Bayesian Optimization for pharmaceutical tablet formulation

Problem statement

Tablet formulation development is expensive because each wet-lab experiment consumes time and material.
With interacting excipients and hard constraints (mass balance + bounds), naive screening methods like OFAT or brute-force grids waste runs and miss high-performing regions.

This project answers one core question: How do we find good formulations faster, with fewer experiments, under realistic formulation constraints?

Explainer (60-second animated overview)

Full video (MP4): bo_explainer.mp4

What is Q45?

Q45 is the percentage of drug dissolved at 45 minutes (0-100%).
In general form:

[ Q45 = 100 \times \frac{\text{drug dissolved at 45 min}}{\text{labeled drug amount}} ]

In this repo, each experiment returns a Q45 value (from the synthetic simulator), and optimization aims to maximize that value under formulation constraints.

Project description

This repository implements a model-based DoE and Bayesian optimization pipeline for pharmaceutical formulation design.
Gaussian Process surrogate models guide sample-efficient exploration of constrained excipient space.

• Single-objective BO: optimize Q45 using GP + EI/LogEI style acquisition (notebooks + Streamlit app)
• Multi-objective BO: optimize trade-offs among Q45, hardness, and friability using qNEHVI (Notebook 4)
• Interactive Streamlit dashboard for design-space exploration, experiment logging, and convergence/strategy comparison

Visual overview

Optimization workflow

Headline benchmark result

Our solution

We use a model-based DoE loop with Bayesian Optimization (BO):

1. Fit a probabilistic surrogate (Gaussian Process) on observed formulation outcomes.
2. Quantify uncertainty over unexplored regions.
3. Select the next experiment using an acquisition function (Expected Improvement).
4. Update the model with the new result and repeat.

In short: we replace blind search with uncertainty-aware sequential experimentation.

Formulation context

• Fixed API: 30% w/w
• Excipients sum to 70% w/w with bounds:
  • HPMC: 0-20%
  • MCC: 20-60%
  • CCS: 1-8%
  • MgSt: 0.25-2%
  • PVP K30: derived by mass balance, constrained to 0-10%
• Primary objective: maximize Q45 (dissolution at 45 min)

How we solve it in this repo

1) Baseline DoE (why naive design is insufficient)

• notebooks/01_doe_baseline.ipynb
• Shows factorial feasibility collapse under constraints, then constrained D-opt proxy + CCD-style baseline, then quadratic RSM.

2) Core BO loop

• notebooks/02_bayesian_optimization.ipynb
• Runs BO end-to-end (init design + sequential suggestions), with convergence, posterior, and acquisition plots.

3) Benchmark vs alternatives

• notebooks/03_comparison.ipynb
• Compares BO against random/grid/RSM-guided search under equal evaluation budget.

4) Multi-objective BO extension

• notebooks/04_multiobj_bo.ipynb
• Uses qNEHVI to jointly optimize dissolution (Q45), hardness, and friability via Pareto trade-offs.

5) Interactive app for scientists

• app/streamlit_app.py
• Explore design space, run one-step BO suggestions, log experiments, view convergence, and compare strategies.

Quick start

python -m venv .venv
source .venv/bin/activate
pip install -r requirements.txt

Run notebooks:

jupyter lab

Run app:

streamlit run app/streamlit_app.py

Why this matters (CMC/QbD relevance)

• Maps directly to model-based DoE under constraints.
• Uses GP uncertainty for design space characterization.
• Prioritizes runs via acquisition for systematic experiment planning.
• Supports multi-CQA trade-offs via Pareto fronts.

Assumptions and limitations

• Uses a physics-informed synthetic simulator (not proprietary lab data).
• Adds Gaussian observation noise to mimic experimental variability.
• Demonstrates method on a 5-variable space; real programs may include more CQAs/process factors/categorical variables.