, encoding the sequential and periodic dynamics into multi-scale dynamic representations. Subsequently, we construct a scale-variable graph to model interactions of the encoded temporal dynamics, where nodes represent scale-variable pairs and edges denote their correlations. After sparsely initializing the graph via nearest neighbors, a parallel graph learning architecture is integrated in SVGL, combining global graph convolutional and sample-specific graph attention to aggregate effective features for classification. Extensive experiments on 30 UEA datasets demonstrate that SVGL outperforms state-of-the-art baselines in accuracy and maintains low training overhead.

Anomaly detection in sequential signals is gaining prominence, especially with limited training data and timeliness requirements. Fully extracting the data-inside changing information, we propose a novel Wavelet-Enhanced Reservoir Computing framework (WE-Res). Our framework uses Discrete Wavelet Transform (DWT) to decompose signals for multi-level detail and trend extraction recursively. Each level is fitted using an Echo State Network (ESN) respectively, extracting its inside dynamic features into fitted models. Integrating these dynamic features creates a "multi-level dynamic feature" that enhances signal representation, aiding in distinguishing between normal and anomalous patterns. We further introduce a dual-objective optimization to refine ESNs’ reservoirs, increasing the fitting accuracy and improving category discrimination among the captured features. Validation on real-world data confirms our method’s effectiveness, especially in data-limited scenarios and less training time compared to recent baselines.

Fault Diagnosis (FD) in time-varying systems faces challenges like limited training data, varying environments, and timeliness. Building upon the framework of model-space learning (MSL), we introduce co-objective learning in Dynamic-Integration network (DynInt) model space as a solution for FD. MSL involves utilizing well-fitted models that capture the dynamics within the data as more stable and parsimonious representations of the original data. DynInt integrates pooling and reservoir computing to adequately capture the data-inherent multi-scale dynamics. Representing the signal with the fitted DynInt model transforms the original signal from data space into the DynInt model space. A co-objective optimization is further introduced on DynInt, improving the fitting accuracy and category discrimination. Validation on real-world data confirms our method’s effectiveness, especially in data-limited scenarios.

Neural implicit reconstruction via volume rendering has demonstrated its effectiveness in recovering dense 3D surfaces. However, it is non-trivial to simultaneously recover meticulous geometry and preserve smoothness across regions with differing characteristics. To address this issue, previous methods typically employ geometric priors, which are often constrained by the performance of the prior models. In this paper, we propose ND-SDF, which learns a Normal Deflection field to represent the angular deviation between the scene normal and the prior normal. Unlike previous methods that uniformly apply geometric priors on all samples, introducing significant bias in accuracy, our proposed normal deflection field dynamically learns and adapts the utilization of samples based on their specific characteristics, thereby improving both the accuracy and effectiveness of the model. Our method not only obtains smooth weakly textured regions such as walls and floors but also preserves the geometric details of complex structures. In addition, we introduce a novel ray sampling strategy based on the deflection angle to facilitate the unbiased rendering process, which significantly improves the quality and accuracy of intricate surfaces, especially on thin structures. Consistent improvements on various challenging datasets demonstrate the superiority of our method.

Fault Diagnosis (FD) in time-varying data presents considerations such as limited training data, intra- and inter-dimensional correlations, and constraints of training time. In response, this paper introduces FD in the Reservoir-Embedded-Directional Network (REDNet) model space. Model-oriented methods utilize well-fitted networks or functions, denoted as "models" that capture data's changing information, as more stable and parsimonious representations of the data. Our approach employs REDNet for data fitting, wherein multiple reservoirs are organized along intrinsic correlation directions to establish intra- and inter-dimensional dependencies, thereby capturing multi-directional dynamics in high-dimensional data. Representing each data instance with an independently fitted REDNet model maps these instances into a class-separable REDNet model space, where FD could be performed on the models rather than the original data. Concentrating on the data-intrinsic dynamics, our method achieves rapid training speeds, and maintains robust performance even with minimal training data. Experiments on several datasets demonstrate its effectiveness.