Related papers: Rapid Bayesian identification of sparse nonlinear …

A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…

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…

This paper presents ``randomized SINDy", a sequential machine learning algorithm designed for dynamic data that has a time-dependent structure. It employs a probabilistic approach, with its PAC learning property rigorously proven through…

Accuracy and generalization capabilities are key objectives when learning dynamical system models. To obtain such models from limited data, current works exploit prior knowledge and assumptions about the system. However, the fusion of…

We consider the problem of designing almost optimal predictors for dynamical systems from a finite sequence of noisy observations and incomplete knowledge of the dynamics and the noise. We first discuss the properties of the optimal (Bayes)…

The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered…

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…

Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities. These tracking data can be used to calibrate mathematical models describing the motility of individual…

We develop a method for reconstructing regulatory interconnection networks between variables evolving according to a linear dynamical system. The work is motivated by the problem of gene regulatory network inference, that is, finding causal…

Kolmogorov-Arnold networks (KANs) have arisen as a potential way to enhance the interpretability of machine learning. However, solutions learned by KANs are not necessarily interpretable, in the sense of being sparse or parsimonious. Sparse…

Time-delayed differential equations (TDDEs) are widely used to model complex dynamic systems where future states depend on past states with a delay. However, inferring the underlying TDDEs from observed data remains a challenging problem…

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…

Effective intervention strategies for epidemics rely on the identification of their origin and on the robustness of the predictions made by network disease models. We introduce a Bayesian uncertainty quantification framework to infer model…

We introduce Fourier Weak SINDy, a minimal noise-robust and interpretable derivative-free equation learning method that combines weak-form sparse equation learning with spectral density estimation for data-driven test function selection. By…

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…

Efficiently quantifying predictive uncertainty in medical images remains a challenge. While Bayesian neural networks (BNN) offer predictive uncertainty, they require substantial computational resources to train. Although Bayesian…

Many studies on acoustic radiation forces focus on characterizing the behavior of acoustic fields. However, the dynamic response of objects, particularly those larger than the wavelength, remains underexplored. Here we bridge this gap by…

This paper begins with considering the identification of sparse linear time-invariant networks described by multivariable ARX models. Such models possess relatively simple structure thus used as a benchmark to promote further research. With…

Detecting symmetry from data is a fundamental problem in signal analysis, providing insight into underlying structure and constraints. When data emerge as trajectories of dynamical systems, symmetries encode structural properties of the…

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…