Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Adjoint-aided inference of Gaussian process driven differential equations
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use adjoint-aided inference instead of a Gaussian process baseline | Round Hill II concentration prediction · Round Hill II, 30s measurements | MSE: 21385 -> 14444 | Helped |
| Use adjoint-aided inference instead of a Gaussian process baseline | Round Hill II concentration prediction · Round Hill II, 180s measurements | MSE: 12968 -> 6628 | Helped |
| Use adjoint-aided inference instead of a Gaussian process baseline | Round Hill II concentration prediction · Round Hill II, 600s measurements | MSE: 8490 -> 4503 | Helped |
| Increase the number of sensors (ablation) | Adjoint-aided inference · Advection-diffusion PDE, held-out data | MSE: Table 2: 1 sensor, 10 features: 3.42 (2.82,4.39); 16 sensors, 10 features: 1.73 (1.23,3.28) | Helped |
| Increase RFF features from 10 to 500 (ablation) | Adjoint-aided inference · Advection-diffusion PDE, held-out data (25 sensors) | MSE: 1.35 (1.19,3.09) -> 1.05 (0.89,1.45) | Helped |
| Use only 10 RFF features rather than 100 (ablation) | Adjoint-aided inference · ODE forcing inference | Posterior fidelity | Hurt |
| Increase observations and features for shorter GP length-scales (ablation) | Adjoint-aided inference · Advection-diffusion PDE, source inference, length-scale l=2 | MSE: 0.68 -> 0.07 | Helped |
| Increase observations and features for shorter GP length-scales (ablation) | Adjoint-aided inference · Advection-diffusion PDE, source inference, length-scale l=1 | MSE: 1.85 for scenario 1; 2.55 for scenario 2 | Mixed |
| Use adjoint-aided inference rather than MCMC | PDE forcing posterior estimation · Advection-diffusion PDE | Forward model solves: 10,000s -> 75 | Helped |
| Use adjoint method rather than Green's function inference | ODE source inference · ODE | MSE: 0.0860 -> 0.079 | Helped |
| Increase Green's function RFF features from 20 to 500 (ablation) | Green's function method · ODE source inference | MSE: 0.099 -> 0.0856 | Helped |
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