Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Learning Stochastic Behaviour from Aggregate Data
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FPP with weak-form Fokker–Planck training instead of NN | Aggregate stochastic dynamics · Synthetic-1, Synthetic-2, and Synthetic-3 (D2 tasks) | Wasserstein error: 1.37 -> 0.05; 0.84 -> 0.03; 4.72 -> 0.02; 3.83 -> 0.04; 4.13 -> 0.08; 3.05 -> 0.12 | Helped |
| Use FPP with weak-form Fokker–Planck training instead of NN | Aggregate gene-expression dynamics · RNA-Mt1 and RNA-Mt2, D2 and D7 | Wasserstein error: 33.86 -> 4.23; 12.69 -> 2.92; 31.45 -> 4.04; 11.58 -> 1.50 | Helped |
| Use FPP instead of rolling means | Daily trading volume prediction · JPM, TSLA, and GOOGL (reported MAPE tasks) | MAPE: JPM 14:35: 0.52 -> 0.01; TSLA 14:35: 0.53 -> 0.02; GOOGL 14:35: 0.49 -> 0.01 | Helped |
| Use FPP to predict aggregate volume when half of training samples are dropped | Daily trading volume prediction · JPM, Group B | prediction quality | Helped |
| Use FPP instead of the Kalman filter-based model | Daily trading volume prediction · JPM, TSLA, and GOOGL | MAPE: 0.28 -> 0.01 (JPM 14:35); 0.31 -> 0.02 (TSLA 14:35); 0.35 -> 0.01 (GOOGL 14:35) | Helped |
| Try to recover the drift from density evolution when the drift is a curl field that leaves the distribution unchanged | FPP · Gaussian distribution under curl field (y, -x) | drift recovery | Hurt |
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