Challenge #3 Use LLMs and differential equations - jtristan123/HW-for-AI-ML-ECE-410 GitHub Wiki

Challenge #3 Use the power of the internet and of LLMs to identify a physical system that solves differential equations inherently, through its physical properties, without executing instructions as a traditional processor does.

I have no ideal what this means..... I heard of differential equations but what does it mean "its" physical properties?!?

To ChatGPT:

challenge 3 # Use the power of the internet and of LLMs to identify a physical system that solves differential equations inherently, through its physical properties, without executing instructions as a traditional processor does

what in the world?

OUTPUT: Challenge 3 is asking you to find a physical system that naturally solves differential equations by how it behaves, without needing to follow step-by-step instructions like a CPU would.

πŸ” What does that mean?

Most computers solve differential equations using algorithms like Euler's method or Runge-Kutta. But some physical systems don't need that β€” their physics is the solution.

βœ… Examples of physical systems that inherently solve differential equations:

1. Analog Computers

  • These use electrical circuits (resistors, capacitors, op-amps) to simulate and solve differential equations directly.

  • Voltage across a capacitor, for instance, obeys the equation:

    $$ V(t) = \frac{1}{C} \int I(t) , dt $$

  • That's an integrator, which is core to solving ODEs!

2. Mechanical Systems

  • A mass-spring-damper system inherently solves:

    $$ m\ddot{x} + c\dot{x} + kx = F(t) $$

  • The physical motion of the mass is the solution to this second-order differential equation.

3. RC and RLC Circuits

  • These solve linear differential equations naturally by their electrical behavior.

  • An RLC circuit follows:

    $$ L\frac{d^2q}{dt^2} + R\frac{dq}{dt} + \frac{q}{C} = V(t) $$

4. Fluid Systems (Hydraulic Integrators)

  • Water flow in connected tanks can model first- and second-order differential equations.
  • The height of water represents a variable, and the flow rate is its derivative.

πŸ’‘ Summary

These systems don’t calculate the solution β€” they are the solution.

They don't "run code" β€” instead, the laws of physics do the math.

Let me know if you want to pick one and go deeper!