Nebula

"Translating physical intuition into 60 FPS mathematical curves and deep scientific reasoning with NVIDIA Nemotron on Nebius Token Factory."

Comment

Inspiration

Mathematics is the universal language of physics and engineering, yet modern graphing software—like Desmos and GeoGebra—remains fundamentally backward: it forces you to already know the exact formula before you can visualize the science.

If a physics student wants to observe a quantum wavepacket, an audio engineer wants to visualize a cardioid microphone pickup pattern, or a mathematician wants to explore a non-linear soliton wave, they must first hunt down formulas or perform tedious algebraic derivations.

We asked: What if graphing tools understood physical intuition? What if you could describe physical phenomena in plain English and have frontier AI translate that intuition into validated, interactive curves at a fluid 60 FPS, while providing deep academic derivations on demand? That vision inspired NEBULA.

What it does

NEBULA bridges human physical intuition and formal mathematical rigor:

Zero-Shot Concept-to-Equation Synthesis: Users can type natural language concepts like "quantum wavepacket" or "soliton wave". Powered by NVIDIA Nemotron 3 Ultra via Nebius Token Factory, NEBULA derives the exact governing equation , calculates domain constraints, and renders it immediately. "✨ Explain with Nemotron": One click in the inspector generates an academic derivation directly from NVIDIA Nemotron covering: Mathematical Intuition & Geometry (asymptotes, decay rates, and symmetries). Physical Applications (Korteweg–de Vries equation balance, optical fibers, shallow water waves). Calculus Landmarks (extrema, curvature, and limit behavior). 60 FPS Interactive Math Canvas: Full parity with leading graphing calculators: Dynamic animated sliders ( y=a⋅sin(x)) with 60 FPS continuous loops. Automatic Point-of-Interest (POI) snapping for roots, extrema, and intercepts. Polar coordinate systems with Degree ( and Radian modes. Real-time calculus tangent lines and adaptive Riemann area shading for definite integrals 1-Click 3-Minute Video Generator: A built-in presentation engine that automatically runs an 8-act choreographed demo with live voiceover and synchronized subtitles, downloading a submission video directly to the user's browser.

How we built it

We implemented a high-performance hybrid architecture:

Cloud AI Inference: Built on Nebius Token Factory (https://api.tokenfactory.nebius.com/v1) using OpenAI-compatible SDK semantics to query nvidia/Nemotron-3-Ultra-550b-a55b (with automatic fallback to nvidia/Llama-3.1-Nemotron-70B-Instruct-HF). High-Speed Dual-Path Pipeline: Input is classified before processing: Pure mathematical formulas evaluate locally via SymPy and NumPy in < 1 ms. Natural language prompts route asynchronously to NVIDIA Nemotron with strict JSON schemas. Backend: Built with FastAPI in Python, delivering asynchronous REST endpoints for /api/plot, /api/ai/query, and /api/ai/explain. Frontend Engine: Pure vanilla JavaScript and HTML5 Canvas with hardware-accelerated 2D matrix transformations for smooth 60 FPS pan, zoom, and slider interpolation.

Challenges we ran into

Eliminating AI Latency for Pure Math: Initially, non-algebraic tokens like coordinate points (2, 2) or quick formula edits were triggering LLM queries, causing noticeable 2-second network pauses. We engineered an intelligent AST fast-path tokenizer that detects valid mathematical syntax instantly, ensuring pure math evaluates in 0.2 ms locally while reserving Nebius Token Factory calls for descriptive queries. Preventing State Desynchronization: Managing real-time animated sliders while simultaneously streaming Nebius explanations required isolating the canvas animation loop from UI state updates so that 60 FPS rendering never stutters during API calls. Structured Physical Derivations: Crafting system prompts that instruct NVIDIA Nemotron to output both precise, parseable LaTeX formulas and rigorous physical breakdowns without hallucinated coordinate bounds.

Accomplishments that we're proud of

Sub-Millisecond Dual Engine: Combining the instant responsiveness of a local calculus engine (<1ms) with the reasoning capabilities of a 550B parameter frontier model. True Physical Understanding: Asking NEBULA for concepts like "acoustic cardioid" or "black hole event horizon" accurately plots and relativistic curves with zero manual formula entry. Deep Explanations: The "Explain with Nemotron" card gives students textbook-quality mathematical and engineering context for every plotted curve. Built-in Video Generator: An automated 3-minute video presentation tool with real-time speech narration and subtitles embedded right inside the web canvas.

What we learned

High-Throughput Inference with Nebius: Working with Nebius Token Factory demonstrated how ultra-low latency token generation enables LLMs to function as real-time computational backends rather than just asynchronous chatbots. The Power of NVIDIA Nemotron: Nemotron-3-Ultra excelled at zero-shot mathematical reasoning, consistently respecting analytical domain constraints and producing syntactically valid LaTeX without needing fine-tuning. Hybrid System Design: The best developer experiences come from combining client-side local computation with cloud-based frontier intelligence.

What's next for Nebula

3D Manifold & Vector Field Visualization: Expanding the canvas to 3D surface plots and vector fields using WebGL. Multimodal Image-to-Graph: Allowing students to photograph textbook diagrams or handwritten curves and have Nemotron reverse-engineer the governing equations. Interactive Physics Simulations: Adding physical constants and differential equation solvers to simulate orbital mechanics, pendulum motion, and heat diffusion directly on the canvas.

Built With

Share this project:

Updates

Submission history