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Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…
Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and…
Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating…
Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski et al. (Phys. Rev. Lett. 109 024101, 2012) introduced a method based on…
Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…
Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string,…
We propose a new adequacy test and a graphical evaluation tool for nonlinear dynamic models. The proposed techniques can be applied in any setup where parametric conditional distribution of the data is specified, in particular to models…
Many safety-critical scientific and engineering systems evolve according to differential-algebraic equations (DAEs), where dynamical behavior is constrained by physical laws and admissibility conditions. In practice, these systems operate…
Spatiotemporal dynamics pervade the natural sciences, from the morphogen dynamics underlying patterning in animal pigmentation to the protein waves controlling cell division. A central challenge lies in understanding how controllable…
Mixed-signal neuromorphic processors with brain-like organization and device physics offer an ultra-low-power alternative to the unsustainable developments of conventional deep learning and computing. However, realizing the potential of…
Standard representation probing for visual models relies on mathematically permutation-invariant operations like Global Average Pooling (GAP) or CLS tokens, treating patch representations as an unstructured bag-of-words. We challenge this…
Equations governing the nonlinear dynamics of complex systems are usually unknown and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences…
The moment quantities associated with the nonlinear Schrodinger equation offer important insights towards the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment…
Supervised machine learning approaches require the formulation of a loss functional to be minimized in the training phase. Sequential data are ubiquitous across many fields of research, and are often treated with Euclidean distance-based…
We propose a general dynamic reduced-order modeling framework for typical experimental data: time-resolved sensor data and optional non-time-resolved PIV snapshots. This framework contains four steps. First, the sensor signals are lifted to…
The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…
Evolving data streams induce joint nonstationarity in continual semantic segmentation, where semantic classes, input distributions, and supervision availability change simultaneously over time. This setting reflects practical structured…
We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to…
Understanding the dynamic nature of biological systems is fundamental to deciphering cellular behavior, developmental processes, and disease progression. Single-cell RNA sequencing (scRNA-seq) has provided static snapshots of gene…