Related papers: Joint Parameter Discovery and Generative Modeling …
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…
Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…
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…
Extracting physical dynamical system parameters from recorded observations is key in natural science. Current methods for automatic parameter estimation from video train supervised deep networks on large datasets. Such datasets require…
Reconstructing the equation of motion and thus the network topology of a system from time series is a very important problem. Although many powerful methods have been developed, it remains a great challenge to deal with systems in high…
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…
The observation and description of collective excitations in solids is a fundamental issue when seeking to understand the physics of a many-body system. Analysis of these excitations is usually carried out by measuring the dynamical…
We present a data-driven numerical approach for modeling unknown dynamical systems with missing/hidden parameters. The method is based on training a deep neural network (DNN) model for the unknown system using its trajectory data. A key…
This paper presents a data-driven algorithm for simultaneous system identification and parameter estimation in control-affine nonlinear systems. Parameter estimation is achieved by training a data-driven predictive model using state-action…
Parameter estimation in structural dynamics generally involves inferring the values of physical, geometric, or even customized parameters based on first principles or expert knowledge, which is challenging for complex structural systems. In…
Accurately estimating parameters in complex nonlinear systems is crucial across scientific and engineering fields. We present a novel approach for parameter estimation using a neural network with the Huber loss function. This method taps…
Modeling dynamical systems plays a crucial role in capturing and understanding complex physical phenomena. When physical models are not sufficiently accurate or hardly describable by analytical formulas, one can use generic function…
We propose a hybrid meta-learning framework for forecasting and anomaly detection in nonlinear dynamical systems characterized by nonstationary and stochastic behavior. The approach integrates a physics-inspired simulator that captures…
Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering. Traditional stability and receptivity…
Physics-based and first-principles models pervade the engineering and physical sciences, allowing for the ability to model the dynamics of complex systems with a prescribed accuracy. The approximations used in deriving governing equations…
Structural monitoring for complex built environments often suffers from mismatch between design, laboratory testing, and actual built parameters. Additionally, real-world structural identification problems encounter many challenges. For…
Multivariate oscillatory signals from complex systems often exhibit non-stationary dynamics and metastable regime structure, making dynamical interpretation challenging. We introduce a ``dynamical microscope'' framework that converts…
Distilling analytical models from data has the potential to advance our understanding and prediction of nonlinear dynamics. Although discovery of governing equations based on observed system states (e.g., trajectory time series) has…
This paper presents a general framework for estimating high-dimensional conditional latent factor models via constrained nuclear norm regularization. We establish large sample properties of the estimators and provide efficient algorithms…
Dynamical systems, that are used to model power grids, the brain, and other physical systems, can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may…