Finite Expression Methods for Discovering Physical Laws from Data
Nonlinear dynamics is a pervasive phenomenon observed in scientific and engineering disciplines. However, the task of deriving analytical expressions to describe nonlinear dynamics from limited data remains challenging. In this paper, we shall present a novel deep symbolic learning method called the "finite expression method" (FEX) to discover governing equations within a function space containing a finite set of analytic expressions, based on observed dynamic data. The key concept is to employ FEX to generate analytical expressions of the governing equations by learning the derivatives of partial differential equation (PDE) solutions through convolutions. Our numerical results demonstrate that our FEX surpasses other existing methods (such as PDE-Net, SINDy, GP, and SPL) in terms of numerical performance across a range of problems, including time-dependent PDE problems and nonlinear dynamical systems with time-varying coefficients. Moreover, the results highlight FEX's flexibility and expressive power in accurately approximating symbolic governing equations.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Discovering symbolic expressions with parallelized tree search
Symbolic regression plays a crucial role in modern scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data. A grand challenge lies in the arduous search fo…
Equation DiscoveryregressionSymbolic RegressionDiscovering Symbolic Models from Deep Learning with Inductive Biases
We develop a general approach to distill symbolic representations of a learned deep model by introducing strong inductive biases. We focus on Graph Neural Networks (GNNs). The technique works as follows: we first encoura…
Deep LearningSymbolic RegressionDiscovering Conservation Laws using Optimal Transport and Manifold Learning
Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficu…
Rediscovering orbital mechanics with machine learning
We present an approach for using machine learning to automatically discover the governing equations and hidden properties of real physical systems from observations. We train a "graph neural network" to simulate the dyna…
BIG-bench Machine LearningGraph Neural Networkscientific discoverySymbolic RegressionDiscovering conservation laws from data for control
Conserved quantities, i.e. constants of motion, are critical for characterizing many dynamical systems in science and engineering. These quantities are related to underlying symmetries and they provide fundamental knowle…