11.6 TensorFlow and scikit-learn examples

Source: Ideas from Computational Physics (Landau, Páez, Bordeianu), §11.5. Rewritten in original wording — no textbook TensorBE.py / SkPolyFit.py / Hubble.py dumps. Continues 11.5b. Next: 11.6b.

Physics toys check that the ML stack’s arithmetic matches nuclear / cosmology formulas. In this course’s sandbox we evaluate the same formulas in pure Python; run TensorFlow / sklearn locally in a notebook when you want the real APIs.

Mass excess, binding, and autodiff

Atomic masses in u (Daltons); nuclear binding lowers rest energy; TF’s GradientTape records ops so $\partial\mathcal{L}/\partial(\text{params})$ can be computed automatically. Walk $\Delta$, $B$, and $\partial\mathcal{L}/\partial x$ for $\mathcal{L}=(y-mx-b)^{2}$ — pick each matching equation among lookalikes.

Hydrogen isotope table (u) for mass-excess checks:

$N$	$M$ (u)	$N$	$M$ (u)
0	1.007827032	4	5.035
1	2.01401778	5	6.045
2	3.016049278	6	7.05
3	4.026

Sklearn-style regression fits a polynomial in $A$ to tabulated $B/A$ points — fine for pedagogy; nuclear physics is not a single polynomial.

Hubble line via MSE

Hubble (1929): recessional speed vs distance, historically $v\approx H_0 r$ (huge $H_0$ by modern standards). TF training loop: predict $y=mr+b$, Loss = mean $(y_{\mathrm{pred}}-y_{\mathrm{true}})^2$, step $m,b$ with $\nabla\mathcal{L}$ for hundreds of iterations. Same SGD story as §11.3, now on astronomy data.

Polynomial features (sklearn)

PolynomialFeatures(degree=k) expands $A\mapsto(A,A^2,\ldots)$; LinearRegression fits coefficients in that basis. Always reshape(-1,1) single-feature columns. High degree overfits seven noisy $B/A$ points — expect ugly curves (that’s the lesson).

Sketch (structure only)

# nuclear_ml_sketch.py — original structure (pure Python or TF locally)
U_TO_MEV = 931.494028

def mass_excess_mev(M_u, A):
    return (M_u - A) * U_TO_MEV

# TF notebook: Z = tf.constant(1); N = tf.constant(2); A = tf.add(Z, N)
# sklearn: poly.fit_transform(mA.reshape(-1, 1)); LinearRegression().fit(...)
# GradientTape: record loss; tape.gradient(loss, x)

Takeaway

Example	Check
$A=Z+N$	Tensor add
Mass excess	$(M-A)\times 931.494028$
$B/A$	Binding curve / poly fit
GradientTape	Autodiff of MSE
Hubble	SGD linear fit

Quiz

TF / sklearn physics

1 / 4

Mass excess (MeV/c²) uses…

Pick an answer to see if you are right.

Next: 11.6b TF / sklearn labs.