Related papers: Data-based Discovery of Governing Equations
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…
Many scientific phenomena are modeled by Partial Differential Equations (PDEs). The development of data gathering tools along with the advances in machine learning (ML) techniques have raised opportunities for data-driven identification of…
With the advent of modern data collection and storage technologies, data-driven approaches have been developed for discovering the governing partial differential equations (PDE) of physical problems. However, in the extant works the model…
We present a method of discovering governing differential equations from data without the need to specify a priori the terms to appear in the equation. The input to our method is a dataset (or ensemble of datasets) corresponding to a…
The modern machine learning methods allow one to obtain the data-driven models in various ways. However, the more complex the model is, the harder it is to interpret. In the paper, we describe the algorithm for the mathematical equations…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first…
Data driven discovery of partial differential equations (PDEs) is a promising approach for uncovering the underlying laws governing complex systems. However, purely data driven techniques face the dilemma of balancing search space with…
Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation…
Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…
The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development…
A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing…
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…
In this work, we demonstrate how physical principles -- such as symmetries, invariances, and conservation laws -- can be integrated into the dynamic mode decomposition (DMD). DMD is a widely-used data analysis technique that extracts…
Many processes in science and engineering can be described by partial differential equations (PDEs). Traditionally, PDEs are derived by considering first principles of physics to derive the relations between the involved physical quantities…
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…
Given that observational and numerical climate data are being produced at ever more prodigious rates, increasingly sophisticated and automated analysis techniques have become essential. Deep learning is quickly becoming a standard approach…
Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…
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…
Model discovery based on existing data has been one of the major focuses of mathematical modelers for decades. Despite tremendous achievements of model identification from adequate data, how to unravel the models from limited data is less…