fluctuation-regularized-optimization

Research code for fluctuation-regularized optimization: Lifshitz-style swarm search, zero-point-smoothed PyTorch optimization, and gradient-pressure balancing for PINNs and other multi-term losses.

This repository contains a research prototype, not a published PyPI package. Install it from source when you want to reproduce the tests, run the benchmarks, or inspect the implementation.

What this is

fluctuation-regularized-optimization explores three concrete optimization mechanisms: Lifshitz-style swarm coupling, zero-point-smoothed gradient updates, and gradient-pressure loss balancing. The Python import remains fluctuation_opt.

The name is intentionally descriptive. This is not "a Casimir optimizer" and not a claim that the code is a complete physical simulator of the Casimir effect. Casimir/Lifshitz physics is one source of the mathematical analogy.

Component	Use it for	Main idea
LifshitzSwarm	Derivative-free black-box search	Candidate solutions act like partially reflective mirrors coupled by short-range Lifshitz-style attraction.
ZeroPointOptimizer	PyTorch training	Optimizes a zero-point-smoothed effective loss, biasing training toward flatter minima.
GradientPressureBalancer	PINNs and multi-term losses	Reweights loss terms by measured gradient pressure so one term does not dominate the others.
fluctuation_opt.core	Physics/numerics utilities	Matsubara schedules, Lifshitz couplings, stochastic Lanczos quadrature, and zero-point-energy diagnostics.

The strongest current evidence is for robustness and stiff/rugged problems, especially PINNs. This is not claimed to beat tuned standard optimizers on every benchmark.

For the actual mechanism mappings, equations, assumptions, and failure modes, read docs/mechanisms.md.

Quick links

• Mechanisms and math
• Public API
• Reproducibility guide
• Benchmark report
• Contributing
• Release checklist
• Draft v0.1.0 release notes
• Roadmap
• Changelog

Current validation status

The repository includes:

Artifact	Location
Validation report	REPORT.md
Paper source	paper/paper.tex
Mechanism/math explanation	docs/mechanisms.md
Unit/integration tests	tests/
Benchmark scripts	benchmarks/
Raw benchmark outputs and figures	benchmarks/results/
Quickstart example	examples/quickstart.py
Contributor/community docs	CONTRIBUTING.md, CODE_OF_CONDUCT.md, SECURITY.md, SUPPORT.md

The report summarizes the existing generated results. The headline results are:

Experiment	Honest result
Classic black-box functions	LifshitzSwarm beats random search by large margins and is now close to PSO/DE on Griewank, but tuned PSO/DE still reach better final precision on several smooth functions.
Poisson PINN	Gradient-pressure balancing prevents Adam failures and gives the best accuracy in the current run; zero-point + pressure gives the best perturbation robustness.
Heat equation PINN	Plain Adam is most accurate; zero-point + pressure balancing is more robust but less accurate.
Burgers equation PINN	Zero-point + pressure balancing gives the best median error and best robustness in the included runs.
Digits classification	Zero-point smoothing ties Adam median test error and improves perturbation robustness.
California housing	Zero-point smoothing is less accurate than Adam but more robust.
Real Casimir data fit	LifshitzSwarm matches scipy differential evolution and recovers a gold plasma frequency near 9.21 eV; the fitted separation offset is pinned at the -0.60 nm bound and should be treated as a caveat.

Install from source

Use Python 3.11 or another PyTorch-supported Python version.

python3.11 -m venv .venv
source .venv/bin/activate
python -m pip install --upgrade pip
python -m pip install -r requirements-dev.txt

For a lighter install without benchmark extras:

python -m pip install -e .[test]

Run checks

pytest
python examples/quickstart.py
python -m build --wheel

Reproduce benchmark artifacts

The full benchmark suite can take a while on CPU.

python benchmarks/blackbox_benchmark.py --seeds 20
python benchmarks/pinn_benchmark.py
python benchmarks/pde_benchmark.py --pde heat
python benchmarks/pde_benchmark.py --pde burgers --budget 18000
python benchmarks/ml_benchmark.py --dataset digits
python benchmarks/ml_benchmark.py --dataset housing
python benchmarks/casimir_data_fit.py

Then compare the regenerated files in benchmarks/results/ against the tables in REPORT.md.

Repository map

fluctuation_opt/
  core/              # Lifshitz, Matsubara, and spectral utilities
  swarm.py           # LifshitzSwarm black-box optimizer
  torch_optim.py     # ZeroPointOptimizer PyTorch optimizer
  pinn.py            # PINN pressure balancer and helpers
benchmarks/          # Reproducible experiment scripts
benchmarks/results/  # Raw CSV/JSON results and generated figures
tests/               # Unit and integration tests
paper/               # Paper source and rebuild note

The paper source was updated with the accurate project/API names. A compiled PDF is not tracked until it can be regenerated from the updated source with a local LaTeX engine.

Scope and caveats

• This is research code at version 0.1.0.
• It is not currently published on PyPI.
• The strongest current use case is stiff/rugged optimization, especially PINN-style training and noisy derivative-free physics fitting.
• On smooth toy functions where machine-precision convergence is the goal, the deliberate zero-point noise floor is a disadvantage.
• The included results should be treated as reproducible experiments, not as proof of universal optimizer superiority.

Contributing

Contributions are welcome when they are scoped, reproducible, and aligned with the mechanism-based naming. Start with CONTRIBUTING.md.

For bugs, feature requests, and benchmark reproduction questions, use the GitHub issue templates. Pull requests should include tests, docs, or benchmark evidence appropriate to the change.

Citation

Citation metadata is provided in CITATION.cff. If you use this repository, cite the repository and describe the exact commit or release used.