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Dynamic mode decomposition (DMD) is a leading tool for equation-free analysis of high-dimensional dynamical systems from observations. In this work, we focus on a combination of delay-coordinates embedding and DMD, i.e., delay-coordinates…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

Exploring the idea of phase retrieval has been intriguing researchers for decades, due to its appearance in a wide range of applications. The task of a phase retrieval algorithm is typically to recover a signal from linear phaseless…

We produce new reconstructions of Northern Hemisphere annually averaged temperature anomalies back to 1000 AD, and explore the effects of including external climate forcings within the reconstruction and of accounting for short-memory and…

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as…

Latent dynamics discovery is challenging in extracting complex dynamics from high-dimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent…

We propose a simple method of constructing a system of differential equations of chaotic behavior based on the regression only from a scalar observable time-series data. The estimated system enables us to reconstruct invariant sets and…

We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…

Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that is routinely generated. In applications that are constrained by memory and computational intensity, excessively large…

Phase retrieval algorithms have become an important component in many modern computational imaging systems. For instance, in the context of ptychography and speckle correlation imaging, they enable imaging past the diffraction limit and…

Multi-scale problems, where variables of interest evolve in different time-scales and live in different state-spaces, can be found in many fields of science. Here, we introduce a new recursive methodology for Bayesian inference that aims at…

Time series forecasting plays a crucial role in diverse fields, necessitating the development of robust models that can effectively handle complex temporal patterns. In this article, we present a novel feature selection method embedded in…

When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are…

The low frequency variability of the extratropical atmosphere involves hemispheric-scale recurring, often persistent, states known as teleconnection patterns or regimes, which can have profound impact on predictability on intra-seasonal and…

In current seismic acquisition practice, there is an increasing drive for sparsely (in space) acquired data, often in irregular geometry. These surveys can trade off subsurface information for efficiency/cost - creating a problem of…

Patterned nanomagnet arrays (PNAs) have been shown to exhibit a strong geometrically frustrated dipole interaction. Some PNAs have also shown emergent domain wall dynamics. Previous works have demonstrated methods to physically probe these…

We propose a novel Bayesian approach to modelling nonlinear alignments of time series based on latent shared information. We apply the method to the real-world problem of finding common structure in the sensor data of wind turbines…

Many systems may switch to an undesired state due to internal failures or external perturbations, of which critical transitions toward degraded ecosystem states are a prominent example. Resilience restoration focuses on the ability of…

In meteorology, finding similar weather patterns or analogs in historical datasets can be useful for data assimilation, forecasting, and postprocessing. In climate science, analogs in historical and climate projection data are used for…

In scientific machine learning, the task of identifying partial differential equations accurately from sparse and noisy data poses a significant challenge. Current sparse regression methods may identify inaccurate equations on sparse and…