中文

L2 · PHYSICS-CONSTRAINED · PINN

PHYSICS-CONSTRAINED · NO LABELED DATA

{{ t.p1a }}{{ t.p1b }}{{ t.p1c }}

{{ t.goal }}

INPUT

(x, y)

NETWORK

→ (u, v, p, θ)

AUTODIFF

∂x, ∂²x, …

RESIDUAL

r_PDE, r_BC

LOSS

Σ r²

CONJUGATE HEAT TRANSFER · THREE-FIN HEAT SINK

FIG 01 {{ t.figT }} {{ t.figN }}

GEOMETRY {{ t.geoT }} {{ t.geoN }}

60 × 20 mm　{{ t.g1d }}

40 × 3 mm　{{ t.g2d }}

15 W　{{ t.g4d }}

u = 0.4 m/s, T = 25 °C, Re ≈ 530

TWO-STAGE SOLVE

INTERFACE

∇·(κ ∇θ) = Pe · χ · (u · ∇θ)

solid: κ = κ_s, χ = 0

fluid: κ = κ_f, χ = 1

CONSERVATION AS LOSS · PHYSICS-BASED VERIFICATION

{{ t.m1t }}{{ t.m1d }}

{{ t.m2t }}{{ t.m2d }}

PHYSICS HEALTH CHECK {{ t.hcT }}

{{ t.thA }}
{{ t.thB }}
{{ t.thC }}

✓

Q_out / Q_in ∈ [0.95, 1.05]

✓

|u|_fluid ∈ [0.8, 1.15]

✓

θ_base > θ_top > 0

✓

θ_fin / θ_base ∈ [0.6, 1.0]

✓

θ_inlet corner ≈ 0

RESULT: PASS (6/6) {{ t.gate }}

WHERE PINN FITS

POSITIONING

PINN

{{ t.opLabel }}

{{ t.compT }}{{ t.compD }}

IMPLEMENTATION · SINGLE-FILE PYTORCH

{{ t.codeT }} PyTorch

def grad(u, X):
    return torch.autograd.grad(u, X, torch.ones_like(u), create_graph=True)[0]

{{ t.lossF }}

{{ t.lossFd }}{{ t.lossFk }}

{{ t.lossT }}

{{ t.lossTd }}{{ t.lossTk }}

{{ t.h1 }}

{{ t.n1 }}