Real plate (full-grid solver)Neural twin (sparse sensors only)
A real thermal plate is solved in full on the left — every grid cell, every frame, straight from the 2D steady heat equation — and drawn as a color heatmap with isotherm contour lines. On the right, a tiny RBF network never sees that grid at all: it only gets readings from a sparse handful of sensors (the yellow dots), plus a physics-informed loss term that penalizes it for disobeying the same governing PDE anywhere in the domain. Drag the physics-loss weight λ down to zero, let training run for a while, and watch the reconstruction ring and overshoot between sensors as it interpolates them almost exactly; raise λ back up and the same trained network snaps back toward the smooth true field — a working, from-scratch model of how physics-informed digital twins reconstruct a full physical state from only a few real-world sensors.