Knowledge-aware equation discovery with automated background knowledge extraction
In differential equation discovery algorithms, a priori expert knowledge is mainly used implicitly to constrain the form of the expected equation, making it impossible for the algorithm to truly discover equations. Instead, most differential equation discovery algorithms try to recover the coefficients for a known structure. In this paper, we describe an algorithm that allows the discovery of unknown equations using automatically or manually extracted background knowledge. Instead of imposing rigid constraints, we modify the structure space so that certain terms are likely to appear within the crossover and mutation operators. In this way, we mimic expertly chosen terms while preserving the possibility of obtaining any equation form. The paper shows that the extraction and use of knowledge allows it to outperform the SINDy algorithm in terms of search stability and robustness. Synthetic examples are given for Burgers, wave, and Korteweg--De Vries equations.
Code (1)
Tasks
Equation DiscoverySimilar Papers 제목 키워드 기반
Automated Mathematical Equation Structure Discovery for Visual Analysis
Finding the best mathematical equation to deal with the different challenges found in complex scenarios requires a thorough understanding of the scenario and a trial and error process carried out by experts. In recent ye…
Equation DiscoveryEvolving Scientific Discovery by Unifying Data and Background Knowledge with AI Hilbert
The discovery of scientific formulae that parsimoniously explain natural phenomena and align with existing background theory is a key goal in science. Historically, scientists have derived natural laws by manipulating eq…
Equation DiscoveryLogical Reasoningscientific discoveryProbabilistic Grammars for Equation Discovery
Equation discovery, also known as symbolic regression, is a type of automated modeling that discovers scientific laws, expressed in the form of equations, from observed data and expert knowledge. Deterministic grammars, …
Equation DiscoverySymbolic RegressionAutomated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systems
The paper surveys automated scientific discovery, from equation discovery and symbolic regression to autonomous discovery systems and agents. It discusses the individual approaches from a "big picture" perspective and in…
AstronomyAutonomous DrivingEquation Discoveryscientific discovery+1Symmetry-Informed Governing Equation Discovery
Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, the…
Equation Discovery