Research map / Probabilistic and scientific modeling / Differential equations and PDEs
AReS and MaRS Adversarial and MMD-Minimizing Regression for SDEs
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use gradient matching with the latent-state noise model and adversarial inference | SDE parameter estimation · Double-Well potential | drift parameter accuracy: 3.68 \pm 1.34 (AReS), 3.85 \pm 1.10 (MaRS); ground truth 4 | Helped |
| Use gradient matching with the latent-state noise model and MMD inference | SDE parameter estimation · Double-Well potential | diffusion variance H: 0.21 \pm 0.09 (AReS and MaRS); 0.20 \pm 0.05 (ESGF) | Helped |
| Estimate a non-diagonal diffusion matrix with the proposed framework | AReS and MaRS · Lotka-Volterra | diffusion variance H: H_1,1: 0.03 \pm 0.004 vs 0.01 \pm 0.03; H_2,2: 0.09 \pm 0.03 vs 0.03 \pm 0.02 | Helped |
| Use AReS or MaRS instead of ESGF for Lotka-Volterra drift inference | SDE parameter estimation · Lotka-Volterra | drift parameter accuracy: theta_0: 2.00 \pm 0.09 (MaRS) vs 2.04 \pm 0.09; theta_2: 3.97 \pm 0.63 (AReS) vs 3.87 \pm 0.59 | Mixed |
| Use AReS or MaRS instead of classical inference methods on locally linear systems | SDE parameter estimation · Ornstein-Uhlenbeck and Lorenz '63 | parameter estimation: Ornstein-Uhlenbeck H: 0.24 \pm 0.09 vs 0.19 \pm 0.06; Lorenz '63 theta_0: 9.82 \pm 0.56 vs 9.97 \pm 0.33 | Mixed |
| Use MMD inference instead of adversarial inference | AReS · Ornstein-Uhlenbeck | theta_1: 1.06 \pm 0.93 (AReS) vs 0.99 \pm 0.25 (MaRS); ground truth 1 | No clear effect |
| Use MaRS instead of AReS | SDE parameter estimation · Double-Well potential | theta_1: 3.68 \pm 1.34 -> 3.85 \pm 1.10; ground truth 4 | Helped |
| Use MMD inference instead of adversarial inference | AReS · Lotka-Volterra | training time: 47.6 \pm 1.3 -> 19.3 \pm 1.1 | Helped |
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