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Continuous deep learning models, referred to as Neural Ordinary Differential Equations (Neural ODEs), have received considerable attention over the last several years. Despite their burgeoning impact, there is a lack of formal analysis…

Inferring stochastic dynamics from data is central across the sciences, yet in many applications only unordered, non-sequential measurements are available-often restricted to limited regions of state space-so standard time-series methods do…

This paper studies the local observability of synchronous machines using a unified approach. Recently, motion sensorless control of electrical drives has gained high interest. The main challenge for such a technology is the poor performance…

Parameter identifiability is a structural property of an ODE model for recovering the values of parameters from the data (i.e., from the input and output variables). This property is a prerequisite for meaningful parameter identification in…

This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…

Structural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications…

Ordinary differential equations (ODEs) are foundational in modeling intricate dynamics across a gamut of scientific disciplines. Yet, a possibility to represent a single phenomenon through multiple ODE models, driven by different…

Recently, learning-based ego-motion estimation approaches have drawn strong interest from studies mostly focusing on visual perception. These groundbreaking works focus on unsupervised learning for odometry estimation but mostly for visual…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

Out-of-distribution (OoD) detection for data-based programs is a goal of paramount importance. Common approaches in the literature tend to train detectors requiring inside-of-distribution (in-distribution, or IoD) and OoD validation…

From organisms to machines, autonomous systems rely on measured sensory cues to estimate unknown information about themselves or their environment. For nonlinear systems, strategic sensor motion can be leveraged to extract otherwise…

Discovering hidden physical laws and identifying governing system parameters from sparse observations are central challenges in computational science and engineering. Existing data-driven methods, such as physics-informed neural networks…

Lines provide the significantly richer geometric structural information about the environment than points, so lines are widely used in recent Visual Odometry (VO) works. Since VO with lines use line tracking results to locate and map, line…

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…

In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…

We present an algorithm for marginalising changepoints in time-series models that assume a fixed number of unknown changepoints. Our algorithm is differentiable with respect to its inputs, which are the values of latent random variables…

In this paper, we introduce the concept of observability of targeted state variables for systems that may not be fully observable. For their estimation, we introduce and exemplify a deep filter, which is a neural network specifically…

This technical report provides the description and the derivation of a novel nonlinear unknown input and state estimation algorithm (NUISE) for mobile robots. The algorithm is designed for real-world robots with nonlinear dynamic models and…

The classical theory of Kosambi-Cartan-Chern (KCC) developed in differential geometry provides a powerful method for analyzing the behaviors of dynamical systems. In the KCC theory, the properties of a dynamical system are described in…

Given ample experimental data from a system governed by differential equations, it is possible to use deep learning techniques to construct the underlying differential operators. In this work we perform symbolic discovery of differential…