Related papers: Sparse Identification of Truncation Errors

We consider a sparse grid collocation method in conjunction with a time discretization of the differential equations for computing expectations of functionals of solutions to differential equations perturbed by time-dependent white noise.…

Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…

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…

Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology, among many others. The physics underlying the patterns is specific to the mechanisms, and is encoded by…

The identification of Partial Differential Equations (PDEs) has emerged as a prominent data-driven approach for mathematical modeling and has attracted considerable attention in recent years. The stability and precision in identifying PDE…

Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…

In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…

We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…

Spatiotemporal forecasting in physical systems, such as large-scale traffic networks, requires modeling a dual dynamic: continuous macroscopic rhythms and discrete, unpredictable microscopic shocks. While Neural Ordinary Differential…

The sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition and its variants have been utilized in multivariate regression, factor analysis, biclustering,…

In this paper, we present a methodology to identify discrete-time state-space switched linear systems (SLSs) from input-output measurements. Continuous-state is not assumed to be measured. The key step is a deadbeat observer based…

The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space,…

Linear system identification and sparse dictionary learning can both be seen as structured matrix factorization problems. However, these two problems have historically been studied in isolation by the systems theory and machine learning…

Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer…

Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…

Time-series imputation benchmarks employ uniform random masking and shape-agnostic metrics (MSE, RMSE), implicitly weighting evaluation by regime prevalence. In systems with a dominant attractor -- homeostatic physiology, nominal industrial…

Understanding the dynamics of complex systems is a central task in many different areas ranging from biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even system failure is sometimes difficult…

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,…

High-dimensional streaming data are becoming increasingly ubiquitous in many fields. They often lie in multiple low-dimensional subspaces, and the manifold structures may change abruptly on the time scale due to pattern shift or occurrence…

Diffusion models have demonstrated remarkable generative capabilities in image processing tasks. We propose a Sparse condition Temporal Rewighted Integrated Distribution Estimation guided diffusion model (STRIDE) for sparse-view CT…