How it's built — Envelope Labv1.0 · 2026-10-25
Method
- Rule simulation + trained model. A steady-state 2D finite-volume conduction solver computes every performance number; a trained FNO (Fourier neural operator) separately predicts the temperature field of the same section, shown side by side with the solver
- Solver: 0.96 m high × sum of layer thicknesses, per 1 m depth. Mesh x 32 × y 48 (non-uniform x aligned to layers: inner finish 3 · structure 12 · insulation 14 · outer finish 3 cells). Cell-centred finite volumes, face conductance from both half-cell resistances in series, surface resistances (Rsi, Rse) inside and outside, adiabatic top and bottom. Direct banded Cholesky solve
- The slab is a band of structure across the middle (with continuous insulation, the insulation layer stays); the window is a 400 mm glass-equivalent layer (k = thickness / (1/Ug − 0.17)) + 80 mm frame-equivalent layer + wall below
- AI: FNO width 12, 6 Fourier modes, 3 layers, 8 input channels (independent 1D row-resistance temperature profile, log k, cell width, x, y, total thickness, Rsi, Rse) → 1D profile + 0.2 × learned 2D correction. Inference never calls the 2D solver, and predictions are not clipped or replaced by solver values
- Trained here · CPU, 4 threads (Windows x64) · Python 3.12.14, PyTorch 2.14.1+cpu, NumPy 2.5.4, SciPy 1.18.1 · epoch 69 of 70 by lowest validation error · seed 20261024 · run 20261023T155215Z
- Web: the solver and the FNO forward pass are ported to JavaScript and run in this browser (no server). Weights float32, 252,548 bytes
- No LLM. U-value, heat flow and surface temperatures all come from the solver; the AI predicts the temperature field only
Data
- Training data: 540 sections generated with this solver (420 train / 60 validation / 60 test) · synthetic · self-generated · section type, thicknesses, properties and surface resistances drawn independently per section
- Properties: assumed values for experimenting (set values). Insulation EPS 0.036 · XPS 0.030 · PIR 0.024 · mineral wool 0.040, structure 1.7, inner finish 0.25 (15 mm), outer finish 0.8 (10 mm) W/(m·K), Rsi 0.13 · Rse 0.04 m²·K/W. Editable on screen
- Stored user input: only when you press save — the A/B inputs, a name and summary numbers, in this browser’s localStorage, up to 100. Nothing sent to a server; no personal data
Validation
- AI conditions: 60 held-out test sections, area-weighted RMSE of dimensionless temperature θ scaled to a 32 K indoor–outdoor difference, run 20261023T155215Z
- AI RMSE 0.223°C (max absolute error 2.87°C) / 1D row-resistance formula 1.742°C (10.59°C) / straight line through the thickness 7.829°C (21.22°C)
- By type, RMSE (AI / 1D formula): slab 0.305 / 2.706°C, window 0.246 / 1.639°C, plane wall 0.090 / 0°C. For a plane wall the 1D formula is exact, so the AI only adds error there
- Train, validation and test sections kept separate. Normalisation from training data only; checkpoint chosen by validation error
- Solver: U within 1e-10 of the exact plane-wall solution, relative energy-balance residual below 1e-9; for the interrupted slab junction, U converges 1.3116 → 1.3188 → 1.3216 on 32×48 → 64×96 → 128×192 meshes
- Browser engine = Python/SciPy reference: over 15 sections, max relative U difference 4e-13, max AI θ difference 5e-10. 13 Node and 8 Python tests pass
- Default slab example (inside 22°C / outside −10°C): A 50 mm insulation, interrupted: U 1.3116 W/(m²·K), lowest inside surface 13.86°C → B 120 mm, continuous: U 0.2716, 20.64°C. Both changes at once — not a savings rate
- Speed (headless Chromium, same machine): about 1.7 ms per solve, about 9.7 ms per AI prediction
Scope
- AI training range: structure 100–300 mm, k 0.6–2.2; insulation 20–240 mm, k 0.022–0.045; Rsi 0.10–0.17; Rse 0.025–0.08; glass Ug 0.8–2.8; frame k 0.15–1.2; slab 80–280 mm; external or internal; continuous or interrupted. Flagged on screen when exceeded
- Solver input range: structure k 0.1–3, insulation k 0.015–0.1, Ug 0.5–3.5, frame k 0.1–2, inside 5–40°C, outside −40–40°C, Rsi 0.08–0.3, Rse 0.02–0.15
- Not modelled: solar gain, air leakage, moisture transport and condensation, phase change, time dependence, 3D effects, real window-frame or balcony geometry
Sources
- Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A. & Anandkumar, A. (2021). Fourier neural operator for parametric partial differential equations. ICLR.
- Patankar, S. V. (1980). Numerical Heat Transfer and Fluid Flow. Hemisphere.
- ISO 6946:2017. Building components and building elements — Thermal resistance and thermal transmittance — Calculation methods.
- LBNL THERM documentation — 2D conduction and thermal bridges in building components (this code is not THERM)
- EnergyPlus Engineering Reference — surface heat balance and boundary conditions
- Fonts: IBM Plex Mono, Inter, Noto Sans KR · SIL Open Font License 1.1 · Google Fonts
History
- 2026-10-25 · v1.0 · Released