Related papers: Data-driven Discovery of Delay Differential Equati…
In this work, we define a practical identifiability criterion, (e, q)-identifiability, based on a parameter e, reflecting the noise in observed variables, and a parameter q, reflecting the mean-square error of the parameter estimator. This…
In differential equation discovery algorithms, a priori expert knowledge is mainly used implicitly to constrain the form of the expected equation, making it impossible for the algorithm to truly discover equations. Instead, most…
The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse…
In this paper we present an approach in which synchronization of chaos is used to address identification problems. In particular, we are able to identify: (i) the discontinuity points of systems described by piecewise dynamical equations…
One critical challenge of time-series modeling is how to learn and quickly correct the model under unknown distribution shifts. In this work, we propose a principled framework, called LiLY, to first recover time-delayed latent causal…
Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data. In many instances, such models are in the form of nonlinear partial differential equations…
Differential-algebraic equations (DAEs) integrate ordinary differential equations (ODEs) with algebraic constraints, providing a fundamental framework for developing models of dynamical systems characterized by timescale separation,…
In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model…
In this paper, we propose a novel data-driven framework for discovering probabilistic laws underlying the Feynman-Kac formula. Specifically, we introduce the first stochastic SINDy method formulated under the risk-neutral probability…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
Discovering conservation laws for a given dynamical system is important but challenging. In a theorist setup (differential equations and basis functions are both known), we propose the Sparse Invariant Detector (SID), an algorithm that…
In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving…
Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…
This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear…
Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…
Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…
To model time series accurately is important within a wide range of fields. As the world is generally too complex to be modelled exactly, it is often meaningful to assess the probability of a dynamical system to be in a specific state. This…
In the context of population dynamics, identifying effective model features, such as fecundity and mortality rates, is generally a complex and computationally intensive process, especially when the dynamics are heterogeneous across the…
The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…
Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise…