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Related Concept Videos

Time-Series Graph00:54

Time-Series Graph

A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct a time-series graph, one must look at both pieces of a paired data set. The horizontal axis is used to plot the time increments, and the vertical axis is used to plot the values of the variable that one is measuring. By using the axes in this way, each point on the graph will correspond to time and a measured quantity. The points on the graph...
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Regression Analysis

Regression analysis is a statistical tool that describes a mathematical relationship between a dependent variable and one or more independent variables.
In regression analysis, a regression equation is determined based on the line of best fit– a line that best fits the data points plotted in a graph. This line is also called the regression line. The algebraic equation for the regression line is called the regression equation. It is represented as:
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Graphs of Equations in Two Variables

An equation with two variables, typically written in the form y = f(x) or Ax + By = C, describes a relationship between quantities represented by x and y. Each solution to such an equation is an ordered pair (x, y) that satisfies the equation when substituted. These pairs can be represented graphically to understand the variables' relationship visually.A common technique for constructing the graph of a two-variable equation is to create a value table. Begin by choosing several values for the...
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Velocity and Position by Graphical Method

Velocity and position can be calculated from the known function of acceleration as a function of time. The total area under the acceleration-time graph and the velocity-time graph gives the change in velocity and position, respectively. In the case of an airplane, its acceleration is tracked using the inertial navigation system. The pilot provides the input of the airplane's initial position and velocity before takeoff. The inertial navigation system then uses the acceleration data to calculate...
Graphs of Polar Equations01:17

Graphs of Polar Equations

The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
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Related Experiment Video

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Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
11:52

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Published on: February 9, 2017

Moving from table to graph in physics-informed spatio-temporal symbolic regression.

Teddy Lazebnik1,2, Alex Liberzon3

  • 1Department of Information Systems, University of Haifa, Haifa, Israel. lazebnik.teddy@gmail.com.

Scientific Reports
|May 23, 2026
PubMed
Summary

This study introduces a novel dual data representation for Symbolic Regression (SR), combining tabular and graph-based methods. This approach enhances the discovery of governing equations from complex spatio-temporal data, improving accuracy and physical consistency.

Keywords:
Equation discoveryGraph neural networksImplicit knowledge-integrationScientific machine learning

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Area of Science:

  • Scientific Computing
  • Data Science
  • Physics-Informed Machine Learning

Background:

  • Symbolic Regression (SR) traditionally uses tabular data, limiting its ability to capture spatio-temporal dynamics and physical laws.
  • Existing SR methods struggle with data that evolves dynamically across time and space, governed by differential equations (ODEs/PDEs).
  • Efficient data representation is crucial for SR performance, especially when generalizing equations from limited datasets.

Purpose of the Study:

  • To develop a solver-agnostic approach for Symbolic Regression (SR) that integrates both explainable and physically informed data representations.
  • To enhance SR by incorporating graph-based spatio-temporal structures alongside standard tabular data within a unified framework.
  • To enable the direct generation of differential equations that accurately describe underlying physical systems.

Main Methods:

  • Proposed a dual data representation combining standard tabular format with a graph-based spatio-temporal representation.
  • Developed a unified SR fitting framework that enhances existing SR solvers without altering their core mechanisms.
  • Utilized graph nodes for spatio-temporal coordinates and state variables, with edges encoding dependencies, to implicitly incorporate physical patterns.

Main Results:

  • Demonstrated high accuracy in recovering governing equations across diverse synthetic datasets, including functional, ODE/PDE, integral, and delayed ODE types.
  • Showcased improved performance of Symbolic Regression (SR) out-of-the-box across various benchmarks, even under noisy data conditions.
  • Validated the method's ability to generate physically consistent and robust equations by enriching SR with graph-based spatio-temporal structure.

Conclusions:

  • Enriching Symbolic Regression (SR) with graph-based spatio-temporal structures offers a practical path toward more robust and physically consistent equation discovery.
  • The proposed dual representation framework effectively enhances existing SR solvers for problems with complex dynamics.
  • Future work involves validating the framework on real-world systems and refining the construction of meaningful spatio-temporal neighborhood structures.