Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Neural Networks Trained to Solve Differential Equations Learn General Representations
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SVCCA rather than transfer learning to measure layer generality | 4-layer DENNs trained on the Poisson BVP family · Continuously-parametrized BVPs | computation time: roughly 15 minutes; hundreds of extra hours | Helped |
| Increase width from 8 to 16 | Third layer of 4-layer DENNs · Poisson BVP family | transfer specificity: roughly 64 at width 8 to 18 at width 16 | Helped |
| Increase width from 8 to 16 | Third layer of 4-layer DENNs · Poisson BVP family | SVCCA specificity: roughly 5% at width 8 to 2% at width 16 | Helped |
| Increase network width up to 24 | DENNs solving the Poisson BVP family · Poisson BVP family | testing performance | Helped |
| Increase network width beyond 24 | DENNs solving the Poisson BVP family · Poisson BVP family | testing performance | Hurt |
| Replace tanh with sigmoid (ablation) | DENNs solving the Poisson BVP family · Poisson BVP family | training performance | Hurt |
| Use rescaled tanh (ablation) | DENNs solving the Poisson BVP family · Poisson BVP family | training performance | No clear effect |
| Replace tanh with a piecewise-linear activation (ablation) | DENNs solving the Poisson BVP family · Poisson BVP family | ability to train | Hurt |
| Replace L2 loss with L1 loss (ablation) | DENNs solving the Poisson BVP family · Poisson BVP family | training performance | Hurt |
| Use the L2 norm rather than the L1 norm (ablation) | DENNs solving the Poisson BVP family · Poisson BVP family | training performance | Helped |
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