Describing something that relies on, uses, or is derived from mathematical equations. This often applies to models, methods, or systems where relationships between variables are expressed and analyzed through formulas. The term highlights the importance of mathematical formalism and the use of equations for solving problems, making predictions, or representing complex phenomena. The focus is on the quantitative aspect of analysis and the utilization of symbolic representation to capture and manipulate relationships within a specific domain.
Equation-based meaning with examples
- The physics simulation was equation-based, utilizing differential equations to model the movement of objects under gravity and other forces. The program updated the positions and velocities of each object based on the equations, allowing for incredibly realistic rendering. This method created a dynamic and believable simulation.
- The financial model was equation-based, deriving its projections from formulas that factored in interest rates, investment returns, and market volatility. Analysts could then adjust these input variables to simulate different economic scenarios and assess potential outcomes.
- The engineering design of the bridge was equation-based. Every stress, strain, and load-bearing capacity was calculated using complex mathematical formulas, ensuring structural integrity.
- Artificial intelligence frequently employs equation-based algorithms in machine learning. These algorithms use mathematical equations to analyze data, identify patterns, and make predictions. Such predictive ability is useful for tasks like image recognition and natural language processing.