Related papers: Governing Equation Discovery from Data Based on Di…
Accurately modeling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data.…
Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or accurate resolution of their solutions may be intractable. Instead,…
Hybrid systems are traditionally difficult to identify and analyze using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations…
In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…
Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification of nonlinear dynamics (SINDy) framework, powered by heuristic…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
We explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the…
Sparse identification of nonlinear dynamics (SINDy) has been widely used to discover the governing equations of a dynamical system from data. It uses sparse regression techniques to identify parsimonious models of unknown systems from a…
Symbolic Regression (SR) is a widely studied field of research that aims to infer symbolic expressions from data. A popular approach for SR is the Sparse Identification of Nonlinear Dynamical Systems (SINDy) framework, which uses sparse…
Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…
We introduce methods for deriving analytic solutions from differential-algebraic systems of equations (DAEs), as well as methods for deriving governing equations for analytic characterization which is currently limited to very small systems…
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…
Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. We…
Discovering the governing laws underpinning physical and chemical phenomena is a key step towards understanding and ultimately controlling systems in science and engineering. We introduce Discovery of Dynamical Systems via Moving Horizon…
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…
Learning causal structure from observational data is a fundamental challenge in machine learning. However, the majority of commonly used differentiable causal discovery methods are non-identifiable, turning this problem into a continuous…
The understanding and modeling of complex physical phenomena through dynamical systems has historically driven scientific progress, as it provides the tools for predicting the behavior of different systems under diverse conditions through…
We propose a novel composite framework to find unknown fields in the context of inverse problems for partial differential equations (PDEs). We blend the high expressibility of deep neural networks as universal function estimators with the…
A novel approach is presented for discovering PDEs that govern the motion of satellites in space. The method is based on SINDy, a data-driven technique capable of identifying the underlying dynamics of complex physical systems from time…
Discovering compact governing equations from experimental observations is one of the defining objectives of quantitative science, yet practical discovery pipelines routinely fail when measurements are noisy, relevant state variables are…