Two-step machine learning enables optimized nanoparticle synthesis

The study addresses the challenge of efficiently discovering synthesis conditions for nanomaterials with predetermined optical properties, a process often hindered by costly and slow experimental data generation and the difficulty of translating ML-suggested materials into synthesizable targets. Recent microfluidic high-throughput experimental platforms mitigate data scarcity by enabling rapid, low-volume experimentation. Prior ML-HTE integrations largely emphasized optimization over sparse datasets, limiting broader knowledge extraction on composition–property relationships. The authors propose a two-step ML framework that spans from sparse to larger datasets to target specific optical spectra and extract mechanistic insight without prior assumptions of model complexity. Silver nanoparticle synthesis is chosen as a testbed due to the nonlinear interplay of nucleation and growth and the strong size/shape-dependent UV-Vis plasmonic signatures. A theoretical absorbance spectrum of triangular nanoprisms serves as the target. While BO is effective for early-stage exploration, it offers limited interpretability and depends on loss design and hyperparameters. Conversely, DNNs can model full spectra but require more data. The central hypothesis is that combining BO (for efficient early exploration) with a DNN (for high-fidelity regression and inverse design once data accumulates) can accelerate optimization and enable knowledge extraction.

The paper situates itself within prior applications of ML in materials science, including drug discovery, imaging, synthesis, molecular generation, and degradation modeling. Previous HTE-ML studies in nanomaterial synthesis primarily optimized scalar spectral features (peak position, FWHM, intensity) and used either substantial initial datasets or static datasets for inverse design, limiting generalization and interpretability. Examples include Kriging-based optimization for perovskite nanocrystals and large RS-initialized datasets to train SVMs/NNs for perovskite discovery. Active learning and BO have been shown effective for exploring mixed discrete/continuous spaces and accelerating discovery, yet they often fix parameter boundaries and focus on optimization rather than learning full spectral relationships. Other regressors (random forests) and Bayesian neural networks have shown potential, but BNNs often need more data to stabilize. The authors highlight gaps: reliance on reduced spectral features, heavy initialization requirements, limited interpretability and transferability, and algorithm sensitivity to parameter scaling—all motivating their two-step BO+DNN approach leveraging full spectra.

• System and targets: A droplet-based microfluidic HTE platform synthesizes Ag nanoparticles using five controlled variables: Qseed (silver seeds), QAgNO3 (silver nitrate), QTSC (trisodium citrate), QPVA (polyvinyl alcohol), and Qtotal (total flow rate). Ascorbic acid flow is held constant. The optical target is a DDSCAT-simulated absorbance spectrum for triangular nanoprisms (50 nm edge, 10 nm thickness). Spectra are recorded in-line.
• Experimental design: Initial parameter bounds (runs 1–5): Qseed, QAgNO3, QTSC in 4–20% of aqueous flow; QPVA 10–40%; Qtotal 200–1000 µL/min. Each suggested condition is executed, droplets flow through a 1.25 m PFA tube; the absorbance spectra of 20 consecutive droplet replicas per condition are collected at 1.4 fps. TEM imaging is performed for best-performing conditions per run for validation of particle morphology/size.
• Two-step algorithmic framework:
  1. Initialization and Step 1 (sparse data): Run 1 uses Latin Hypercube sampling (15 conditions). From run 2 onward, batch BO (batch size 15) with a Gaussian Process surrogate and local penalization (for batch diversity) is applied. The acquisition is EI-based with LP to balance exploration/exploitation. The median loss over 20 droplet replicas per condition is used to update BO. In parallel, an offline DNN is trained on accumulated experimental data.
  2. Step 2 (larger dataset and inverse design): If BO suggestions cluster near parameter bounds across two runs, the parameter space is expanded (from run 6) by relaxing constraints: Qseed, QAgNO3, QTSC, PVA must sum to <90% of aqueous flow; each of Qseed, QAgNO3, QTSC ≥ 0.5%; QPVA remains 10–40%. BO continues suggesting 15 conditions; additionally, a trained DNN performs grid-based inverse design to propose 15 conditions by predicting spectra over a parameter grid and ranking by loss. Example grid: Qseed in [0.5, 80]% (5% steps), QPVA 10–40% (5% steps), Qtotal 200–1000 µL/min (100 µL/min steps); analogous grids for other variables. DNN6 is trained on BO runs 1–6; DNN7 on BO runs 1–7; DNN8 on BO runs 1–8.
• Loss function: Loss = 1 − cosine_similarity(measured, target) − amplitude_penalty, where amplitude penalty β enforces maximal absorbance within spectrometer dynamic range: β(Ameasured/A target) is 1 for ratios below 1.2 and ensures suggestions avoid saturation while prioritizing spectral-shape matching via cosine similarity.
• Model interpretation and validation: SHAP is used to rank feature importances. Pearson correlations between loss components (shape vs amplitude) and total loss are computed across runs. Surrogate minima are projected in key 2D subspaces (e.g., {QAgNO3, Qseed}) comparing GP vs DNN. DNN regression accuracy is assessed by comparing predicted vs measured spectra using cosine similarity and mean squared error (MSE) across runs, employing non-training data (DNN-suggested conditions, last-run BO data, RS data) for validation.
• Simulation and imaging: DDSCAT simulates the target spectrum using silver optical constants over 380–800 nm (25 wavelengths). TEM (JEM-2100F) provides morphology and size distributions; hundreds of particles per best-performing condition are analyzed in MATLAB.
• Data handling: All droplet replicate spectra are used to train BO (probabilistic GP) and DNN (non-probabilistic). Batch size 15 was chosen to reduce experimental overhead (cleaning time/solvents) while maintaining computational tractability with LP.

• Rapid optimization: The BO+DNN framework converged toward the target spectrum after 120 tested conditions (8 runs × 15 conditions, including 15 LH initialization), achieving progressively lower losses per run. DNN-suggested conditions (introduced from run 6) achieved a significantly lower median loss than BO by run 8.
• Spectral convergence: BO best performers rapidly shifted the main absorbance peak to the target (≈645 nm) and reduced sub-600 nm intensity. DNN best performers likewise converged, with predicted spectra smoothing as training data increased.
• Morphological validation: TEM revealed mainly nanospheres and triangular nanoprisms (~30% triangular fraction across runs). Triangular prism edge lengths and sphere diameters increased with runs, with prism edges converging to ≈65 nm (about 30% larger than the simulated 50 nm), consistent with an estimated prism thickness of ~13 nm and aspect ratio effects on plasmon resonance.
• Interpretable optimization dynamics: Correlation analyses showed that from runs 1–5 the loss was more correlated with spectral shape (r ≈ −0.93) than amplitude (r ≈ −0.55), while from runs 6–8 amplitude dominated (r ≈ −0.95 vs shape r ≈ −0.63), reflecting the two-step strategy.
• Feature importance and subspace behavior: SHAP ranked QAgNO3 and Qseed as most important, followed by QTSC, Qtotal, QPVA. In {QAgNO3, Qseed} space, both GP and DNN surrogates localized similar global minima; DNN captured more nuanced features and avoided spurious local minima seen in GP, particularly after parameter-space expansion.
• DNN outperforms BO under unnormalized parameters: BO’s GP struggled with Qtotal due to higher resolution in that dimension (unnormalized inputs), yielding striped artifacts in {QTSC, Qtotal} projections; DNN handled this dimension well.
• Predictive accuracy: DNN predicted spectra whose cosine similarities to the target aligned closely with measured values; MSE between predicted and measured spectra decreased across runs, dropping below 0.02 by run 8, meeting the stopping criterion. The DNN-generated map of accessible colours across parameter space matched experimental spectra trends.
• Full-spectrum advantage: Using entire absorbance spectra (rather than selected features) enabled both effective optimization and robust regression suitable for colour prediction and inverse design.

The two-step framework effectively addresses the dual goals of rapid optimization and knowledge extraction. Early-stage BO efficiently explores sparse data regimes and pushes toward promising regions, even enabling dynamic expansion of the parameter space when boundary-constrained. As data accumulates around the target, the DNN leverages full-spectrum information to refine regression fidelity, outperforming BO in locating low-loss regions and capturing complex, nonlinear relationships between process variables and optical responses. The interpretability analyses (correlations, SHAP, surrogate minima projections) elucidate how the optimization emphasis transitions from spectral shape to amplitude, and identify QAgNO3 and Qseed as dominant levers, with QTSC and Qtotal shaping spectral features and intensities. The DNN’s stability improves with data; once accurate and stable, it enables mapping of accessible colours and inverse design beyond the initial target. While BO’s GP can be sensitive to input scaling (eg., Qtotal), the complementary strengths of the GP (probabilistic exploration with small data) and DNN (high-capacity regression with larger data) make the combined approach robust and transferable. The morphological TEM validation corroborates spectral convergence and provides physical interpretation (aspect ratio effects). Overall, the framework achieves efficient, interpretable optimization while producing a reusable surrogate for subsequent design tasks.

The study introduces a generalizable two-step ML framework that couples batch Bayesian optimization (GP with local penalization) and a deep neural network to guide a microfluidic HTE platform for the synthesis of silver nanoprisms with target optical spectra. The approach accelerates convergence (120 experiments), maintains interpretability throughout, and, once sufficient data are gathered, enables accurate full-spectrum regression and inverse design, including mapping of accessible colours. Key insights include the primary influence of silver nitrate and seed flow ratios, the differential roles of variable ratios on spectral shape vs amplitude, and the necessity of sufficient data for stable DNN performance. The final trained DNN is transferable to new targets, supporting rapid re-optimization and inverse design. Future work could benchmark alternative acquisition functions and regressors within this two-step framework (including adaptive kernels, BNNs, and ensembles), employ algorithm-selection criteria (AIC/BIC) for resource-efficient closed-loop labs, evaluate normalization strategies, and extend the methodology to diverse materials and HTE platforms.

• The DNN surrogate provides point predictions without uncertainty quantification, unlike the GP in BO; probabilistic DNNs/ensembles could improve decision-making.
• Early-stage DNN training on sparse data was unstable; sufficient data density is required before deploying DNN-driven sampling.
• Unnormalized parameters adversely affected BO’s GP fit along Qtotal, producing artifacts; while intentional to allow space expansion flexibility, this reduced BO’s regression fidelity.
• The simulated target spectrum is inherently challenging to realize due to nanoparticle polydispersity; thus, exact target matching is limited by synthesis variability and measurement noise.
• The HTE loop relied on batch grid-based DNN inverse design; grid resolution limits may miss finer optima without adaptive refinement.
• TEM validation, while informative, was limited to best-performing conditions per run due to time constraints, potentially overlooking broader morphology distributions.