Upload README.md with huggingface_hub

README.md

@@ -15,9 +15,9 @@ library_name: pytorch
 
 A physics-embedded flow-matching neural surrogate that replaces FDTD for full-field
 electromagnetic prediction of silicon photonic devices. Given a permittivity map
-$\varepsilon(x,y)$, a source-port mask, and a free-space wavelength $\lambda$, PIC-Flow
-generates the complex $E_z$ field in a single multi-step ODE integration — typically
-in well under a second on a single A100, vs. seconds-to-minutes for CPU FDTD.
+ε(x,y), a source-port mask, and a free-space wavelength λ, PIC-Flow generates the
+complex field E_z in a single multi-step ODE integration — typically in well under
+a second on a single A100, vs. seconds-to-minutes for CPU FDTD.
 
 This repo hosts the **FM + phase + residual** checkpoint from epoch 300 (the headline
 model from the paper). All training code, dataset-generation tooling, and inference
@@ -57,20 +57,21 @@ in the GitHub repo.
 
 ## Model
 
-- **Architecture**: real-valued U-Net, 63.3M parameters. Real and imaginary $E_z$ are
-  separate input channels; permittivity and source-mask maps are visible at every layer;
-  flow-matching integration time $t$ and wavelength $\lambda$ are scalar conditioning inputs.
+- **Architecture**: real-valued U-Net, 63.3M parameters. Real and imaginary E_z
+  components enter as separate input channels; the permittivity and source-mask maps
+  are visible at every layer; the flow-matching integration time `t` and the wavelength
+  `λ` enter as scalar conditioning inputs.
 - **Generative framework**: conditional flow matching (Lipman et al., 2023). Inference
-  integrates a learned velocity field from Gaussian noise to a physically valid $E_z$
+  integrates a learned velocity field from Gaussian noise to a physically valid E_z
   using Euler or Heun ODE steps.
-- **Physics constraint**: masked Helmholtz residual loss
-  $\mathcal{L}_\text{res}$ (PML, source, and dielectric-interface pixels excluded), with
-  per-sample compliance metric $\rho_R = \sqrt{\mathcal{L}_\text{res}} \times 100\%$.
+- **Physics constraint**: masked Helmholtz residual loss `L_res` (PML, source, and
+  dielectric-interface pixels excluded), with a per-sample compliance metric
+  `ρ_R = sqrt(L_res) × 100%`.
 
 ## Training data
 
-- 22,500 Meep FDTD simulations at $\lambda = 1.55\,\mu$m
-- Three device families: $2\times2$ MMIs, Y-branches, directional couplers (7,500 each)
+- 22,500 Meep FDTD simulations at λ = 1.55 µm
+- Three device families: 2×2 MMIs, Y-branches, directional couplers (7,500 each)
 - Latin-hypercube parameter sweeps over geometric variables per family
 - 18,000 / 2,250 / 2,250 train / val / test split
 
@@ -81,25 +82,25 @@ ablation runs (FM only, FM+phase, FM+phase+residual).
 
 On the held-out test split (200-step Heun sampler):
 
-| Device family | $\rho_R$ |
+| Device family | ρ_R |
 |---|---|
-| $2\times 2$ MMI | 2.7% |
+| 2×2 MMI | 2.7% |
 | Y-branch | 2.5% |
 | Directional coupler | 2.2% |
 
 Out-of-distribution (same checkpoint, geometries never seen during training):
 
-| Device | $\rho_R$ |
+| Device | ρ_R |
 |---|---|
-| Aggressive Euler S-bend (tight $R$, large offset) | 12% |
+| Aggressive Euler S-bend (tight R, large offset) | 12% |
 | Short, steep taper | 4.0% |
 | Long, wide taper | 3.6% |
-| Cascaded $1\times3$ Y-branch (new device class) | 9.1% |
+| Cascaded 1×3 Y-branch (new device class) | 9.1% |
 
 Wall clock on a single NVIDIA A100 (fp16 autocast, vs. 16-thread Meep FDTD on the
 same node):
 
-| Sampler | Wall time | Speedup | $\rho_R$ |
+| Sampler | Wall time | Speedup | ρ_R |
 |---|---|---|---|
 | FDTD (reference) | 5.61 s | 1.0× | (reference) |
 | Euler 100 step | 2.19 s | 2.6× | 1.9% |