Table 10 Ablation study on transformer physical constraints (20 test episodes per configuration).

From: A hybrid APF-DQN framework with transformer-based current prediction for USV path planning in dynamic ocean environments

Configuration

Pred. MSE

Div. error

Path success (%)

Path length (m)

No constraints

0.0847

0.312

85.0

\(298.42 \pm 24.31\)

Mass only (\(\lambda _1\))

0.0623

0.089

92.5

\(278.15 \pm 15.67\)

Mass + Vorticity (\(\lambda _1, \lambda _2\))

0.0512

0.067

95.0

\(271.33 \pm 11.24\)

Mass + Vort. + Stat. (\(\lambda _1, \lambda _2, \lambda _4\))

0.0456

0.051

97.5

\(268.92 \pm 8.56\)

Full constraints (Ours)

0.0398

0.042

100.0

\(262.85 \pm 4.18\)