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Related Concept Videos

Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
Lagrange Multipliers: Problem Solving01:30

Lagrange Multipliers: Problem Solving

A silo with a cylindrical base, flat bottom, and hemispherical roof is a common design in agricultural and industrial storage due to its structural efficiency and ease of construction. Optimizing its dimensions to maximize storage capacity for a given amount of material—i.e., a fixed surface area—is a classic problem in applied calculus and engineering design. The key parameters are the radius r of the base and the height h of the cylindrical section.The total volume of the silo is obtained by...
Lagrange Multipliers: Two Constraints01:28

Lagrange Multipliers: Two Constraints

The method of Lagrange multipliers with two constraints is used to optimize a function subject to two independent constraints. In many applications, the objective function represents a quantity to be maximized or minimized, such as cost, area, distance, or energy. The two constraints represent requirements that the solution must satisfy, such as fixed volume, limited resources, or prescribed dimensions.For a function of three variables, each constraint forms a surface in three-dimensional space.
Ampere-Maxwell's Law: Problem-Solving01:17

Ampere-Maxwell's Law: Problem-Solving

A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of the problem,...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Lagrange Multipliers: One Constraint01:29

Lagrange Multipliers: One Constraint

In constrained optimization, the objective is to maximize or minimize a quantity while satisfying a fixed condition. A standard example is a rectangular pen built against a barn wall using 100 meters of fencing. Because the wall provides one side of the enclosure, only the other three sides require fencing. The problem is to find the dimensions that produce the greatest possible area.Let L represent the length parallel to the wall and W the width perpendicular to it. The area of the pen is A =...

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Related Experiment Videos

Discovering multiscale deep formulas in complex systems via neural-guided lambda calculus.

Hanqiao Yu1,2, Shusen Yang3,4, Xuebin Ren5,6

  • 1National Engineering Laboratory for Big Data Analytics, Xi'an Jiaotong University, Xi'an, Shaanxi, China.

Nature Communications
|June 16, 2026
PubMed
Summary
This summary is machine-generated.

Deflex, a new AI method, automatically extracts multiscale formulas from complex systems. This approach enhances scientific discovery by efficiently identifying scale-specific patterns in diverse systems.

Related Experiment Videos

Area of Science:

  • Complex Systems Science
  • Artificial Intelligence
  • Mathematical Modeling

Background:

  • Identifying concise mathematical formulas for complex systems is a fundamental scientific challenge.
  • Current AI methods struggle with scale-specific formula extraction in multiscale systems.

Purpose of the Study:

  • To present Deflex, an end-to-end AI method for automated multiscale formula discovery.
  • To extract diverse formulas, including invariants and distributions, from complex systems.

Main Methods:

  • Deflex utilizes two subsystems: Deflexformer (a deep energy model) and Deflexpressor (a symbolic regression model).
  • Deflexpressor pre-trains Deflexformer using synthetic data, enabling the decoupling of multiscale latent relationships for formula discovery.

Main Results:

  • Deflex demonstrates up to 7-fold higher efficiency compared to state-of-the-art methods across six diverse complex systems.
  • The method successfully automates the discovery of multiscale formulas, including invariants and distributions.

Conclusions:

  • Deflex offers an efficient and automated solution for extracting multiscale formulas from complex systems.
  • This AI-driven approach has broad applicability for scientific discovery across various disciplines.