Learn Math and Physics through Simulations with AI

Create beautiful 3D simulations using AI,
no programming experience required.

Examples of math and physics simulations in GPUSims

How the Simulation Works

GPUSims runs simulations using WebGPU.
This technology is supported by modern browsers like Chrome, Safari, and Edge.

Because WebGPU programming can be complex, GPUSims simplifies the process into these steps:

  1. An AI generates a simulation blueprint, called a schema.
  2. GPUSims builds a shader skeleton (the program running on the GPU) from this schema.
  3. The AI completes the shader implementation.

You do not need to understand how the schemas or shaders work.

The AI focuses on formulating math equations and writing the code.
GPUSims handles all the complexities of WebGPU in the background.
Separating the math from the WebGPU mechanics is what makes these advanced simulations possible.

How to Use GPUSims

Watch this short YouTube tutorial to see how it works.

Using the Simulation Page

  • Click Restart to replay the simulation.
  • Click Edit Code to go back to the schema and shader editors.
  • Click Capture Image to take a screenshot of the canvas and download it.
  • Click Thumbnail to select an image for the Gallery.
  • Drag with the left mouse button to rotate the 3D view.
  • Drag with the right mouse button to move the viewing area.
A simulation running in GPUSims with controls beside the canvas

AI Models Tested with GPUSims

I primarily use Gemini 3.1 Pro (Extended) and ChatGPT-5.6 Sol.
I use Opus 4.8 High for advanced simulations.
In my tests, free AI models often produced less accurate results.

Prompting the AI

As shown in the video, using GPUSims is mostly just clicking and copying.
The only step requiring your input is telling the AI what to build.

Here is the prompt used in the tutorial video:

prompt


Create a schema for an N-body simulation.

You can also provide more detailed instructions:

prompt


Create a simulation schema for multiple spheres undergoing elastic collisions within a cube.
Include sliders to adjust the coefficient of restitution and gravity.

Displaying calculation results on-screen makes it easier to verify the simulation.

prompt


Display the kinetic energy, the potential energy, and the sum of both.

For complex setups, asking the AI to output intermediate results to a separate canvas helps with debugging.

prompt


Output the intermediate calculation results to an additional canvas.

Basic Shapes

You can use these basic shapes to render your simulations:

Here is how to request specific shapes:

prompt


Create a schema for a pendulum simulation.
Represent the pendulum's string as a tube and the weight as a sphere, 
and draw the forces acting on the pendulum as arrows.

The AI can also render custom curved surfaces.

prompt


Create a schema to render a complex exponential function.

Troubleshooting Errors

If GPUSims displays an error dialog,
you can ask the AI to fix it:

  • Click Copy Error Message.
  • Paste the message into the AI chat.
  • Ask the AI to fix the error.

prompt


Fix this error.
Expected ':' but found '.' at index 319
An error message displayed by GPUSims

​​Verifying Calculations

A simulation might run without errors but still be mathematically incorrect.
Here is how to check your values with the AI:

  • Click the button to copy your parameters and results.
  • Paste them into the AI chat.
  • Ask the AI to verify if the calculations are correct.
Simulation controls and numerical results in GPUSims

Verifying the Visuals

Even if a simulation looks realistic, it might be inaccurate. Use the AI to check the canvas image:

  1. Click Capture Image to download the canvas as an image file.
  2. Upload the image file to the AI chat.
  3. Ask the AI to verify the visual accuracy.

System Prompt

Below is the system prompt used to guide the AI.
System Prompt
The AI uses these rules to structure your simulation schemas.

Learn Math and Physics with AI

Complex simulations can sometimes yield incorrect results.
If this happens, ask the AI to explain its algorithms.
You can also research alternative algorithms online.
You might also find better results simply by switching to a different AI model.
Working through these problems with AI is a great way to deepen your theoretical understanding.
I hope GPUSims enhances your journey into math and physics.

Vibe Coding Workflow

  1. Click to copy the System Prompt, then paste and run it in your AI chat.

  2. Give the AI instructions to generate a simulation schema.


    Example:
    Create a schema for an N-body simulation.

  3. Copy the generated schema and paste it into the editor below.

  4. Click to generate and copy the shader skeleton, then paste and run it in your AI chat.

  5. Copy the finalized shader code from the AI and paste it below.



  6. Click to compile the code and launch your WebGPU simulation.

GPU Fatal Error

Copy the error message, paste it into your AI chat, and ask the AI to fix it.


    

        
        
    





    

        
            
        
        
            
            

            
            

            


            
            



        

    

    

        

            
            

                

                

                    
                

                
                
                


            

        


        

        

            
                
                    
                    

                    
                
            
        

        

    






    

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