The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying attractor. Chaotic systems thus pose a unique challenge to modern statistical learning techniques, while retaining quantifiable mathematical properties that make them controllable and interpretable as benchmarks. Here, we present a growing database currently comprising 131 known chaotic dynamical systems spanning fields such as astrophysics, climatology, and biochemistry. Each system is paired with precomputed multivariate and univariate time series. Our dataset has comparable scale to existing static time series databases; however, our systems can be re-integrated to produce additional datasets of arbitrary length and granularity. Our dataset is annotated with known mathematical properties of each system, and we perform feature analysis to broadly categorize the diverse dynamics present across the collection. Chaotic systems inherently challenge forecasting models, and across extensive benchmarks we correlate forecasting performance with the degree of chaos present. We also exploit the unique generative properties of our dataset in several proof-of-concept experiments: surrogate transfer learning to improve time series classification, importance sampling to accelerate model training, and benchmarking symbolic regression algorithms.
Failure in brittle materials led by the evolution of micro- to macro-cracks under repetitive or increasing loads is often catastrophic with no significant plasticity to advert the onset of fracture. Early failure detection with respective location are utterly important features in any practical application, both of which can be effectively addressed using artificial intelligence. In this paper, we develop a supervised machine learning (ML) framework to predict failure in an isothermal, linear elastic and isotropic phase-field model for damage and fatigue of brittle materials. Time-series data of the phase-field model is extracted from virtual sensing nodes at different locations of the geometry. A pattern recognition scheme is introduced to represent time-series data/sensor nodes responses as a pattern with a corresponding label, integrated with ML algorithms, used for damage classification with identified patterns. We perform an uncertainty analysis by superposing random noise to the time-series data to assess the robustness of the framework with noise-polluted data. Results indicate that the proposed framework is capable of predicting failure with acceptable accuracy even in the presence of high noise levels. The findings demonstrate satisfactory performance of the supervised ML framework, and the applicability of artificial intelligence and ML to a practical engineering problem, i.,e, data-driven failure prediction in brittle materials.
A theoretical framework that supports automated construction of dynamic prime models purely from experimental time series data has been invented and developed, which can automatically generate (construct) data-driven models of any time series data in seconds. This has resulted in the formulation and formalisation of new reverse engineering and dynamic methods for automated systems modelling of complex systems, including complex biological, financial, control, and artificial neural network systems. The systems/model theory behind the invention has been formalised as a new, effective and robust system identification strategy complementary to process-based modelling. The proposed dynamic modelling and network inference solutions often involve tackling extremely difficult parameter estimation challenges, inferring unknown underlying network structures, and unsupervised formulation and construction of smart and intelligent ODE models of complex systems. In underdetermined conditions, i.e., cases of dealing with how best to instantaneously and rapidly construct data-consistent prime models of unknown (or well-studied) complex system from small-sized time series data, inference of unknown underlying network of interaction is more challenging. This article reports a robust step-by-step mathematical and computational analysis of the entire prime model construction process that determines a model from data in less than a minute.
Contributions: Prior studies on education have mostly followed the model of the cross sectional study, namely, examining the pretest and the posttest scores. This paper shows that students' knowledge throughout the intervention can be estimated by time series analysis using a hidden Markov model. Background: Analyzing time series and the interaction between the students and the game data can result in valuable information that cannot be gained by only cross sectional studies of the exams. Research Questions: Can a hidden Markov model be used to analyze the educational games? Can a hidden Markov model be used to make a prediction of the students' performance? Methodology: The study was conducted on (N=854) students who played the Save Patch game. Students were divided into class 1 and class 2. Class 1 students are those who scored lower in the test than class 2 students. The analysis is done by choosing various features of the game as the observations. Findings: The state trajectories can predict the students' performance accurately for both class 1 and class 2.
Neural Controlled Differential Equations (Neural CDEs) are the continuous-time analogue of an RNN, just as Neural ODEs are analogous to ResNets. However just like RNNs, training Neural CDEs can be difficult for long time series. Here, we propose to apply a technique drawn from stochastic analysis, namely the log-ODE method. Instead of using the original input sequence, our procedure summarises the information over local time intervals via the log-signature map, and uses the resulting shorter stream of log-signatures as the new input. This represents a length/channel trade-off. In doing so we demonstrate efficacy on problems of length up to 17k observations and observe significant training speed-ups, improvements in model performance, and reduced memory requirements compared to the existing algorithm.
Following the increasingly popular trend of social interaction analysis in egocentric vision, this manuscript presents a comprehensive study for automatic social pattern characterization of a wearable photo-camera user, by relying on the visual analysis of egocentric photo-streams. The proposed framework consists of three major steps. The first step is to detect social interactions of the user where the impact of several social signals on the task is explored. The detected social events are inspected in the second step for categorization into different social meetings. These two steps act at event-level where each potential social event is modeled as a multi-dimensional time-series, whose dimensions correspond to a set of relevant features for each task, and LSTM is employed to classify the time-series. The last step of the framework is to characterize social patterns, which is essentially to infer the diversity and frequency of the social relations of the user through discovery of recurrences of the same people across the whole set of social events of the user. Experimental evaluation over a dataset acquired by 9 users demonstrates promising results on the task of social pattern characterization from egocentric photo-streams.
We represent the sequence of fMRI (Functional Magnetic Resonance Imaging) brain volumes recorded during a cognitive stimulus by a graph which consists of a set of local meshes. The corresponding cognitive process, encoded in the brain, is then represented by these meshes each of which is estimated assuming a linear relationship among the voxel time series in a predefined locality. First, we define the concept of locality in two neighborhood systems, namely, the spatial and functional neighborhoods. Then, we construct spatially and functionally local meshes around each voxel, called seed voxel, by connecting it either to its spatial or functional p-nearest neighbors. The mesh formed around a voxel is a directed sub-graph with a star topology, where the direction of the edges is taken towards the seed voxel at the center of the mesh. We represent the time series recorded at each seed voxel in terms of linear combination of the time series of its p-nearest neighbors in the mesh. The relationships between a seed voxel and its neighbors are represented by the edge weights of each mesh, and are estimated by solving a linear regression equation. The estimated mesh edge weights lead to a better representation of information in the brain for encoding and decoding of the cognitive tasks. We test our model on a visual object recognition and emotional memory retrieval experiments using Support Vector Machines that are trained using the mesh edge weights as features. In the experimental analysis, we observe that the edge weights of the spatial and functional meshes perform better than the state-of-the-art brain decoding models.
Parameterized state space models in the form of recurrent networks are often used in machine learning to learn from data streams exhibiting temporal dependencies. To break the black box nature of such models it is important to understand the dynamical features of the input driving time series that are formed in the state space. We propose a framework for rigorous analysis of such state representations in vanishing memory state space models such as echo state networks (ESN). In particular, we consider the state space a temporal feature space and the readout mapping from the state space a kernel machine operating in that feature space. We show that: (1) The usual ESN strategy of randomly generating input-to-state, as well as state coupling leads to shallow memory time series representations, corresponding to cross-correlation operator with fast exponentially decaying coefficients; (2) Imposing symmetry on dynamic coupling yields a constrained dynamic kernel matching the input time series with straightforward exponentially decaying motifs or exponentially decaying motifs of the highest frequency; (3) Simple cycle high-dimensional reservoir topology specified only through two free parameters can implement deep memory dynamic kernels with a rich variety of matching motifs. We quantify richness of feature representations imposed by dynamic kernels and demonstrate that for dynamic kernel associated with cycle reservoir topology, the kernel richness undergoes a phase transition close to the edge of stability.
Medical crowdfunding is a popular channel for people needing financial help paying medical bills to collect donations from large numbers of people. However, large heterogeneity exists in donations across cases, and fundraisers face significant uncertainty in whether their crowdfunding campaigns can meet fundraising goals. Therefore, it is important to provide early warnings for fundraisers if such a channel will eventually fail. In this study, we aim to develop novel algorithms to provide accurate and timely predictions of fundraising performance, to better inform fundraisers. In particular, we propose a new approach to combine time-series features and time-invariant features in the deep learning model, to process diverse sources of input data. Compared with baseline models, our model achieves better accuracy and requires a shorter observation window of the time-varying features from the campaign launch to provide robust predictions with high confidence. To extract interpretable insights, we further conduct a multivariate time-series clustering analysis and identify four typical temporal donation patterns. This demonstrates the heterogeneity in the features and how they relate to the fundraising outcome. The prediction model and the interpretable insights can be applied to assist fundraisers with better promoting their fundraising campaigns and can potentially help crowdfunding platforms to provide more timely feedback to all fundraisers. Our proposed framework is also generalizable to other fields where diverse structured and unstructured data are valuable for predictions.
Tens of millions of new variable objects are expected to be identified in over a billion time series from the Gaia mission. Crossmatching known variable sources with those from Gaia is crucial to incorporate current knowledge, understand how these objects appear in the Gaia data, train supervised classifiers to recognise known classes, and validate the results of the Variability Processing and Analysis Coordination Unit (CU7) within the Gaia Data Analysis and Processing Consortium (DPAC). The method employed by CU7 to crossmatch variables for the first Gaia data release includes a binary classifier to take into account positional uncertainties, proper motion, targeted variability signals, and artefacts present in the early calibration of the Gaia data. Crossmatching with a classifier makes it possible to automate all those decisions which are typically made during visual inspection. The classifier can be trained with objects characterized by a variety of attributes to ensure similarity in multiple dimensions (astrometry, photometry, time-series features), with no need for a-priori transformations to compare different photometric bands, or of predictive models of the motion of objects to compare positions. Other advantages as well as some disadvantages of the method are discussed. Implementation steps from the training to the assessment of the crossmatch classifier and selection of results are described.
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