📐 Advanced AIML — Mathematics + Physics Focus

Advanced AI & Machine Learning for Mathematics and Physics

This track is designed for students who want strong fundamentals, scientific reasoning, and research-ready work (EE support included).

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Course modules (Advanced level)

  • Linear Algebra: eigenvalues/eigenvectors, SVD, projections, PCA from first principles
  • Calculus: gradients, Jacobians, Hessians, chain rule in vector form
  • Optimization: GD/SGD, momentum, Adam intuition + convergence basics
  • Probability: Bayes theorem, priors/posteriors, expectation/variance, LLN/CLT intuition
  • Statistics: MLE/MAP, confidence intervals, hypothesis testing, p-values (correct interpretation)

  • Bias–variance tradeoff and why it appears mathematically
  • Regularization: L1/L2, early stopping, shrinkage, model complexity control
  • Cross-validation strategies and leakage prevention (critical in research)
  • Metrics beyond accuracy: calibration, uncertainty, error decomposition
  • Interpretable ML: SHAP intuition, sensitivity analysis, stability checks

  • Noise models: Gaussian, Poisson; measurement uncertainty & propagation
  • Signal processing basics: smoothing, filtering, FFT intuition, peak detection
  • Time-series modeling: stationarity, autocorrelation, feature extraction
  • Parameter estimation: fitting physical models to data (linear/nonlinear least squares)
  • Outliers and robust regression (Huber / RANSAC intuition)

  • Bayesian methods: posterior reasoning, credible intervals, uncertainty
  • Gaussian Processes: regression with uncertainty + kernel choice intuition
  • State-space models: Kalman filter overview + where it is used
  • Inverse problems: estimating hidden parameters from observed data
  • Physics-Informed ML overview (PINNs concept + when it helps / fails)

  • How to choose a research question (RQ) with measurable outcomes
  • Dataset design: simulation vs real data, controls, fairness, limitations
  • Experimental design: ablation, baselines, error bars, sensitivity testing
  • Writing methodology like a scientist (reproducibility + transparency)
  • Ethics + academic integrity (no black-box claims, proper citations)

Who this is for

✅ Strong Math-first learning
We focus on linear algebra, calculus, optimization, uncertainty, and scientific evaluation.
✅ Physics + ML integration
Projects connect ML to motion, oscillations, signals, noise, and real experimental-style data.
✅ EE-ready research approach
We emphasize methodology, baselines, limitations, and reproducibility — not just model training.

Physics + Maths AIML projects (Advanced)

Projectile Motion: Parameter Estimation (with Drag)

Advanced
Math focus: Nonlinear regression, error propagation
Outcome: Estimate drag/initial velocity; compare model vs data; analyze residuals.

Pendulum / Damped Oscillator: ODE Fit to Data

Advanced
Math focus: Differential equations + optimization
Outcome: Fit damping constant; validate using held-out trials; uncertainty intervals.

Spectral Peak Detection (FFT + ML Features)

Advanced
Math focus: FFT, smoothing, feature engineering
Outcome: Detect peaks reliably under noise; compare filters + thresholds + ML classifier.

Inverse Problem: Estimate Material Constant from Thermal Data

Advanced
Math focus: Curve fitting + model selection
Outcome: Infer parameter from heat/cooling curve; compare linear vs nonlinear models.

Chaos / Lorenz System: Short-horizon Forecasting

Advanced
Math focus: Dynamical systems + time-series
Outcome: Feature-based forecasting; show limits of predictability.

Gravitational Field Mapping (Regression + Uncertainty)

Advanced
Math focus: Regression, uncertainty estimation
Outcome: Predict field intensity from inputs; show confidence bounds and limitations.

Extended Essay support in AIML (Math/Physics angle)

We help students build a research-quality EE: clear RQ, correct methodology, strong evaluation, and honest limitations.

What you get

  • Selecting a strong RQ (specific, measurable, not too broad)
  • Method design: baselines, variables, controls, and evaluation strategy
  • Data strategy: simulation vs real data + justification
  • Write-up structure: intro → theory → method → results → evaluation → limitations
  • Academic integrity: tool usage disclosure + citations + reproducibility

EE structure (recommended)

  1. Introduction: context + clear RQ + why it matters
  2. Theory: physics model + relevant math/ML theory (not textbook dump)
  3. Methodology: data collection/simulation + preprocessing + models + metrics
  4. Results: tables/plots + uncertainty + error analysis
  5. Discussion: why results happened + limitations + improvements
  6. Conclusion: answer the RQ directly (with evidence)

Sample EE research questions (AIML)

  • To what extent can Gaussian Process Regression model the relationship between temperature and resistance for a conductor under varying measurement noise?
  • How does the choice of kernel in a Gaussian Process affect prediction uncertainty when modeling a damped oscillator from experimental data?
  • To what extent can regularization (L1 vs L2) improve generalization when estimating parameters of projectile motion with air resistance from noisy measurements?
  • How accurately can FFT-based features classify different oscillation regimes (underdamped/critical/overdamped) under controlled noise levels?
  • To what extent can a state-space model (Kalman filter) reduce measurement noise compared to moving-average filtering for motion tracking data?
  • How does dataset generation method (simulation vs real measurements) affect the validity of conclusions in an ML-based physics model?