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Academic / Technical

Mathematical Modeling and Optimization

A chip thermal management modeling project using surrogate models, multi-objective optimization, weight sensitivity analysis, and Monte Carlo robustness checks.

Status
Completed computational modeling workflow
Role
Independent practice project
Tools
Python, NumPy, pandas, matplotlib, LaTeX

Overview

This project records a computational modeling and optimization workflow for a high-performance chip thermal management problem. The work combines data processing, exploratory analysis, surrogate modeling, multi-objective optimization, weight sensitivity analysis, and robustness checks.

The emphasis is on building a defensible modeling pipeline with clear assumptions, reproducible outputs, and readable tables and figures.

What I Studied / Implemented

  • Data cleaning and normalization for chip thermal performance data
  • Surrogate models for thermal resistance, pressure drop, and temperature nonuniformity
  • Model comparison with Gaussian process regression and polynomial response-surface models
  • Pareto analysis, weighted-sum ranking, and TOPSIS ranking
  • Dense surrogate search over the design space
  • Weight-scenario analysis and random weight sampling
  • Monte Carlo manufacturing-perturbation checks and flow-rate fluctuation analysis

Methods or Workflow

The workflow begins with cleaning and exploring the provided performance data, then builds surrogate models for the three target quantities. The optimization stage compares sample-space candidates and surrogate-search candidates using Pareto filtering, weighted sums, and TOPSIS.

The robustness stage studies how recommendations change under different objective weights, local parameter perturbations, discrete pin-row changes, Monte Carlo manufacturing errors, and approximate flow-rate fluctuations.

Outputs

  • Processed and normalized datasets
  • Saved surrogate models and model-selection summaries
  • Tables for data description, model metrics, Pareto candidates, top ranked designs, weight scenarios, robustness metrics, and Monte Carlo outputs
  • Figures for main effects, correlation heatmap, model prediction checks, Pareto fronts, candidate comparison, weight sensitivity, robustness metrics, local sensitivity, Monte Carlo distributions, and flow-rate fluctuation
  • A written modeling paper and supporting figure/table checklists

What I Learned

The project helped me practice connecting modeling assumptions to numerical outputs. The optimization did not reduce to a single universal answer: the main recommended design and robust alternatives depend on how average performance, stability, and risk are weighted.

Limitations

The project is presented as a computational modeling workflow, not as a competition result or a research claim. The conclusions are based on surrogate predictions and engineering approximations, not new CFD simulations. They depend on the chosen normalization, objective weights, perturbation assumptions, and available data.