Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Solving PDE-Constrained Control Problems Using Operator Learning
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the reconstruction regularizer during control search (ablation) | Operator-learning control method · Poisson source control | distance of optimized control from analytic optimum | Helped |
| Use operator learning with a reconstruction regularizer instead of adjoint optimization | Nonlinear wave equation inverse design · Nonlinear wave equation | time (s): 0.210 $\pm$ 0.017 vs 473.909 $\pm$ 43.622 | Helped |
| Use operator learning with a reconstruction regularizer instead of adjoint optimization | Nonlinear wave equation inverse design · Nonlinear wave equation | objective: 0.014 $\pm$ 0.005 vs 0.012 $\pm$ 0.005 | No clear effect |
| Use operator learning with a reconstruction regularizer instead of adjoint optimization | Burgers' equation force control · Burgers' equation | time (s): 7.714 $\pm$ 1.600 vs 12.965 $\pm$ 4.306 | Helped |
| Use operator learning with a reconstruction regularizer instead of adjoint optimization | Burgers' equation force control · Burgers' equation | objective: 0.002 $\pm$ 0.002 vs 0.004 $\pm$ 0.003 | Helped |
| Use residual loss rather than supervised loss to train the operator (ablation) | Poisson source control method · Poisson source control, m_init=x+y | relative error of control: 3.320\times10^{-2} -> \pmb{2.631\times10^{-2}} | Helped |
| Use residual loss rather than supervised loss to train the operator (ablation) | Poisson source control method · Poisson source control, m_init=xy | relative error of control: 4.721\times10^{-2} -> \pmb{2.738\times10^{-2}} | Helped |
| Use residual loss rather than supervised loss to train the operator (ablation) | Poisson source control method · Poisson source control, m_init=xy(1-x)(1-y) | relative error of control: 2.131\times10^{-2} -> 2.531\times10^{-2} | Hurt |
| Use the operator-learning method rather than adjoint optimization | Poisson source control method · Poisson source control | sensitivity of relative control error to initial guess | Helped |
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