Explo/presentation.html at master · Wvidit/Explo · GitHub

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<!DOCTYPE html>
<html lang="en">
<head>
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    <title>Computational Design of Wollastonite</title>
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</head>
<body>

<!-- Slide 1: Introduction -->
<div class="slide-container" id="slide1">
    <div class="title-layout">
        <h1>Computational Design of Wollastonite</h1>
        <p class="subtitle">A Mathematical Framework for RVE Generation, PDE Integration, and Gradient Boosted Surrogate Modeling</p>
    </div>
    <div class="slide-counter">1 / 7</div>
</div>

<!-- Slide 2: RVE Generation -->
<div class="slide-container" id="slide2">
    <h2 class="slide-title">Phase I: Microstructure Generation (RVE)</h2>
    <div class="content-area">
        <div class="two-column">
            <div>
                <ul>
                    <li><strong>Random Sequential Adsorption (RSA):</strong> The <code>rve_generator.py</code> engine places non-overlapping spherical wollastonite inclusions into the matrix, iteratively checking for spatial collisions.</li>
                    <li><strong>Dynamic Meshing:</strong> The <code>geometry_meshing.py</code> script automatically discretizes the complex multi-phase domain, handling varying volume fractions and inclusion radii.</li>
                    <li><strong>Statistical Reliability:</strong> By computationally matching real-world microstructural distributions, the generated domain becomes a highly accurate digital twin for physical composite samples.</li>
                </ul>
            </div>
            <div>
                <div class="image-wrapper">
                    <img src="rve_visualization.png" alt="RVE Visualization">
                </div>
                <p class="image-caption">Fig 1: Mathematically generated 3D phase-domain with spatial constraints.</p>
            </div>
        </div>
    </div>
    <div class="slide-counter">2 / 7</div>
</div>

<!-- Slide 3: FEA Simulation -->
<div class="slide-container" id="slide3">
    <h2 class="slide-title">Phase II: PDE Multiphysics Integration (FEA)</h2>
    <div class="content-area">
        <div class="two-column">
            <div>
                <ul>
                    <li><strong>Ansys PyMAPDL Automation:</strong> Using <code>fe_simulations.py</code>, we solve \( \nabla \cdot \boldsymbol{\sigma} = 0 \). Effective Young's Modulus (\( E_{eff} \)) is computed via volume-averaged integration:</li>
                </ul>
                <div class="math-block">
                    \[ E_{eff} = \frac{\langle \sigma_{11} \rangle}{\varepsilon_{11}^{0}} = \frac{1}{V_{RVE} \cdot \varepsilon_{11}^{0}} \int_{V} \sigma_{11}(\mathbf{x}) \, dV \]
                </div>
                <ul>
                    <li><strong>Steady-State Thermal Conduction:</strong> Solving \( \nabla \cdot (k(\mathbf{x}) \nabla T) = 0 \), Fourier's law yields the effective macroscopic thermal conductivity \( k_{eff} \):</li>
                </ul>
                <div class="math-block">
                    \[ k_{eff} = \frac{-1}{\nabla T_{applied}} \left( \frac{1}{V_{RVE}} \int_{V} q_x(\mathbf{x}) \, dV \right) \]
                </div>
            </div>
            <div>
                <div class="image-wrapper">
                    <img src="property_vs_porosity.png" alt="Property vs Porosity Plot">
                </div>
                <p class="image-caption">Fig 2: Non-linear decay mapping of numerical PDE solutions relative to porosity \(\phi\).</p>
            </div>
        </div>
    </div>
    <div class="slide-counter">3 / 7</div>
</div>

<!-- Slide 4: ML Parity -->
<div class="slide-container" id="slide4">
    <h2 class="slide-title">Phase III: Non-Linear Surrogate Architecture</h2>
    <div class="content-area">
        <div class="two-column">
            <div>
                <ul>
                    <li><strong>Gradient Boosting Regressors:</strong> <code>ml_surrogate.py</code> trains separate models for \( E_{eff} \) (GPa), \( k_{eff} \) (W/mK), CTE (ppm/K), Density (kg/m³), and Vickers Hardness (HV) using an additive expansion:</li>
                </ul>
                <div class="math-block">
                    \[ \hat{f}_{ML}(\mathbf{x}) = F_0 + \sum_{m=1}^{M} \gamma_m h_m(\mathbf{x}) \]
                </div>
                <ul>
                    <li><strong>Loss Minimization:</strong> Each iteration minimizes the differentiable loss over the <code>simulation_database.json</code>:</li>
                </ul>
                <div class="math-block">
                    \[ \gamma_m = \arg\min_{\gamma} \sum_{i=1}^{N} L\left(y_i, F_{m-1}(\mathbf{x}_i) + \gamma h_m(\mathbf{x}_i)\right) \]
                </div>
            </div>
            <div>
                <div class="image-wrapper">
                    <img src="ml_parity_plots.png" alt="ML Parity Plots">
                </div>
                <p class="image-caption">Fig 3: Tight dispersion around \( y = \hat{y} \), indicating high predictive \( R^2 \) confidence.</p>
            </div>
        </div>
    </div>
    <div class="slide-counter">4 / 7</div>
</div>

<!-- Slide 5: Feature Importance -->
<div class="slide-container" id="slide5">
    <h2 class="slide-title">Phase IV: Sensitivity Analysis</h2>
    <div class="content-area">
        <div class="two-column">
            <div>
                <ul>
                    <li><strong>Identifying Drivers:</strong> Tree-based feature importance algorithms calculate the relative contribution of microstructural parameters to the final material properties.</li>
                    <li><strong>Porosity Impact:</strong> The analysis highlights porosity as the overwhelming primary factor dictating mechanical stiffness, thermal conductivity, and Vickers Hardness.</li>
                    <li><strong>Analytical Validation:</strong> Predictions are rigorously validated against <code>analytical_fallback.py</code>, which computes theoretical continuum boundaries (e.g., Voigt, Reuss, Hashin-Shtrikman) to ensure physical viability.</li>
                </ul>
            </div>
            <div>
                <div class="image-wrapper">
                    <img src="feature_importance.png" alt="Feature Importance Chart">
                </div>
                <p class="image-caption">Fig 4: Gini impurity reduction showing porosity \( \phi \) as the dominant mathematical driver.</p>
            </div>
        </div>
    </div>
    <div class="slide-counter">5 / 7</div>
</div>

<!-- Slide 6: Reverse Design -->
<div class="slide-container" id="slide6">
    <h2 class="slide-title">Phase V: Reverse Design Strategy</h2>
    <div class="content-area">
        <div class="two-column">
            <div>
                <ul>
                    <li><strong>Objective-Driven Discovery:</strong> Target performance constraints (e.g., minimum \( E_{eff} \), maximum CTE) are mapped backward to discover the optimal microstructural parameters.</li>
                    <li><strong>Design Space Mapping:</strong> Visualizing the trade-offs between competing properties to find the ideal material "Goldilocks" zone across the multi-objective \( \mathbb{R}^n \) parameter space.</li>
                    <li><strong>Rapid Prototyping:</strong> The digital pipeline rapidly identifies the precise porosity and filler volume fractions required, eliminating months of trial-and-error physical testing.</li>
                </ul>
            </div>
            <div>
                <div class="image-wrapper">
                    <img src="reverse_design_map.png" alt="Reverse Design Map">
                </div>
                <p class="image-caption">Fig 5: Traversing the multi-objective \( \mathbb{R}^n \) parameter space for optimal solutions.</p>
            </div>
        </div>
    </div>
    <div class="slide-counter">6 / 7</div>
</div>

<!-- Slide 7: Outro -->
<div class="slide-container" id="slide7">
    <div class="content-area">
        <div class="qa-layout">
            <h2>Questions?</h2>
            <p class="subtitle">Thank you for your attention.</p>
            <div class="contact-info">
                Project: Explo/Wollastonite | Integrated Computational Materials Engineering (ICME)
            </div>
        </div>
    </div>
    <div class="slide-counter">7 / 7</div>
</div>

</body>
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