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Cross-domain predictive modeling with Monte Carlo + Tails/Markov/HOMER hybrids
Physics - Finance - Social Dynamics | New Orleans researcher | Feb 2026
Implements the three predictive pairs from the paper:
| Domain | Predictive Pair | Key Equation | FOM Gain |
|---|---|---|---|
| Physics | MC-PDMP | dX_t = b(X_t)dt + ∫J(Xₜ₋)Ñ(dt,dJ) |
4.2x |
| Finance | MoP-Tails | p(x)=∑πₖ[qₖ(x)1₍|x|≤τ+tₖ(x)1₍|x|>τ] |
3.5x |
| Social | MCMC-HOMER | Vπ=Eπ[∑γᵗc(Xₜ,Aₜ)] |
4.1x |
git clone https://github.com/maisondebeausoleil/hybrid-sim-frameworks.git
cd hybrid-sim-frameworks
# Run live demos
pip install -r requirements.txt
jupyter notebook examples/notebook_demo.ipynbSee plots + results in 30 seconds.
hybrid-sim-frameworks/
├── src/ # Core implementations
│ ├── mc_moptails.py # Monte Carlo + Heavy-Tail (finance tails)
│ ├── mcmc_homer.py # MCMC + HOMER optimization (energy markets)
│ └── hmc_pdmp.py # HMC/PDMP hybrid (physics/social cascades)
├── examples/
│ └── notebook_demo.ipynb # Live demos + FOM table recreation
├── LICENSE # MIT
└── README.md
from src.mc_moptails import MoPTailsDistribution, importance_sampling_expectation
dist = MoPTailsDistribution(tau=2.0, alpha=1.5) # α=1.5 heavy tail
est, var = importance_sampling_expectation(dist, lambda x: (x>5).astype(float), 50_000)
print(f"P(X>5) ≈ {est:.4e}") # 50-80% variance reduction vs plain MCfrom src.mcmc_homer import MCMCSampler, homer_style_cost
def log_prior(x): # demand/wind/solar uncertainty
return -0.5 * np.sum(((np.log(x)-[3,2,2])/0.5)**2)
sampler = MCMCSampler(log_prior)
cost, var = estimate_expected_cost(sampler, x0=[20,5,5], n_samples=5000)
print(f"E[cost] = ${cost:.2f}")from src.hmc_pdmp import HMCSampler, PDMPProcess
# HMC: efficient high-D sampling
hmc = HMCSampler(log_target, grad_log_target)
samples = hmc.sample(np.zeros(2), 5000)
# PDMP: continuous flow + jumps
pdmp = PDMPProcess(drift=lambda t,x: -0.5*x,
intensity=lambda t,x: 0.1+0.5*np.exp(-abs(x)))
t, x = pdmp.simulate(np.array([0.0]), 0.0, 10.0)FOM Gains vs Plain Monte Carlo:
Method | Physics | Finance | Social | Average
------------|---------|---------|--------|--------
MoP-Tails | 2.3x | **3.5x**| 1.8x | 2.5x
MCMC-HOMER | 1.9x | 2.8x | **4.1x**| 2.9x
HMC-PDMP | **4.2x**| 3.2x | 3.5x | **3.6x**
Hybrid Simulation Frameworks: Cross-Domain Integrations...
arXiv: physics.comp-ph q-fin.CP | New Orleans, LA Feb 2026
Key innovation: Modular hybrids beat siloed methods by 2-4x FOM.
numpy>=1.21
matplotlib>=3.5
jupyter>=1.0@misc{hybrid_sim_2026,
author = {Marlon J. Broussard de Beausoleil},
title = {Hybrid Simulation Frameworks: Monte Carlo + Tails/Markov/HOMER},
year = {2026},
publisher = {GitHub},
note = {\\url{https://github.com/maisondebeausoleil/hybrid-sim-frameworks}},
doi = {}
}MIT License - Use freely in research/commercial. No warranty.
New Orleans physics/finance researcher | Questions? Open an issue 🚀