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Recurrent neural networks (RNNs) are difficult to train on sequence processing tasks, not only because input noise may be amplified through feedback, but also because any inaccuracy in the weights has similar consequences as input noise. We…

Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems. Neural operators specifically employ deep neural networks to approximate…

Takens' Embedding Theorem remarkably established that concatenating M previous outputs of a dynamical system into a vector (called a delay coordinate map) can be a one-to-one mapping of a low-dimensional attractor from the system state…

Tasking machine learning to predict segments of a time series requires estimating the parameters of a ML model with input/output pairs from the time series. Using the equivalence between statistical data assimilation and supervised machine…

Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and…

A deep neural network (DNN) model consisting of two hidden layers was proposed for predicting the immediate environments of specific atoms based on X-ray absorption near-edge spectra (XANES). The output layer of the DNN can be adjusted to…

Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…

In the presence of system-environment coupling, classical complex systems undergo stochastic dynamics, where rich phenomena can emerge at large spatio-temporal scales. To investigate these phenomena, numerical approaches for simulating…

Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development…

Time series prediction is an important problem in machine learning. Previous methods for time series prediction did not involve additional information. With a lot of dynamic knowledge graphs available, we can use this additional information…

Machine learning (ML) tools such as encoder-decoder convolutional neural networks (CNN) can represent incredibly complex nonlinear functions which map between combinations of images and scalars. For example, CNNs can be used to map…

Recent work has focused on data-driven learning of the evolution of unknown systems via deep neural networks (DNNs), with the goal of conducting long term prediction of the dynamics of the unknown system. In many real-world applications,…

The identification of the governing equations of chaotic dynamical systems from data has recently emerged as a hot topic. While the seminal work by Brunton et al. reported proof-of-concepts for idealized observation setting for…

In long-term time series forecasting (LTSF) tasks, an increasing number of models have acknowledged that discrete time series originate from continuous dynamic systems and have attempted to model their dynamical structures. Recognizing the…

Time series anomaly detection has applications in a wide range of research fields and applications, including manufacturing and healthcare. The presence of anomalies can indicate novel or unexpected events, such as production faults, system…

Weather prediction is a quintessential problem involving the forecasting of a complex, nonlinear, and chaotic high-dimensional dynamical system. This work introduces an efficient reduced-order modeling (ROM) framework for short-range…

Given a sequence of sets, where each set contains an arbitrary number of elements, the problem of temporal sets prediction aims to predict the elements in the subsequent set. In practice, temporal sets prediction is much more complex than…

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

Machine learning (ML) tools such as encoder-decoder deep convolutional neural networks (CNN) are able to extract relationships between inputs and outputs of large complex systems directly from raw data. For time-varying systems the…

Extracting relevant properties of empirical signals generated by nonlinear, stochastic, and high-dimensional systems is a challenge of complex systems research. Open questions are how to differentiate chaotic signals from stochastic ones,…