Scientific ML notebooks you can run
Start with a problem, finish with a numerical check. These notebooks include the equations, exact package pins, full initialization, plots, and assertions. They execute against the published omnibias distributions on CPU with float64 tensors.
4 runnable notebooks · PyTorch · verified prereleases
A fourth-order beam PINN in PyTorch
Solve a clamped Euler–Bernoulli beam with a nonuniform load, forward Taylor jets, exact boundary conditions, and independent solution checks.
A Poisson PINN without a full Hessian
Train a two-dimensional Poisson PINN using direct Laplacian contraction, then inspect solution error, boundary error, and residual error separately.
Train differentiable regions and local experts
Learn a soft split and two regional regressors together, validate held-out predictions, and measure what changes when routing is hardened.
Calibrate a scientific model with Gauss–Newton
Recover amplitude, decay rate, and offset in a nonlinear least-squares inverse problem using a verified residual Jacobian and functional Gauss–Newton steps.
Choose a starting point
- New to omnibias? Read the first derivative quickstart and the PyTorch high-order derivative guide.
- Training a physics residual? The beam example uses fourth-order jets and exact boundary constraints. Poisson uses a direct Laplacian and a boundary penalty.
- Learning regime-dependent behaviour? Regional regression trains the routing and experts jointly and measures the effect of hardening.
- Recovering scientific parameters? The decay example checks residual sensitivities before taking Gauss–Newton steps.
These are deliberately checkable problems with known or manufactured targets. Their results establish the displayed examples, not universal convergence or performance guarantees. Each tutorial links to its raw output and numerical assumptions.
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Documentation status
These four notebooks are fully executed and checked. The broader API reference still has an independently tracked editorial and example backlog; generated API coverage does not imply complete usage guidance for every entry. See API reference status.