Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Spline-PINN: Approaching PDEs without Data Using Fast, Physics-Informed Hermite-Spline CNNs
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use Hermite spline coefficients with a physics-informed loss instead of an implicit PINN | PDE solver on DFG benchmark · DFG benchmark Re=2, Re=20 and Re=100 | drag coefficient C_D: Re=2: 25.3 -> 29.7; Re=20: 3.299 -> 4.7; Re=100: 1.853 -> (2.985 / 3.068 / 3.188)* | Helped |
| use spatial spline order l,m=2 instead of l,m=1 (ablation) | Spline-PINN · Wave oscillator domain | L_z: 8.511e-02 -> 5.294e-02 | Helped |
| use spatial spline order l,m=2 instead of l,m=1 (ablation) | Spline-PINN · Wave oscillator domain | L_v: 1.127e-02 -> 6.756e-03 | Helped |
| use spatial spline order l,m=2 instead of l,m=1 (ablation) | Spline-PINN · Wave oscillator domain | L_b: 1.425e-03 -> 1.356e-03 | Helped |
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