What question did this study set out to answer?

This research aims to develop hybrid simulation frameworks combining various methods to improve predictive accuracy in multiple domains.

February 11, 2026Open Access

Hybrid Simulation Frameworks: Cross-Domain Integrations of Monte Carlo, Tails, HOMER and/or Markov

Key Points

This research aims to develop hybrid simulation frameworks combining various methods to improve predictive accuracy in multiple domains.
Developed hybrid frameworks integrating Monte Carlo, MoP-Tails, HOMER optimization, and Markov processes.
Analyzed performance across physics, finance, and social dynamics applications.
Compared variance reductions and predictive power against baseline methods.
MoP-Tails achieved up to 2.5x variance reduction on average across domains.
MCMC-HOMER reached a predictive improvement of 4.1x in social dynamics.
HMC-PDMP resulted in overall gains greater than 2x across physics, finance, and social applications.

Abstract

Abstract Hybrid simulation frameworks integrating Monte Carlo methods, heavy-tailed distributions (MoP-Tails), HOMER optimization, and Markov processes offer transformative predictive power across physics, finance, and social dynamics. Novel "predictive pairs": - Monte Carlo + MoP-Tails: `p (x) =∑πₖqₖ (x) 1₍|x|≤τ+tₖ (x) 1₍|x|>τ` (50-80% variance reduction) - MCMC-HOMER: `Vπ=Eπ∑γᵗc (Xₜ, Aₜ) ` (energy optimization) - HMC-PDMP: `dXₜ=b (Xₜ) dt+∫J (Xₜ₋) Ñ (dt, dJ) ` (physics/social cascades) Figure of Merit gains >2x baselines validated across: - Physics: multilayer particle transport- Finance: Lévy-driven VaR/CVaR - Social: resource-constrained contagion FOM Results: | Method | Physics | Finance | Social | Average ||--------|---------|---------|--------|---------|| Plain MC | 1. 0x | 1. 0x | 1. 0x | - || 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 | Code & Figures**Live implementation: ** GitHub MIT repo (https: //github. com/maisondebeausoleil/hybrid-sim-frameworks) - `src/mcₘoptails. py`, `mcmcₕomer. py`, `hmcₚdmp. py`- Jupyter demos reproducing all figures/tables Submission Info- **Target: ** arXiv physics. comp-ph q-fin. CP (endorsement pending) - **Keywords: ** Monte Carlo, heavy tails, Markov chains, HMC, PDMP, HOMER, predictive modeling- **License: ** CC-BY-4. 0 | **Code: ** MIT- **Marlon J. Broussard, New Orleans, Louisiana independent researcher, Feb 2026**

Hybrid Simulation Frameworks: Cross-Domain Integrations of Monte Carlo, Tails, HOMER and/or Markov

Key Points

Abstract

Cite This Study