Original chibi mascot sprite (line-art, brand palette only) — reused via everywhere below
ψ
USEL v1.0.0-cpu
Get USEL
Open-Source Scientific Computing • CPU-First

Scientific computing.
Built for physics.

USEL is a restrained, CPU-native numerical framework for computational physics, continuous wave mechanics, and deterministic spectral simulation.

INSTALL KERNEL arrow_forward SOURCE REPO • 4 ★
AVX-512 / AVX2 / NEON / 8 GB RAM BASELINE / DETERMINISTIC SEEDING / MIT PERMISSIVE
PROJECT MASCOT
CHIBI STUDY EDITION
Chibi study mascot with headphones at desk taking notes
lo-fi physics study
Ready to Compute
STATUS: Studying Harmonics 100% Focused
ψ(x, t) CONTINUOUS EVOLUTION SIMULATOR DEV-NODE 01
SOLVER: CRANK-NICOLSON SPECTRAL GRID: 1024 FFT STATUS: DETERMINISTIC OK
|ψ(x)|² Probability Density Function
∫ |ψ(x)|² dx = 1.00000000 POTENTIAL: Harmonic Oscillator Trap HAMILTONIAN TRACE: 12.438 eV
SPECTRAL EIGENSYSTEM CONVERGED
λ₀ (Ground)
3.000000
λ₁ (Excited)
1.000000
Residual: ≤ 1e-16 Iterations: 14
HAMILTONIAN FORM H = -∇²/2m + V(x)
Continuous Wave Operator
Sparsity: 99.1% Tridiagonal: Yes
Execution Target
Host CPU Native
Resident RSS
38.4 MB
The Foundation

Algorithmic workflow pipeline.

Linear algebra primitives composable into continuous time-dependent simulations with zero memory overhead.

01 / PRIMITIVES
usel.math

Dense ndarray primitives, aligned vectors, inner products.

Float64 Core
02 / SPECTRAL
usel.linalg

Eigendecomposition, SVD, Cholesky, QR, and LU factorizations.

LAPACK Bind
03 / DYNAMICS
usel.solvers

Symplectic integrators, adaptive RK45, Crank-Nicolson.

ODE / PDE
04 / FREQUENCY
usel.fft

Split-operator kinetic momentum transformations.

k-Space
05 / ENSEMBLES
usel.random

Wigner surmise, Gaussian Orthogonal Ensembles (GOE).

Seeded PRNG
06 / SIMULATION
Physics Sim

Wave packets, quantum barriers, and observable dynamics.

Observable
TECHNICAL ARCHITECTURE • FIVE CORE DISCIPLINES

Five modules. Mathematically razor-sharp.

Strict IEEE-754 • Five Core Execution Disciplines • 100% Offline CPU Iron

DYNAMICS CORE
usel.solvers

Kinetic Wavepackets & Symplectic Integrators

Governs continuous wave mechanics and rotational harmonic loops with energy-conserving adaptive Runge-Kutta 4th order (RK45) time evolution.

Chibi mascot avatar for Dynamics Core
rk45(), crank_nicolson() 0.0000 ΔE Drift
SPECTRAL FFT
usel.fft

Split-Operator Momentum & Vector Transforms

Lightning-speed split-operator kinetic momentum transformations. Conducts 1024/2048 FFT grid translations in pure unrolled SIMD host registers.

Chibi mascot avatar for Spectral FFT
fft(), ifft(), k_space() O(N log N) Exact
DETERMINISTIC LINALG
usel.linalg

Precision Matrix State Space & Eigensystems

Calm, disciplined Hermitian matrix factorizations. High-precision SVD, Cholesky decomposition, and deterministic spectral radii down to 1e-16 residual.

Chibi mascot avatar for Deterministic Linalg
eigenvalues(), svd(), qr() 1e-16 Residual
RUNTIME TELEMETRY
usel.utils

Microsecond Diagnostics & Machine Parity

Zero-overhead function profiling, hardware instruction inspection, and bit-for-bit host parity validation across environments.

Chibi mascot avatar for Runtime Telemetry
timer(), profile(), verify() 0.14 ms Latency
SPATIAL TENSORS & MEMORY
usel.math

Dimensional Projection & Zero-Copy Memory

Dimensional matrix projection, higher-order tensor contractions, and zero-copy contiguous memory array slices aligned to CPU cache lines.

ALLOCATION Zero Heap Thrash
ALIGNMENT 64-Byte Cache
matrix(), tensor_dot(), fold() Strict 8 GB Ceiling
01 / CPU-FIRST memory

SIMD Instruction Native

Engineered purely for AVX-512, AVX2, and NEON instructions. Zero GPU driver dependencies.

02 / 8 GB LIMIT speed

Strict Memory Ceiling

Contiguous memory arrays, in-place operator mutations, and zero allocation during calculation steps.

03 / PRECISION check_box

Deterministic Seeding

Bit-for-bit host parity across Linux, macOS, and Windows with strict IEEE-754 compliance.

04 / AIR-GAPPED lock

Zero Outbound Network

Zero telemetry and zero external calls. Safe for sensitive computational physics labs.

Clean Namespace Architecture

Nine delineated packages.

Zero circular imports. Orthogonal, strictly typed Python modules.

usel.math Core

Matrix creation, dense vectors, operator norms, spectral radii, and precision casting.

matrix(), norm(), inner(), fft()
usel.linalg Linear

Exact eigenvalues, SVD, Cholesky factorization, QR, and LU forward/backward substitution.

eigenvalues(), svd(), qr(), lu()
usel.solvers Calculus

Adaptive Runge-Kutta (RK45), Crank-Nicolson parabolic PDE integrator, Newton-Raphson.

rk45(), crank_nicolson(), newton()
usel.random Stochastic

Gaussian Orthogonal Ensembles (GOE), Wigner surmise distributions, and deterministic PRNG seeding.

goe(), wigner_surmise(), seed()
usel.utils Instrumentation

High-precision microsecond profiler, Hermitian matrix predicates, and memory floor assertions.

timer(), is_hermitian(), profile()
usel.logging Telemetry

Structured NDJSON stream sinks, simulation step milestones, and step telemetry buffers.

get_logger(), record_state()
usel.config Profiles

Declarative experimental run profiles via TOML and JSON schemas with strict validation.

load_experiment(), validate_spec()
usel.io Storage

Zero-copy binary tensor dumps, native NumPy .npy array exports, and streaming CSV matrices.

save_matrix(), export_vtk()
usel.cli Terminal

Host diagnostics, CPU vector instruction probe, and automated precision verification harness.

usel doctor, usel benchmark
Syntax & Semantics

Physics-native code. Immediate feedback.

Zero boilerplate • Deterministic output
Hamiltonian Matrix A:
[ , ; , ]
hamiltonian_solve.py
01from usel.math import matrix
02from usel.linalg import eigenvalues
03
04# Construct Hamiltonian test operator (2-state coupling)
05A = matrix([
06 [2.0, 1.0],
07 [1.0, 2.0]
08])
09
10# Compute exact real spectra & orthonormal eigenspace
11values, vectors = eigenvalues(A)
12print("Eigenvalues:", values)
13print("Ground state:", vectors[:, 0])
Python 3.12 (USEL native engine) Encoding: UTF-8
EXECUTION LOG 0.14 ms
$ python hamiltonian_solve.py
Eigenvalues:
[3.00000000, 1.00000000]
Ground state vector:
[0.70710678, 0.70710678]
Spectral Gap Δε: 2.000000
Hermitian Residual: 0.000e+00
Target Hardware: CPU Native SIMD
Sub-microsecond precision PID: 49201
Command Line Diagnostics

Built-in system doctor.

Verify machine instructions and run standardized numerical benchmarks with a single command.

usel-terminal • zsh
$ usel doctor
[✓] Python 3.12.2 (CPython x86_64 target)
[✓] CPU SIMD: AVX-512 extensions active
[✓] System Memory: 16.0 GB Total • 11.4 GB Free (Exceeds 8 GB budget)
[✓] BLAS Backend: OpenBLAS 0.3.26 with SIMD dispatch
→ 4/4 checks passed. Environment is fully optimized for USEL simulations.
$ usel benchmark --size 200
[*] Generating 200x200 symmetric random matrix (Wigner Ensemble)...
[*] Running divide-and-conquer tridiagonal solver...
[+] Matrix Dimension: 200 x 200 (40,000 floats)
[+] Execution Time: 1.42 seconds
Residual Norm ||AX - λX||_F: 2.11e-15 (Machine Epsilon Preserved)
$
Technical Milestones

Roadmap for computational physics.

Expanding supported continuous differential equations strictly on the CPU.

v1.0 Released
Foundation
  • • Matrix & vector primitives
  • • LAPACK eigensystem
  • • Basic ODE integrators
  • • System doctor CLI
Production Stable
v1.1 Released
Schrödinger PDE
  • • Crank-Nicolson complex
  • • Split-operator FFT
  • • Tunneling barriers
  • • Wave packet propagation
Completed
v1.2 Released
Dirac Equation
  • • Relativistic 4-spinors
  • • Pauli matrix algebra
  • • Klein tunneling physics
  • • Zitterbewegung dynamics
Completed
v1.3 Released
Maxwell Field
  • • FDTD time-domain waves
  • • PML boundary conditions
  • • Dielectric interfaces
  • • Poynting energy vectors
Completed
v1.4 Released
Stochastic PDE
  • • Black-Scholes solver
  • • Ito calculus step engine
  • • Greeks sensitivity analysis
  • • Heat transform mappings
Completed
v1.5 Next
Wave Equation
  • • Finite-difference wave solver
  • • Acoustic propagation
  • • Electromagnetic waves
  • • Boundary reflections
Planned Milestone
v1.6 Planned
PDE Framework
  • • Heat & diffusion equations
  • • Poisson equation
  • • Boundary-value problems
  • • Finite-difference operators
Planned Milestone
v1.7 Planned
Nonlinear Dynamics
  • • Nonlinear ODE solvers
  • • Nonlinear PDE models
  • • Bifurcation analysis
  • • Chaos & attractors
Research Track
v1.8 Planned
Tensor Calculus
  • • Tensor operations
  • • Metric & inverse metric
  • • Christoffel symbols
  • • Curvature tensors
Research Track
v1.9 Future
Quantum Chromodynamics
  • • SU(3) gauge fields
  • • Lattice discretization
  • • Gauge-field dynamics
  • • Quark & gluon interactions
Advanced Research
Architectural Non-Goals

Deliberately focused.

What we refuse to build is just as intentional as what we ship.

✕ NO QUANTUM CIRCUIT HYPE

USEL is not a noisy quantum gate simulator. We model continuous wave functions and real physical Hamiltonians.

✕ NO BULKY ML WEIGHTS

Zero 10GB neural network weights, PyTorch runtime bloat, or black boxes. Pure analytic mathematics and exact numerical solvers.

✕ NO GPU DRIVER LOCK-IN

No CUDA compilation headaches or fragile display driver updates breaking reproducible scientific calculations.

✕ NO CLOUD SUBSCRIPTIONS

Zero remote API keys, usage metering, or cluster logins. You compile the library and run it completely on your local workstation.

AIR-GAPPED COMPLIANT

Nothing leaves your machine.

USEL is packaged with zero telemetry and zero external telemetry listeners. Install via uv, pip, or inspect the entire codebase from GitHub.

✓ Zero HTTP/gRPC telemetry calls
✓ Zero phone-home crash reporters
✓ MIT Permissive License
GET STARTED IN SECONDS POSIX / WINDOWS
Recommended (Modern Fast Package Manager)
uv add usel && uv run usel version
Standard pip
pip install usel
Run Hardware Verification
python -m usel.cli doctor
01

Getting Started Manual

Setup guide covering environment isolation, virtualenv configuration, and first numerical integrals.

Read manual →
02

Complete API Reference

Mathematical signatures, float tolerances, algorithmic Big-O complexities, and exact matrix type specifications.

Explore APIs →
03

Physics Cookbook

Ready-to-run scripts for 1D quantum tunneling, coupled harmonic oscillators, and spectral wave packet expansion.

View recipes →

Frequently Asked Questions

Answers regarding hardware compatibility and licensing.

What is USEL in one sentence? ↓

USEL (Universal Scientific Engineering Library) is an open-source, CPU-first numerical framework designed specifically for physicists requiring deterministic simulation without bulky ML runtimes.

Will USEL ever require a GPU or CUDA? ↓

No. It is an explicit architectural contract to keep the entire engine executable on standard CPU SIMD instructions (AVX-512, AVX2, NEON) so calculations remain accessible and fully portable.

How does USEL guarantee reproducible simulations? ↓

We use strict IEEE-754 double precision floating-point algorithms and deterministic random number harnesses that yield bit-identical eigenvalues regardless of whether executed on macOS or Linux.

Is USEL free for academic and commercial use? ↓

Yes. USEL is licensed under the permissive MIT License. You may freely use it in proprietary software, research papers, and industrial simulation pipelines.

STABLE RELEASE • MIT LICENSE

The foundation for deterministic physics.

Join researchers and engineers using USEL for reproducible numerical physics.

INSTALL USEL v1.0 terminal STAR ON GITHUB
pip install usel • SHA-256 Verified • No Telemetry