One primitive. Every derivative-heavy workload.
Derivon's closed-form derivative tower powers a spectrum of scientific-ML solutions. Pick the one that matches your inner loop.
Local kinetic energy without the autodiff tax
Variational Monte Carlo with neural wavefunctions spends most of its compute on the Laplacian of the log-wavefunction. Derivon replaces it with a closed-form, bit-identical kernel.
- folx-compatible forward_laplacian adapter, bit-identical to FermiNet's default on closed-shell systems
- Relativistic mass-velocity Δᵏψ corrections stay flat in derivative order k
- value, gradient, and Laplacian from one envelope evaluation
- Verified to rel-err 0.0 (ULP) versus the trusted baseline
Stop letting the kinetic-energy step dominate your VMC wall-clock.
from omnibias.ferminet.folx_compat import forward_laplacian
from omnibias.ferminet.integration import (
make_omnibias_envelope_local_kinetic_energy,
)
# Drop-in for FermiNet laplacian_method = "default".
local_kinetic = make_omnibias_envelope_local_kinetic_energy(...)Stable Laplacians and high-order PDE residuals
Physics-informed networks live or die on the quality of their differential operators. Closed-form towers make even 4th- and 6th-order residuals cheap and numerically clean.
- Biharmonic, Kuramoto-Sivashinsky, Cahn-Hilliard and other high-order residuals
- Structural cages enforce incompressibility and conservation by construction
- No torch.autograd.grad in the inner loop - the fast path runs end to end
- Cross-backend bit-parity between PyTorch and JAX field operators
Remove a hyperparameter and a failure mode from PINN training.
from omnibias.pinn.torch import equations, cage
# Hard incompressibility: u = curl(A), so div u = 0 by construction.
field = cage.VectorPotentialField(base_field)
residual = equations.NavierStokes(viscosity=1e-3)(field, coords)Enclosures and certificates your reviewers will accept
The same derivative tower runs in a rigorous register: outward-rounded interval and Taylor-model arithmetic that provably bounds the true value, sealed in tamper-evident certificates.
- Interval / affine / Taylor-model arithmetic with dependency cancellation
- Hash-sealed certificate format with independent replay twins
- A Mathlib-free Lean 4 kernel re-checks finite, rational obligations
- Robustness, Lipschitz, monotonicity, and reachable-set certificates - tighter than IBP
Turn a research demo into something a safety board will sign off on.
from omnibias.core.verified.information import kl_divergence_enclosure
iv = kl_divergence_enclosure(p, q) # provably contains KL(p||q)
assert iv.lo <= true_kl <= iv.hi # rigorous, not a point estimateClosed-form Hessian, Fisher, and KFAC factors
Curvature-aware training needs second-order information that autodiff makes expensive. For Riccati-class fields, Derivon gives it to you in closed form.
- One-layer parameter Hessian and Gauss-Newton Fisher matrices
- Newton-step and KFAC factors for natural-gradient optimization
- Validated against jax.grad / jax.hessian on the one-layer field
- Composes with the Sobolev / Jacobian regularization surface
Make second-order methods practical instead of prohibitively expensive.
How teams use it
Curvature-aware optimizers and Bayesian-PINN Fisher information become tractable when the Hessian is a closed-form contraction rather than a nested-autodiff graph. Start from the one-layer field and compose upward.
Recover the governing law from data
Because the activation derivative jet is exact, you can read off y, y', y'', ... in closed form and search for the implicit relation that generated your data - a library-free SINDy variant.
- Recover ODE/PDE identities (dy = y, d2y = -y, dy = 1 - y²) without a named basis
- Multivariate vector-calculus and PDE-coefficient recovery (heat, wave, Burgers)
- Coefficient uncertainty, certified intervals, and model-order selection
- Dimensional analysis (Buckingham-Pi) and latent-state ODE discovery
Get interpretable physics out of black-box surrogates.
from omnibias.symbolic import discover_field_pde_law, make_heat_field_split
train, val, test, hidden = make_heat_field_split(seed=0)
result = discover_field_pde_law(train, val, test, lhs_index=(0, 1), time_axis=1)
print(result["equation"]) # -> "u_t = 0.12*u_xx"Curvature and Laplace-Beltrami on learned manifolds
Field derivatives are exact closed form; metric derivatives are exact forward-mode autodiff. Together they give a full Riemannian operator surface, validated against the round sphere.
- Metric, inverse metric, Christoffel symbols, covariant derivative
- Riemann / Ricci / scalar curvature and the Laplace-Beltrami operator
- Exterior calculus: exterior derivative, wedge, Hodge star, codifferential
- Pullback metric g = JᵀhJ of a learned chart
Do geometry on learned spaces with operators you can trust.
How teams use it
Curvature-aware optimizers and Bayesian-PINN Fisher information become tractable when the Hessian is a closed-form contraction rather than a nested-autodiff graph. Start from the one-layer field and compose upward.
Not sure which solution fits?
Tell us about your derivative bottleneck and we will map it to the right closed-form path - or tell you honestly if autodiff is already the better tool.
Or email info@derivon.ai