Integrating 3D Heat Equation into a PINN for Real-Time Aerospace Simulation (C++ WASM Engine)[P]

Hey everyone,

I’ve been exploring Physics-Informed Neural Networks (PINNs) to solve high-velocity thermal problems. I built Met-Shield, a re-entry simulator that uses a PINN to predict thermal gradients on a spacecraft shield.

The PINN Phase:

• Architecture: I’m using a fully connected network trained to satisfy the 3D Heat Equation as its primary loss function.
• Physics Constraints: The model is constrained by the thermal diffusivity and conductivity of Ti-6Al-4V (Titanium alloy).
• The Goal: I wanted to see if a PINN could provide more robust generalization than a standard FDM solver when dealing with noisy atmospheric trajectory data.

The Performance Handoff: Once trained, I integrated the model logic into a custom C++ engine compiled to WebAssembly. This allows the simulation to run natively in the browser at 60fps, predicting metallurgical phase transitions (Alpha-to-Beta Titanium) on the fly.

The Struggle: While the PINN's math is solid, I’m seeing some convergence issues when the heat flux spikes during the "Max Q" phase of re-entry. I’m also looking for advice on better ways to weight the physics-loss vs. the data-loss in the total loss function.

I’ve open-sourced the repo and would love for some ML engineers to look at my training loop and architecture.

https://preview.redd.it/enkuqo7vg11h1.png?width=1920&format=png&auto=webp&s=7c69248a43e9c0488015ebbad1c78d6079c43e5f

https://preview.redd.it/auh9uq6wg11h1.png?width=1920&format=png&auto=webp&s=5cb270a224012c68f33d0897fbd66742bb7a5152

Repo:[https://github.com/Lak23James/met-shield]()
Live Site:[https://met-shield-58n1.vercel.app/]()