⚡ New single function
from
y
,
y'
& logic filter
🔬 Two noisy curves + ODE constraint · filter decides
when
physics is trusted
📐 ODE model
dy/dt = f(t, y)
Decay: dy/dt = −0.6·y
Sine: dy/dt = cos(t)
Logistic: dy/dt = 0.8·y·(1−y/3)
📊 Noise level
added to both y and y'
0.25
🧠 Logic filter type
gates the ODE residual
Dead‑zone (ignore small errors)
Huber (robust)
Binary mask (physics ON/OFF)
⚙️ Filter threshold / δ
dead‑zone size · Huber δ · mask switch t₀
0.40
⚖️ Physics weight γ
strength of ODE penalty
3.0
▶ Run optimization
Fit loss (y + y')
—
ODE residual (filtered)
—
Iterations
0
Filter active (%)
0%
💡
Dead‑zone
: ODE ignored if residual < threshold.
Huber
: smooth transition from L2 to L1.
Binary
: physics enforced only after t₀.
📈 fitted function
( y_hat ) vs noisy y & y'
🧩 ODE residual
| y'_hat − f(t, y_hat) |
dead‑zone
⚡ The optimiser finds a polynomial
P(t)
that balances fit to
y
, fit to
y'
, and the ODE constraint — gated by your logic filter.