Yu Zhang

The development of topical drug formulations typically requires reliable assessment of both drug release and permeation characteristics. In vitro release testing (IVRT) is routinely used for quality control and early screening, while in vitro permeation testing (IVPT) has been commonly used as the standardised approach for evaluating skin permeation performance. However, the extent to which IVRT corresponds to IVPT outcomes remains insufficiently quantified when both experiments are conducted under the same conditions. Here, using fifteen ibuprofen formulations previously characterised by IVPT on a Strat-M membrane, we performed IVRT with a nylon membrane and examined the IVRT-IVPT relationship from correlation, predictability and structural-consistency perspectives. IVRT release rate exhibited a strong positive association with IVPT steady-state flux (Pearson r = 0.95, R-2 = 0.92, p < 0.001), and largely preserved formulation ranking (five of the top six IVRT formulations were also top-ranked in IVPT). Gaussian process regression further revealed a highly aligned similarity structure between IVRT- and IVPT-based models (kernel alignment = 0.97). This suggests that the two experimental models capture closely related representations of the formulation space, even though their response variables differ. Combined with repeatability and discriminatory capability of IVRT, these results support IVRT as an initial screening tool prior to conducting more resource-intensive permeation evaluations.

Formulating effective pharmaceutical products for dermal delivery requires optimising complex mixtures of excipients under a tight experimental budget. While surrogate model-based optimisation is widely used, most approaches typically rely on predefined acquisition strategies to balance exploitation (prediction performance) and exploration (model uncertainty), which may underexplore informative regions or miss optimal designs in data-scarce conditions. This study introduces an active learning-based optimisation framework that adaptively guides formulation development by dynamically adjusting acquisition priorities. In the proposed framework, Gaussian process regression is employed to model the relationship between formulation composition and in vitro release test (IVRT)-measured drug release. The surrogate predictions are then used to generate a candidate set that spans the trade-off between high predicted release and model uncertainty. A novel adaptive allocation strategy subsequently selects the next experimental batch by assigning candidate formulations between expected improvement-ranked and hypervolume contribution-ranked lists according to their observed empirical effectiveness. This adaptive mechanism improves the use of a limited per-batch evaluation budget and maintains an effective exploration-exploitation balance. Across five benchmark functions, the framework is the strongest batch acquisition strategy, best on most cells and tied with the best alternative on the remainder, and remains competitive with sequential Bayesian optimisation despite using roughly six times fewer model updates. Its practical value is demonstrated on a real-world, inherently batch ibuprofen-loaded poloxamer 407-based formulation task evaluated by IVRT, where it identified formulations substantially exceeding the initial best, highlighting its potential for accelerating dermal drug formulation development.

This paper concerns chemical, biological and other experiments used in R&D labs, where the aim is to optimise some performance indicator by adjusting the materials and processing parameters. Such experiments require significant resources and time, motivating the use of early stopping strategies to terminate unpromising runs before completion. However, stopping an ongoing experiment based on incomplete observations carries the risk of incorrectly terminating runs that would have achieved satisfactory outcomes, a quantity we term the false stop rate (FSR). To address this, we propose Confidence-Bound Early Stopping with Sequential Calibration (CBES), a two-layer framework that employs Gaussian process regression to predict the final outcome from partial observations and combines a confidence-bound decision rule with a calibration procedure to ensure that the FSR remains below a user-specified level. We compare CBES against four baseline stopping criteria on two distinct domains: in vitro permeation testing (IVPT) for pharmaceutical formulation and LCBench for hyperparameter optimisation. The results demonstrate that CBES achieves reliable FSR control with substantial time savings. This work offers a flexible framework for experimental processes, with broad applicability in fields such as chemical engineering, biotechnology, and material science. •A confidence-bound early stopping framework with sequential calibration (CBES) is proposed.•Gaussian process regression provides probabilistic predictions of final experimental outcomes.•Sequential calibration controls the false stop rate at a user-specified level without manual tuning.•A Hoeffding-based bound provides a formal generalisation guarantee on the false stop rate.•CBES achieves reliable false stop rate control with substantial time savings across two domains.

Formulating effective skin products requires navigating complex chemical mixtures,skin biophysical and biochemical properties and manufacturing processes, all under budgetary and time constraints. Controlling dermal permeation, a key driver of efficacy, often presents the primary development bottleneck. Conventional development methods are slow, hampered by low-throughput, variable test assays (e.g., in vitro release and permeation testing) and limited access to biologically relevant in vitro skin models. This review argues for a shift towards autonomous, assay-aware formulation design, outlining a closed-loop framework that unifies intelligent candidate generation, automated experiment selection and robust analysis across a skin-specific multi-tiered assay strategy. The foundations of barrier transport and formulation behaviour are first synthesised. Key enabling technologies are then systematically surveyed, including automation technologies (e.g., microfluidic and modular platforms), automated analytics (e.g., chromatographic pipelines, auto-sampling for diffusion cells) and artificial intelligence (e.g., hybrid mechanistic/data-driven surrogates and constraint-aware active learning). Building upon this foundation, a practical framework is discussed that foregrounds cross-tier calibration between rapid screens and pivotal assay endpoints. Its workflow centres on model generalisation, uncertainty quantification and robust system orchestration. The goal is to provide a credible path towards faster, more reproducible and acceptance criteria-aligned decisions for skin product formulation efficacy.

Formulated topical drugs (and personal care products) contain diverse and varied mixtures. The experiments for formulation design can be time-consuming, especially those for optimising the delivery of active ingredients into the skin, the so-called in vitro permeation test (IVPT). A single IVPT typically takes 24 hrs and consumes significant resources for sample collection and chemical analysis. In this study, an early decision-making algorithm (EDMA) that can terminate unpromising experiments early, thereby prioritising resources on promising ones and potentially accelerating formulation design is proposed. The algorithm relies on a flexible Gaussian process regression (GPR) model for prediction during the experiments, while the prediction uncertainty is accounted for by a statistical measure, the probability of exceedance (PoE), to guide decision-making. This algorithm was applied to maximise ibuprofen permeation from a gel-like formulation through IVPT. The results show that it is feasible to determine whether a certain formulation has the potential to achieve higher permeation before the end of experiment, leading to significant savings on time and resources.

Dynamic kernel principal component analysis (DKPCA) has been frequently implemented for nonlinear and dynamic process monitoring of complex industrial processes. However, traditional DKPCA focuses only on the global structural analysis of data sets and strongly neglects the local information, which is equally essential for process detection and identification. In this paper, an improved DKPCA, referred to as the local DKPCA (LDKPCA), is proposed based on local preserving projections (LPP) for nonlinear dynamic process fault diagnosis. The method combines the advantages of LPP and DKPCA by utilizing the local structure feature to maintain the geometric structure of the data in a unified framework. To achieve a highly comprehensive feature extraction, the local characteristics are fused in DKPCA to produce an optimization objective. The neighbouring points of the new objective function projection in the feature space are still maintained in proximity, and the variance information is retained simultaneously. For the purpose of fault detection, two statistics, known as the T-2 and squared prediction error (SPE) statistics, are constructed, based on the LDKPCA model, and used to monitor the latent variable space and the residual space, respectively. In addition, the sensitivity analysis is brought in for fault identification of the two statistics. Based on the experimental analysis using the shaft breakage data of an offshore oilfield electric submersible pump (ESP), the proposed method outperforms the conventional DKPCA in terms of fault monitoring performance. The experimental results demonstrate the potential of the method in nonlinear dynamic process fault diagnosis.

Electric submersible pump (ESP) in offshore oilfields is one of the important artificial lifting methods to achieve high and stable production. The complexity of the ESP system and the long pumping cycle result in data having the typical characteristics of "a large amount of data and a small amount of information". Therefore, the scarcity of valid samples causes a major challenge for ESP fault diagnosis. To address these practical problems, we propose an intelligent virtual sample generation method that introduces the idea of multi-distribution mega trend diffusion (MD-MTD) into conditional generative adversarial networks (MCGAN-VSG). In the MCGAN-VSG method, the acceptable diffusion range of the sample attributes is first obtained by estimating the samples using the triangular probability distribution model constructed in MD-MTD. Secondly, the Borderline-SMOTE and uniform distribution were added to describe the small sample properties, and suitable output samples are generated to fill the information gap between samples for resampling with Bootstrap. Thirdly, CGAN is used to generate the input samples corresponding to the output samples. Finally, the accuracy of the classification model is improved by generating a large number of virtual samples with an extremely limited number of fault samples. In order to verify the advantages of the proposed MCGAN-VSG, the quality of the input and output virtual samples generated via the method is investigated through a two-dimensional standard function. The proposed method is further applied to the fault diagnosis of ESP in an offshore oil field, and the effectiveness of MCGAN-VSG is verified with actual industrial data. The MCGAN-VSG was compared with most advanced methods such as MTD, TTD, Bootstrap and MD-MTD, and the experimental results show that the proposed method is superior to all other methods.