ML-driven prediction of phononic bandgaps in rhombic unit cells with air hole inclusions. Select geometric parameters below to visualize the unit cell, view COMSOL-computed band structures, and get ML predictions for bandgap presence and width — trained on 3,000 COMSOL simulations.
Geometric Parameters
Select parameters and click Analyze.
Nearest COMSOL Data Point
Thickness Ratio—
Filling Fraction—
Distance—
ML Prediction
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Predicted Bandgap—
Actual (COMSOL)—
Dirac Cone Detection
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Cone Frequency—
Band Pair—
Gap at Cone—
COMSOL Bandgap Data
Bandgap Width—
Lower Edge—
Upper Edge—
Center Freq—
ML Model Info
Classification
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Regression
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Band Structure NN
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Dirac Cone Classifier
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Dataset
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3D Unit Cell Geometry
a01.000 mm
a = a0√3—
r0 (hole radius)—
h (thickness)—
Band Structure — Dispersion Relation
ML Bandgap Prediction Map
Inverse Design — Target Bandgap Optimizer
Specify a target frequency and minimum bandgap width. The optimizer will search
the design space to find geometric parameters that maximize the bandgap at your
desired frequency.
1200 kHz
50 kHz
Shape Explorer — Fourier Inclusion Optimization
Explore non-circular inclusion shapes using Fourier descriptors:
r(θ) = r0 + Σ[ancos(nθ) + bnsin(nθ)].
The NN predicts band structure using physics-informed shape correction.
Area—
Perimeter—
Shape Factor—
Eccentricity—
Predicted Bandgap: —
Sensitivity Analysis & Advanced Metrics
Sensitivity maps show how the predicted bandgap changes with each geometric parameter.
Gradient magnitude reveals regions of rapid change in the design space.
Group Velocity Dispersion
Group velocity vg = dω/dk computed from band structure data.
Zero crossings indicate van Hove singularities; negative values show backward-wave propagation.
Analyze a sample first to populate this plot.
Density of States & Transmission
Phononic DOS computed from the band structure histogram. Transmission spectrum via Transfer Matrix Method (TMM)
for N periodic layers. Analyze a sample first.
SHAP Feature Attribution
Perturbation-based Shapley value approximation showing how each feature contributes
to the bandgap prediction. Analyze a sample first.
Crystal Plate 3D Visualization
Full tiled phononic crystal plate with rhombic array of circular air holes (BOROFLOAT® 33 borosilicate glass).
Interactive 3D view with orbit controls. ExtrudeGeometry with actual through-holes matching COMSOL geometry.
Unit Cell Geometry
Single rhombic unit cell with two circular air holes. Vectors: v1=(a,0), v2=(a/2, a√3/2).
Material Properties
Substrate: BOROFLOAT® 33 borosilicate glass (Schott). ASTM E 438-92 Type 1, Class A.
Simulation Parameters
FEA solver: COMSOL Multiphysics (Solid Mechanics + PDE)
Boundary: Floquet-Bloch periodic conditions
k-path: Γ → K → M → Γ (61 points)
Eigenfrequencies: 15 bands per k-point
Topological Phase Analysis
Band inversion detection, Zak phase computation, and topological phase diagram
across the full design space. Identifies trivial vs non-trivial topological phases.
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Design Space Atlas (t-SNE)
t-SNE dimensionality reduction of the full design space. Click any point
to navigate to that design in the Analysis tab. Distinct clusters reveal
bandgap vs no-bandgap regions and design families.
ML Pipeline Architecture
InputThicknessRatio, FillingFraction
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Feature Engineering16 derived features
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ClassifierHas bandgap? (Y/N)
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RegressorBandgap width (kHz)
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PredictionBandgap + Band Structure
COMSOL FEA Data
3,000 rhombic unit cell simulations with air hole inclusions. 61 k-points along the irreducible Brillouin zone path, 15 frequency bands per sample.