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We address the problem of learning the parameters of a stable linear time invariant (LTI) system or linear dynamical system (LDS) with unknown latent space dimension, or order, from a single time--series of noisy input-output data. We focus…

Powerful deep learning tools, such as convolutional neural networks (CNN), are able to learn the input-output relationships of large complicated systems directly from data. Encoder-decoder deep CNNs are able to extract features directly…

A major tenet in theoretical neuroscience is that cognitive and behavioral processes are ultimately implemented in terms of the neural system dynamics. Accordingly, a major aim for the analysis of neurophysiological measurements should lie…

We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). We use observed data to locate a low-dimensional, attracting slow SSM and compute a…

Diffusion models have been used for probabilistic time series forecasting and show strong potential. However, fixed noise schedules often produce intermediate states that are hard to invert and a terminal state that deviates from the near…

We consider the problem of making a quick decision in favor of one of two possible physical signal models while the numerical measurements are acquired by sensing devices featuring minimal digitization complexity. Therefore, the digital…

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

Deep generative models for anomaly detection in multivariate time-series are typically trained by maximizing data likelihood. However, likelihood in observation space measures marginal density rather than conformity to structured temporal…

We show how the recent extension of spectral submanifold (SSM) theory to delay differential equations (DDEs) enables data-driven model reduction of nonlinear delay systems. First, using a scalar DDE with a single discrete delay, we compare…

Foresighted robot navigation in dynamic indoor environments with cost-efficient hardware necessitates the use of a lightweight yet dependable controller. So inferring the scene dynamics from sensor readings without explicit object tracking…

Time series data is a prevalent form of data found in various fields. It consists of a series of measurements taken over time. Forecasting is a crucial application of time series models, where future values are predicted based on historical…

We develop a data-driven framework for learning and correcting non-autonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need…

Model-based paradigms for decision-making and control are becoming ubiquitous in robotics. They rely on the ability to efficiently learn a model of the system from data. Structured Mechanical Models (SMMs) are a data-efficient black-box…

Event-driven sensors such as LiDAR and dynamic vision sensor (DVS) have found increased attention in high-resolution and high-speed applications. A lot of work has been conducted to enhance recognition accuracy. However, the essential topic…

We propose an efficient thermodynamics-informed latent space dynamics identification (tLaSDI) framework for the reduced-order modeling of parametric nonlinear dynamical systems. This framework integrates autoencoders for dimensionality…

Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all of the relevant state variables governing the dynamics. Delay embedding allows us, in principle, to account for unobserved state variables.…

Modeling high-dimensional, nonlinear dynamic structural systems under natural hazards presents formidable computational challenges, especially when simultaneously accounting for uncertainties in external loads and structural parameters.…

Anomaly detection is the task of detecting data which differs from the normal behaviour of a system in a given context. In order to approach this problem, data-driven models can be learned to predict current or future observations.…

State space models (SSMs) leverage linear, time-invariant (LTI) systems to effectively learn sequences with long-range dependencies. By analyzing the transfer functions of LTI systems, we find that SSMs exhibit an implicit bias toward…

The development of compact and energy-efficient wearable sensors has led to an increase in the availability of biosignals. To analyze these continuously recorded, and often multidimensional, time series at scale, being able to conduct…