Experimental Design in Pharmaceutical Formulation Development: Achievements, Limitations and the Transition Toward Intelligent Optimization

Abstract

Historically, pharmaceutical formulation development relied heavily on trial-and-error experimentation, which was useful for empirical progress but often provided limited mechanistic understanding and insufficient efficiency for increasingly complex drug products. The introduction of Design of Experiments (DoE) and Quality by Design (QbD) established a more systematic framework for studying formulation variables, manufacturing parameters, and Critical Quality Attributes (CQAs). Approaches such as factorial designs, response-surface methodology, and mixture designs have therefore become central to modern pharmaceutical development because they improve experimental efficiency and support the definition of design space. However, as formulations become more nonlinear, high-dimensional, and multi-objective, these classical approaches may no longer be sufficient on their own. This review examines the evolution of experimental design in pharmaceutical research, from one-factor-at-a-time experimentation to structured DoE/QbD strategies, and then to emerging intelligent optimization methods. Its central objective is to clarify when conventional DoE/QbD remains appropriate and when it should be complemented by machine learning, Bayesian optimization, digital twins, and closed-loop experimental systems. The review first summarizes the foundations and strengths of classical experimental design; then, it discusses its practical limitations in complex formulation settings, and finally evaluates how data-driven and hybrid approaches can extend pharmaceutical development. Evidence from tablets, capsules, nanocarriers, transdermal patches, and biotherapeutic systems suggests that intelligent optimization can improve predictive performance and experimental efficiency when used alongside, rather than instead of, established pharmaceutical development principles.

1. Introduction

Pharmaceutical formulation development has traditionally relied on empirical experimentation, in which excipients, process variables, and manufacturing conditions are adjusted iteratively until acceptable product performance is achieved [1]. Although this approach has produced many successful dosage forms, it often provides limited insight into the relationships between formulation composition, process parameters, and product quality [2]. As pharmaceutical products have become more complex—through multifunctional excipients, advanced drug-delivery systems, nanoscale materials, and increasingly demanding quality requirements—purely trial-and-error methods have become less efficient and less informative [3,4]. This shift has driven the adoption of Quality by Design (QbD) principles, as reflected in ICH guidelines Q8–Q14, which emphasize systematic development, risk management, process understanding, and the use of Design of Experiments (DoE) to identify critical variables and define design space.

Classical DoE methods, including factorial, central composite, and Box–Behnken designs, have greatly improved formulation development by enabling efficient screening, response modeling, and structured optimization. Nevertheless, these methods are typically based on low-order polynomial approximations and can become difficult to apply when formulation behavior is strongly nonlinear, high-dimensional, dynamic, or governed by multiple competing objectives [5]. The central question, therefore, is not whether intelligent optimization should replace DoE/QbD, but how and when conventional DoE/QbD should be complemented by machine learning, adaptive optimization, Bayesian methods, and digital twin frameworks. Accordingly, this review is structured in three parts: first, it outlines the historical progression from empirical experimentation to DoE/QbD; second, it examines the strengths and limitations of classical experimental designs in pharmaceutical applications; and third, it discusses how intelligent optimization approaches can extend these frameworks in complex formulation and process-development problems.

Literature Search Strategy

This narrative review was based on a structured literature search conducted across three major bibliographic databases—PubMed (MEDLINE), Web of Science (Core Collection), and Scopus—covering publications available up to early 2026, with particular emphasis on the past two decades to reflect the regulatory framework established by the ICH Q8–Q14 guidelines. The search strategy combined controlled vocabulary and free-text terms using Boolean operators (AND, OR), including “design of experiments”, “DoE”, “quality by design”, “QbD”, “response surface methodology”, “central composite design”, “Box–Behnken design”, “mixture design”, “pharmaceutical formulation”, “drug delivery systems”, “critical quality attributes”, “design space”, “machine learning”, “artificial neural networks”, “Bayesian optimization”, “adaptive experimentation”, and “digital twins”. Eligible records were peer-reviewed original research articles, reviews, and regulatory guidance documents published in English, focusing on pharmaceutical formulation or process development and addressing classical experimental design, QbD implementation, or data-driven and intelligent optimization approaches; conference abstracts, non-peer-reviewed preprints, and editorials were excluded. Additional references were retrieved through manual screening of the bibliographies of selected publications and through regulatory documents issued by the ICH, U.S. FDA, and EMA. As the present work is a narrative review, no formal meta-analytical or systematic risk-of-bias procedure was applied; instead, source selection prioritized conceptual relevance, methodological soundness, and representativeness across the dosage forms discussed, including tablets, capsules, nanocarriers, transdermal patches, and biotherapeutic systems.

2. Foundations of Experimental Design in Pharmaceutical Sciences

2.1. One-Factor-At-a-Time (OFAT): Historical Perspective

The One-Factor-at-a-Time (OFAT) strategy is one of the earliest and most direct methods for developing pharmaceuticals. The objective is to modify a single variable while maintaining all other conditions constant, and thereafter observe the impact on the measured outcome (Figure 1A).

Figure 1. (A) illustrates the OFAT approach, where one factor is varied while the other is held constant. The blue line varies Factor A with Factor B at 0.5; the orange line varies Factor B with Factor A at 0.5. (B) depicts a full factorial DoE matrix, exploring multiple levels of Factor A and Factor B simultaneously to capture interactions (Blue dots represent the experimental design points evaluated in the full factorial design, illustrating simultaneous variation of Factor A and Factor B).

For an extended period, OFAT has been the predominant method in formulation work due to its simplicity in comprehension and execution, requiring minimal statistical knowledge. This indicates it is accessible to formulators with limited knowledge in experimental planning. Furthermore, OFAT aligns well with the typical progression of growth and is often employed in laboratories, especially during first examinations and scientific investigations. Although OFAT remains prevalent, it is widely acknowledged to have inherent flaws. It cannot recognize the relationships among the many components in a formulation, which are often both common and significant in pharmaceuticals. Modifications to the quantities of excipients, processing methods, or types of solvents can frequently result in synergistic or antagonistic effects, although OFAT will not identify these interactions. The OFAT approach is inefficient in terms of time, as it requires numerous tests to explore a limited range of possibilities, yielding few insights into the system’s functionality. These difficulties frequently lead to formulations that are suboptimal, cannot be consistently replicated, and provide limited insight into the interrelationship between the medication’s production, the process, and its efficacy [6].

2.2. Emergence of Design of Experiments (DoE)

The limitations of the OFAT methodology have led to the development of DoE as a more systematic and statistically robust alternative. DoE enables researchers to investigate multiple factors simultaneously, allowing for the evaluation of key responses, as well as the interactions between variables, within a well-controlled experimental framework, as illustrated in Figure 1B. Moreover, DoE reduces the overall experimental burden by organizing studies in a structured and efficient manner, thereby improving reliability and interpretability [7]. DoE methodologies commonly employ factorial designs, in which all possible combinations of selected factor levels are examined. Full factorial designs provide a comprehensive understanding of both the main effects of individual factors and their interactions, making them particularly valuable for the initial exploration of formulation behavior. However, as the number of variables increases, full factorial designs become impractical due to the exponential growth in the number of required experiments. To address this limitation, fractional factorial designs are employed as efficient alternatives. These designs evaluate a carefully selected subset of experimental combinations, enabling the identification of critical factors while significantly reducing the number of experiments required [8]. A key advantage of DoE lies in its structured approach, which clearly separates the identification of significant factors from their subsequent optimization. The methodologies used to screen and identify critical variables differ from those applied during optimization; the latter typically involves response surface methodologies, which are used to determine optimal conditions and to model potential non-linear relationships between variables and responses [9].

3. Classical DoE Methodologies in Formulation Development

3.1. Response Surface Methodologies (RSM)

Response Surface Methodology (RSM) is one of the most widely applied experimental design approaches in pharmaceutical sciences for formulation optimization. These methodologies enable the straightforward construction of experimental, typically second-order polynomial, mathematical models to describe the relationship between formulation or process variables and one or more CQAs. By incorporating curvature and interaction effects, RSM facilitates the systematic identification of optimal operating conditions within a defined experimental domain [10].

Central Composite Design (CCD) is a commonly used approach within RSM. It combines factorial or fractional factorial points with axial (or “star”) points and center points to effectively estimate curvature within the design space, as illustrated in Figure 2A. CCD is particularly suitable for optimizing process parameters such as mixing time, temperature, solvent volume, and drying conditions, as it supports a flexible range of experimental settings and provides robust predictive models. However, CCD often requires experimentation at extreme levels of the studied variables, which may be impractical or unsafe for certain pharmaceutical systems [11].

Figure 2. Comparative analysis of response surface approach designs employed in pharmaceutical formulation development. (A) Central Composite Design (CCD) demonstrates factorial, axial, and center points that facilitate robust quadratic model estimation; (B) Box–Behnken Design (BBD) incorporates mid-edge sampling to circumvent harsh experimental conditions; (C) Doehlert Design, exhibiting consistent and progressively expanded coverage of the experimental domain.

The Box–Behnken Design (BBD), another RSM approach, avoids experiments at the extreme boundaries of the design space. By positioning experimental points at the midpoints of factor edges and including center points, BBD reduces the total number of experimental runs while still maintaining adequate predictive capability (Figure 2B). This design is particularly advantageous for processes sensitive to extreme conditions, such as nanoparticle synthesis, drug loading, and the optimization of transdermal drug delivery systems [10].

Doehlert Design provides uniform coverage of the experimental space with a relatively small number of trials, allowing efficient exploration of the design domain (Figure 2C). Due to its geometric adaptability, it is straightforward to examine formulations whose factor values fluctuate rapidly; yet, it is hardly utilized in pharmaceutical applications, as it is not particularly user-friendly [12].

3.2. Mixture Designs in Pharmaceutical Formulation

RSM primarily focuses on independent variables within its experimental frameworks. In contrast, mixture designs are specifically developed for formulations in which the variables represent the proportions of components that collectively sum to a fixed total. Because the performance of such systems depends on relative composition rather than absolute quantity, an alternative experimental approach is required [13].

In the formulation of polymer blends, mixture designs systematically vary polymer ratios to improve mechanical strength, optimize drug release profiles, and enhance stability [14]. Similarly, lipid-based pharmaceutical carriers, including self-emulsifying drug delivery systems and solid lipid nanoparticles, utilize mixture designs to improve solubility, emulsification efficiency, and physical stability [15].

In adhesive drug matrices, such as transdermal drug delivery systems (TDDS), the composition of the adhesive critically influences properties such as viscosity, cohesion, drug permeation, and skin adhesion. For this reason, mixture designs are particularly important in these systems. They provide a rational and systematic approach for optimization by enabling the investigation of interactions between formulation components, whether synergistic or antagonistic [16,17].

3.3. Strengths of Classical DoE in Formulation Development

Conventional experimental design approaches continue to offer important advantages in pharmaceutical formulation development. These methodologies reduce the number of experiments needed to obtain meaningful results compared with trial-and-error experimentation and help identify and quantify interactions among formulation variables. Within the QbD framework, regulatory agencies emphasize the use of structured experimental designs to establish scientifically justified design spaces consistent with ICH and FDA guidance. Such approaches improve understanding of the relationships among formulation variables, process parameters, and product quality, thereby supporting robust and reproducible pharmaceutical development [18].

4. Quality by Design (QbD) and Regulatory Integration

4.1. QbD Framework and Regulatory Logic

QbD provides a structured methodology for integrating scientific knowledge, risk assessment, and regulatory standards into the formulation of pharmaceutical products. Figure 3 shows that QbD begins with the creation of the Quality Target Product Profile (QTPP). These profiles outline expected clinical effectiveness and quality characteristics of products such as dosage form, administration route, release profile stability, and patient acceptability [18]. The quality target product profile is the basis for identifying CQAs, which are measurable traits that must be controlled to ensure product quality and effectiveness [19].

Figure 3. Schematic representation of the QbD framework and its integration with experimental design and regulatory expectations. Created in BioRender. Türkdoğan, A. (2026) https://BioRender.com/b0ahymq, (accessed on 2 May 2026).

Upon the establishment of CQAs, prospective Critical Material Attributes (CMAs) and Critical Process Parameters (CPPs) that may affect these CQAs are carefully identified. CMAs often encompass the attributes of raw materials and excipients (e.g., polymer grade, viscosity, particle size, surface features), while CPPs pertain to processing parameters such as mixing duration, coating thickness, drying temperature, or curing time. The interconnections among CMAs, CPPs, and CQAs constitute the scientific foundation of pharmaceutical development in accordance with ICH Q8(R2) and associated standards [20,21].

4.2. Risk Assessment Tools Supporting QbD

Risk assessment is a fundamental component of the QbD paradigm, guiding the selection of initial experiments during pharmaceutical development. These tools are commonly applied in the early stages to identify potential sources of variability in CQAs across key domains, including materials, processes, equipment, environment, and personnel. A range of qualitative and quantitative techniques can be employed for this purpose, such as Failure Mode and Effects Analysis (FMEA), Failure Mode, Effects, and Criticality Analysis (FMECA), Hazard Analysis and Critical Control Points (HACCP), Ishikawa (fishbone) diagrams, and risk ranking and filtering methods [22].

Among these, FMEA is one of the most widely used approaches, as it enables systematic prioritization of risks by evaluating their severity, likelihood of occurrence, and detectability. By focusing on the most critical variables, these methods enhance the efficiency of formulation and process development and ensure that experimental efforts are directed toward the most impactful factors. Importantly, regulatory guidelines such as ICH Q9 emphasize that risk assessment tools should support and enhance scientific decision-making throughout the product lifecycle, rather than replace sound scientific judgment [23].

4.3. Design Space and Regulatory Expectations

Defining a design space is one of the most critical outcomes of implementing the QbD approach. The ICH Q8 (R2) defines design space as the multidimensional combination and interaction of CMAs and CPPs that have been demonstrated to ensure product quality. As illustrated in Figure 3, the design space is established using experimental data, mechanistic understanding, and/or statistical modeling, and is supported by a robust control strategy. Regulatory authorities, including the FDA and the EMA, endorse the application of QbD principles and design space concepts when they are supported by sound scientific justification. Furthermore, when a comprehensive pharmaceutical quality system, as outlined in ICH Q10, is implemented, operating within an approved design space may provide regulatory flexibility in post-approval lifecycle management [24,25].

4.4. Where QbD Succeeds—And Where It Struggles

QbD has significantly advanced formulation development by enabling systematic experimentation, enhancing process and product understanding, and strengthening control strategies [2]. However, as pharmaceutical systems become increasingly complex, new challenges emerge. In high-dimensional systems involving multifunctional excipients, nanomaterials, or advanced drug delivery platforms, the relationships among CMAs, CPPs, and CQAs are often nonlinear, multivariate, and time-dependent [26]. Under such conditions, conventional experimental designs and low-order statistical models may be insufficient to define a robust and predictive design space. Consequently, there is a growing need to integrate advanced modeling approaches and data-driven methodologies to adequately capture system complexity and improve decision-making in pharmaceutical development [27].

5. Practical Limitations of DoE and QbD in Modern Pharmaceutical Systems

Regulators have approved and validated classical DoE and QbD frameworks, but these frameworks are difficult to apply in modern, complex pharmaceutical systems. These limitations stem not from flawed concepts but from the growing divergence between model assumptions and the system’s actual dynamics.

Table 1 illustrates several significant and often challenging issues encountered when trying to implement traditional DoE and QbD methodologies with complex mixtures. These issues include the ‘curse of dimensionality,’ non-linear responses with multiple objectives, variability in ingredient quantities, complications arising from scaling up, and temporal changes in the system.

Table 1. Outlines the main practical problems with classical DoE and QbD in modern. Highly complex formulation systems.

Limitation	Core Issue	Practical Impact in Formulation	Typical Example	Key References
Curse of dimensionality	Experimental runs increase exponentially with the factor number	DoE becomes impractical; factor reduction may oversimplify the system	Multi-excipient, multi-process formulations	[28,29]
Nonlinear/non-stationary responses	Quadratic models cannot capture regime shifts	Poor prediction outside the narrow design space	Polymer transitions, nanoparticle aggregation, crystallization	[30,31,32,33,34]
Multi-objective conflicts	Single desirability functions mask trade-offs	Unreal “optima”; needed compromise solutions	Strength vs. dissolution; adhesion vs. flux	[35,36]
Material variability	Batch variability violates model assumptions	Reduced reproducibility and model transferability	Polymer MW variation	[37,38,39]
Scale-up disconnect	Lab-scale models fail at manufacturing scale	Design space is not robust in production	Mixing, drying, coating, scale changes	[20,40,41,42]
Static models for dynamic systems	Time-dependent behavior was not captured	Weak lifecycle prediction	Drug release evolution; adhesive aging	[43,44,45]
Nanoparticle trade-offs	Strong nonlinear interactions among variables	Local optima only; poor extrapolation	Size–PDI–EE conflicts	[46,47,48]

This evolution indicates that pharmaceutical formulation has undergone a substantial transformation. Although QbD and DoE remain foundational frameworks, they are often insufficient to address the complexity of modern systems, which are characterized by high-dimensional variable spaces, nonlinear interactions, diverse material properties, and variable performance outcomes. To effectively navigate these challenges, there is a growing need for integrated and intelligent experimental strategies that combine established theoretical frameworks with advanced data-driven approaches, such as machine learning. Such methodologies enable more efficient optimization, improved predictive capability, and a closer representation of real operational mechanisms, as discussed in the subsequent sections of this paper.

6. Transition Toward Intelligent Optimization Strategies

Given the limitations of traditional DoE and QbD approaches in handling complex, nonlinear, and dynamic pharmaceutical systems, there is increasing interest in more advanced methodologies for identifying optimal solutions. Rather than replacing established experimental design principles, these approaches seek to augment DoE by leveraging data-driven insights, enabling adaptive experimentation, and enhancing predictive accuracy. In this context, machine learning–assisted experimental design and Bayesian optimization have emerged as powerful tools in modern pharmaceutical development, supporting more efficient exploration of complex design spaces and facilitating informed decision-making during formulation and process optimization.

6.1. Machine Learning–Assisted Experimental Design

Machine learning (ML) provides a powerful framework for modeling the complex relationships between formulation or process inputs and CQAs, without requiring prior assumptions about the underlying functional forms. Owing to their ability to capture nonlinear trends, intricate interactions, and potential discontinuities in system behavior, ML models often outperform traditional polynomial regression approaches used in DoE [49,50].

In pharmaceutical formulation research, a variety of ML techniques are widely applied, including artificial neural networks (ANNs), random forests (RFs), support vector regression (SVR), and Gaussian process (GP) models. Among these, ANNs are particularly well suited for modeling highly complex and nonlinear relationships between variables [51,52]. Random forests are robust in handling noisy or heterogeneous datasets and offer valuable insights into variable importance. Support vector regression performs well with limited datasets by effectively capturing generalizable patterns. Gaussian process models are especially advantageous due to their ability to quantify prediction uncertainty, which is critical for risk-informed decision-making in pharmaceutical development [53,54,55].

6.1.1. ML vs. Classical Regression

Classical DoE predominantly relies on relatively simple polynomial regression models, which facilitate interpretation and align well with established regulatory frameworks; however, they often fail to capture complex system behaviors. In contrast, machine learning models prioritize predictive accuracy over interpretability and are capable of analyzing highly complex, multivariate relationships [56,57]. Nevertheless, purely data-driven machine learning approaches may be prone to overfitting and often provide limited mechanistic insight when applied without proper validation or domain knowledge [58]. Therefore, machine learning should not be viewed as a replacement for experimental design, but rather as a complementary tool that enhances conventional DoE, particularly under complex conditions [59].

6.1.2. Hybrid DoE–ML Workflows

An increasingly effective strategy involves integrating DoE with machine learning techniques. In this approach, carefully designed DoE studies generate high-quality, information-rich datasets, which are subsequently analyzed using machine learning algorithms [60]. Within this framework, DoE ensures efficient and statistically robust data generation, while ML improves predictive performance and enables exploration beyond the initially defined design space. Such hybrid methodologies preserve regulatory transparency and traceability, while significantly enhancing model flexibility and optimization capability [61].

6.1.3. Challenges and Limitations of Machine Learning-Assisted Formulation Design

Classical DoE remains highly valuable in pharmaceutical development, particularly in relatively simple systems with a limited number of variables, modest datasets, and a strong need for interpretable factor–response relationships [62]. In such contexts, factorial and response-surface designs offer transparent model structures, efficient screening, and direct alignment with QbD principles [63]. By contrast, machine learning approaches become especially advantageous when formulation behavior is strongly nonlinear, high-dimensional, or governed by multiple competing objectives that low-order polynomial models cannot adequately capture [26]. Nevertheless, the apparent flexibility of ML should not obscure its practical limitations. When trained on sparse, noisy, or unrepresentative datasets, ML models are prone to overfitting and may yield impressive internal performance without demonstrating robust generalizability [64,65]. Their predictive utility also depends heavily on data quality, preprocessing, and bias control, while limited explainability may reduce mechanistic insight and complicate scientific justification. From a regulatory perspective, these issues reinforce the need for rigorous validation, transparent reporting, and careful positioning of ML as a complementary decision-support tool rather than a substitute for experimental understanding [66].

6.2. Bayesian Optimization and Adaptive DoE

Bayesian Optimization (BO) is a sequential, surrogate-assisted optimization strategy that iteratively updates a statistical model and uses an acquisition function to select promising new solutions, and it is widely used in applications such as hyperparameter tuning in machine learning [67]. BO enables adaptive learning, in which each experimental outcome informs subsequent decisions, thereby reducing both experimental cost and effort. This approach is particularly advantageous in time-intensive or resource-constrained pharmaceutical research, compared with traditional DoE strategies that rely on fixed experimental designs [68,69]. Furthermore, BO operates as a “learning-by-doing” framework, prioritizing experimentation in regions of the design space that exhibit high uncertainty or significant impact on the response. This facilitates the rapid identification of optimal formulations, even in complex systems characterized by competing objectives, regime shifts, or evolving behaviors [70].

Challenges and Limitations of Bayesian Optimization

Despite its efficiency in sequential experimentation, BO is not universally straightforward to implement in pharmaceutical formulation projects. Its performance depends strongly on the choice of surrogate model and acquisition function, both of which influence how effectively the method balances exploration of uncertain regions against exploitation of promising candidates [71]. In low- to moderate-dimensional spaces, these probabilistic strategies can be highly effective; however, scalability becomes more difficult as dimensionality increases, particularly when formulation variables are heterogeneous, constrained, or strongly interacting [72]. Under such conditions, surrogate modeling may become less stable, and optimization performance may deteriorate unless dimensionality reduction, informative priors, or structured search strategies are incorporated [73,74,75]. In addition, BO requires computational expertise for model updating, uncertainty handling, and acquisition optimization, which may limit routine adoption in formulation laboratories that lack a strong quantitative infrastructure [76]. Accordingly, while BO offers substantial benefits for expensive and data-limited experiments, its practical success depends on careful problem framing, appropriate model selection, and realistic integration into experimental workflows [71,77]. The conceptual and operational differences among Classical DoE, ML, and BO are summarized in Figure 4.

Figure 4. In pharmaceutical formulation development, optimization methodologies—Classical Design of Experiments (DoE), Machine Learning (ML), and Bayesian Optimization—are evaluated. The diagram illustrates three methodologies: DoE employs a predetermined experimental plan, fitting a model and optimizing the response surface to identify a singular optimal outcome before concluding; Machine Learning (ML) utilizes iterative data generation, model training, and predictive cycles to perpetually enhance the optimal result as additional data becomes available; and Bayesian Optimization leverages a surrogate model, incorporating our confidence in the measurements, to consistently direct new experiments towards the overall optimal outcome. The graphic illustrates the distinctions in adaptivity, data utilization, and iteration framework among the three methodologies. Created in BioRender. Türkdoğan, A. (2026) https://biorender.com/70r0r1t, (accessed on 2 May 2026).

6.3. Implications for Pharmaceutical Formulation Development

The integration of machine learning–enhanced modeling with Bayesian optimization represents a shift from fixed, predetermined experimental protocols toward more flexible, knowledge-driven approaches to formulation development [60]. These advanced methodologies align well with QbD principles, as they promote enhanced process understanding and support risk-based decision-making, even as regulatory frameworks governing their application continue to evolve [78]. When implemented in a transparent and scientifically justified manner, intelligent optimization algorithms provide a scalable and practical means of addressing the complexity of modern pharmaceutical systems. This is particularly evident within hybrid DoE–ML frameworks, where data efficiency, predictive performance, and adaptive experimentation are effectively combined to improve formulation and process optimization [60].

7. Digital Twins and Mechanistic–Data Hybrid Models

7.1. Definition of Digital Twins in Pharmaceutical Sciences

In pharmaceutical development, a digital twin is a dynamic virtual representation of a physical product, process, or system. It integrates experimental data, mechanistic models, and real-time measurements to predict product performance throughout its lifecycle. Unlike static empirical models or purely data-driven approaches, digital twins continuously evolve as new data become available, enabling ongoing learning and more informed decision-making. In formulation science, digital twins aim to bridge the gap between laboratory-scale experimentation, manufacturing processes, and clinical performance by providing a unified and predictive framework for system understanding and optimization [79].

7.2. Linking Process–Structure–Performance Relationships

One of the key advantages of digital twins is their ability to explicitly link formulation microstructure, process parameters, and product performance. In addition to formulation composition, process-induced structural attributes—such as particle morphology, pore architecture, polymer chain organization, and coating uniformity—play a critical role in determining pharmaceutical outcomes, including drug release, stability, adhesion, and bioavailability [80]. Mechanistic–data hybrid models, which integrate data-driven learning with first-principles knowledge (e.g., diffusion, dissolution, and heat and mass transfer), enable digital twins to capture both complex nonlinear behaviors and underlying causal relationships. This integrated process–structure–performance coupling represents a significant advancement over traditional DoE approaches and stand-alone machine learning models [81].

7.3. Application Examples in Pharmaceutical Development

7.3.1. Drug Release Modeling

Digital twins for drug release typically begin with a mechanistic transport core that captures the key coupled phenomena governing release behavior. These include diffusion with dissolution and solubility limitations, water ingress, and, where necessary, moving boundaries and time-dependent parameters associated with swelling, erosion, or microstructural evolution of the dosage form (e.g., changes in porosity or tortuosity). Foundational models of controlled release emphasize that real dosage forms often involve more than simple diffusion processes—such as polymer swelling and matrix erosion—and that the appropriate governing equations and boundary conditions depend on both the geometry and internal structure of the system. This mechanistic foundation provides the essential “physics backbone” required for reliable extrapolation [82]. Hybrid release digital twins incorporate data-driven correction layers through so-called gray-box modeling approaches. In this framework, a machine learning component is used to learn systematic discrepancies between mechanistic predictions and experimental dissolution or disintegration data, or to infer difficult-to-measure effective parameters (e.g., effective diffusivity or mass transfer coefficients) from formulation and process descriptors. The ability of machine learning to predict full release profiles and extract kinetic parameters from formulation data supports the residual-learning paradigm as an effective strategy for addressing formulation variability and unmodeled physical effects, while preserving mechanistic interpretability [83]. A representative “twin-style” implementation involves the development of a digital twin encompassing both the dosage form and the dissolution environment. Such approaches have demonstrated how hydrodynamic conditions and shear forces can significantly influence apparent dissolution and disintegration behavior, highlighting the need for release-focused digital twins to model not only the formulation itself but also the surrounding test and apparatus conditions [84].

7.3.2. Manufacturing Processes

Digital twins are increasingly applied in pharmaceutical manufacturing, particularly in unit operations where product quality is highly state-dependent and disturbances can propagate rapidly across the process. Such operations include continuous direct compression, coating, granulation, blending/mixing, and drying. A typical digital twin architecture integrates (i) mechanistic models (e.g., residence time distribution (RTD) or flowsheet models, population balance models (PBM), discrete element method (DEM), computational fluid dynamics (CFD), or reduced-order surrogates), (ii) continuous data acquisition, and (iii) data integration with model updating. This framework enables the estimation of unmeasured process states and CQAs in near real time through the use of “soft sensors” [79]. This approach aligns closely with the FDA Process Analytical Technology (PAT) framework, which promotes innovative strategies for pharmaceutical development, manufacturing, and quality assurance based on enhanced process understanding and real-time measurements [85]. From a regulatory science perspective, manufacturing digital twins are particularly well suited to continuous manufacturing environments. The ICH guideline ICH Q13 establishes scientific and regulatory principles for the development, implementation, and lifecycle management of integrated continuous manufacturing systems. In such systems, unit operations are interconnected, and variations introduced upstream can directly impact downstream product quality. Digital twins facilitate this integration by enabling predictive monitoring and supporting advanced control strategies across the entire process, thereby reducing reliance on end-product testing when the system is appropriately validated [86].

7.3.3. Personalized Dosage Forms

Patient-centered digital twins extend the concept from a “product twin” to a “product–patient twin” by integrating formulation and performance models with individualized physiological characteristics—typically through physiologically based pharmacokinetic/pharmacodynamic (PBPK/PD) or exposure–response models. This integration enables model-informed precision dosing (MIPD) and supports adaptive therapeutic decision-making. For example, a MIPD approach employing “virtual twins” has been used to predict steady-state concentrations of clozapine and to identify dosing regimens that achieve therapeutic targets in hospitalized patients, demonstrating how patient-specific covariates and concomitant medications can be translated into actionable dosing recommendations [87]. In advanced drug delivery applications, personalized digital twins have also been developed for transdermal fentanyl therapy. These systems combine physics-based skin permeation and uptake models with pharmacokinetic/pharmacodynamic components to recommend patient-specific therapeutic adjustments and to evaluate potential improvements in clinical outcomes in silico [88]. Furthermore, pharmaceutical 3D printing technologies facilitate personalized dosage form design by enabling precise control over geometry and internal architecture, thereby allowing modulation of drug dose and release behavior for small-batch or individualized production. Recent reviews highlight both the technological capabilities and the translational considerations associated with personalized pharmaceutical manufacturing [89].

7.4. Regulatory Readiness and Challenges

Although digital twins are increasingly promoted as transformative tools for pharmaceutical formulation and process development, their routine use in regulatory settings remains more aspirational than established. Regulators are generally open to advanced modeling within model-informed drug development, but acceptance depends less on novelty than on whether a model is credible, transparent, and demonstrably fit for purpose. In practice, this sets a high bar art [79,81]. A useful digital twin requires not only large volumes of well-curated data, but also a mechanistic core that captures the relevant system behavior with sufficient fidelity—an especially difficult requirement in pharmaceutical environments characterized by raw-material variability, multiscale process interactions, and evolving product understanding [43]. Hybrid mechanistic–data-driven models may improve predictive performance, yet they also introduce additional concerns regarding interpretability, traceability, updating, and control of model drift [90]. Moreover, predictive accuracy alone is not sufficient: digital twins intended to inform quality or regulatory decisions must be supported by rigorous verification, validation, and uncertainty quantification to demonstrate that their outputs remain reliable under changing conditions and across the product lifecycle [91]. This creates a substantial maintenance burden, as credible twins must be continuously governed through recalibration, version control, documentation of assumptions, and formal lifecycle oversight. Consequently, the main barrier to wider adoption is not simply model development, but the absence of sufficiently mature operational and regulatory frameworks for documenting, reviewing, updating, and trusting these models within existing pharmaceutical quality systems and QbD practice. The future impact of digital twins will therefore depend not only on improved predictive sophistication but on whether the field can establish robust standards for credibility, maintainability, and regulatory accountability [92,93].

8. Autonomous and Self-Optimizing Experimental Platforms

Autonomous experimental systems represent a significant advancement in pharmaceutical research, as they are capable of conducting experiments, collecting and analyzing data, performing computations, and autonomously determining subsequent actions [94]. Laboratory automation platforms, including robotic systems, can synthesize and characterize compounds with high precision, while integrating artificial intelligence, machine learning, and Bayesian optimization to guide experiment selection based on prior results [95,96]. These adaptive systems enable the efficient exploration of complex formulation spaces, accelerate the identification of optimal solutions, improve reproducibility, and maintain comprehensive digital records. They are particularly valuable for high-throughput screening of excipients, microscale formulation development, and the investigation of polymer interactions and bonding mechanisms [97]. However, successful implementation of such systems requires careful integration within existing quality management and control frameworks, along with rigorous documentation to ensure compliance with regulatory standards. Rather than replacing researchers, these automated approaches enhance scientific productivity by shifting the focus from manual experimentation toward deeper analysis, interpretation, and informed decision-making [98].

Challenges and Implementation Considerations for Autonomous and Self-Optimizing Laboratories

Autonomous and self-driving laboratories represent an important extension of intelligent experimental design, but their translation into pharmaceutical practice raises substantial implementation challenges [99]. In regulated environments, automated experimentation must operate within established GMP expectations and satisfy data-integrity requirements throughout the full data lifecycle [100]. This includes adherence to ALCOA+ principles, robust audit trails, validated computerized systems, and risk-based control of interfaces between instruments, software, and decision algorithms [101]. Although automation may reduce certain forms of manual error, it does not eliminate the need for oversight; rather, it shifts attention toward the validation of automated decision-making, governance of model updates, and clear accountability for system actions [50,102]. Additional barriers include high infrastructure costs, integration complexity, the need for interdisciplinary technical expertise, and workforce training in both pharmaceutical science and data-driven automation [61]. The success of emerging autonomous systems depends not only on technological capability, but also on institutional readiness, regulatory frameworks, and data governance [103].

9. Case Studies in Pharmaceutical Formulation Development

Table 2 below summarizes peer-reviewed, formulation-relevant case studies showing that (i) classical DoE facilitates early-stage understanding and interpretable factor–response mapping, whereas (ii) AI/ML-assisted optimization (e.g., ANN, Gaussian processes, Bayesian optimization) generally excels in nonlinear, multi-objective, high-dimensional, or data-fused scenarios (e.g., PAT + process history + composition).

Table 2. Case-study evidence comparing classical DoE and AI-assisted approaches across formulation classes.

Formulation Class	Typical CQAs/Objectives	Classical DoE Case (Design → Outcome)	AI-Assisted/Hybrid Case (Model → Outcome)	Reported Quantitative Benefit (AI vs. Classical)
Oral solid dosage forms (tablets)	Hardness, tensile strength, dissolution profile, content uniformity; optimization of polymer level, excipient ratio, and compression settings.	CCD/RSM optimized sustained-release matrix tablets and linked polymer–filler ratios to >12 h release behavior [104].	Hybrid DoE + ANN approaches improved modeling of nonlinear relationships in osmotic tablets and PAT-based dissolution prediction [105,106].	Hybrid CCD + ANN: r2 = 1.00 training/testing; ANN ≈ CCD optimum (p = 0.9705); ANN release fit RSQ = 0.9966 [105]; PAT-ANN ↓ RMSEP ≈ 3% vs. PLS [106]; classical RSM benchmark [104].
Mesoporous silica nanoparticles	Surface area, pore characteristics, particle size, zeta potential, loading capacity, cytotoxicity.	BBD optimized MSN synthesis and identified a formulation giving targeted surface area, particle size, and low toxicity after DOX loading [107].	Sequential BO refined a lipid-coated silica platform more efficiently than broad manual screening [108].	BO reached EC50 ≈ 87 ng/mL with fewer runs than exhaustive screening [108], vs. BBD-optimized MSNs [107].
Polymeric nanoparticles (PLGA and analogs)	Particle size, PDI, encapsulation efficiency, release kinetics, stability, and route-specific performance.	BBD optimized lorazepam-loaded PLGA nanoparticles and achieved EE around 90% with sustained release up to 24 h [109].	Gaussian-process surrogate models predicted EE and therapeutic efficacy across candidate nanoparticle formulations [110].	GP surrogate: normalized RMSE ≈ 0.187 (EE) from small datasets [110], vs. BBD PLGA NPs with EE ≈ 90%, 24 h release [109].
Solid lipid nanoparticles	Particle size, PDI, zeta potential, encapsulation efficiency, stability, and oral bioavailability.	CCD optimized acyclovir SLNs to ~109 nm with EE ~91%, stability for at least 3 months, and a 5-fold increase in oral bioavailability versus solution [111].	ANN outperformed RSM for predicting diameter and EE in rivaroxaban SLNs built from a 32-run CCD dataset [112].	On a 32-run CCD dataset, ANN > RSM for size and EE prediction [112], vs. CCD acyclovir SLNs (~109 nm, EE ≈ 91%, 5-fold bioavailability) [111].
Transdermal drug delivery systems	Flux, lag time, tack, shear adhesion, crystallization risk, matrix compatibility.	DoE and mixture-design approaches mapped the effect of adhesive blends and solvent systems on TDDS performance [113].	RSM + ANN optimization of a melatonin transdermal vehicle simultaneously handled solubility, flux, and lag time [114].	RSM + ANN: flux ≈ 12.75 µg/cm2·h, lag ≈ 5 h, ANN closer to experimental optimum than RSM for multi-response problem [114], vs. mixture-design TDDS [113].
Biopharmaceutical formulations (proteins/mAbs)	Thermal stability, aggregation, viscosity at high concentration, interfacial stability, and excipient selection.	Conventional screening and DoE remain useful for structured excipient and pH screening, but become burdensome in high-dimensional multi-property optimization [60,69].	BO and ML have been used to optimize antibody-fragment formulations and to predict aggregation and viscosity in high-concentration biologics [60,69,115].	BO: 25 runs (<1/3 classical) [60]; multi-objective BO: 33 runs [69]; ML aggregation r ≈ 0.89, viscosity accuracy ≈ 0.86 [115].

Industrial Adoption: Providers, Barriers, and Readiness

Although much of the literature remains academic, industrial adoption is clearly emerging. Recent reviews and case-based studies indicate that digital twins, mechanistic/data-driven hybrid models, and AI-enabled process optimization are increasingly being explored across pharmaceutical development and manufacturing, particularly in process development, scale-up, and biomanufacturing. The main barriers to wider adoption remain cost, data infrastructure, software integration, model validation, and shortages of interdisciplinary expertise. As a result, industrial readiness is still uneven: process-oriented twins and predictive manufacturing analytics are closer to routine use, whereas fully autonomous, formulation-centered optimization remains at an earlier stage of deployment [116,117,118,119].

10. Future Perspectives and Research Directions

The ongoing shift toward intelligent experimental design methodologies is expected to fundamentally transform the role of formulation scientists. In the future, scientists will increasingly act as model interpreters, system architects, and decision-makers, placing greater emphasis on integrating experimental insights with data-driven technologies rather than performing manual experimentation [120]. A major challenge associated with this transition lies in the disparity between traditional training in DoE and the competencies required for artificial intelligence–driven approaches. While DoE emphasizes statistical rigor and interpretability, modern data-driven methods demand additional expertise in data science, model validation, and uncertainty quantification. Addressing this gap will require interdisciplinary education and enhanced collaboration across scientific and computational domains. From a regulatory perspective, the integration of AI-driven models, Bayesian optimization, and digital twins presents challenges in achieving consensus among stakeholders. To fully incorporate intelligent optimization within the QbD framework, clear guidance is needed regarding model credibility, documentation practices, and lifecycle management [121]. Establishing standards for transparency, validation, and governance will be essential to ensure regulatory acceptance and practical implementation. Ultimately, pharmaceutical development is progressing toward a fully digital paradigm, in which experimental data, predictive models, and decision-making processes are continuously interconnected throughout the product lifecycle. This transition toward digitalization is expected to enhance efficiency, robustness, and knowledge retention, thereby enabling more streamlined and resilient pharmaceutical development processes [122].

11. Conclusions

Pharmaceutical formulation development has unquestionably moved beyond purely empirical trial-and-error practice, and DoE/QbD now provides the essential foundation for structured experimentation, formulation understanding, and regulatory communication. Yet the continued expansion of complex dosage forms does not mean that conventional methods have become obsolete; rather, classical DoE/QbD remains fully adequate when the design space is relatively constrained, the dominant variables are experimentally accessible, and system behavior can be described with interpretable statistical models. The real challenge arises in systems that are highly nonlinear, high-dimensional, dynamically evolving, or governed by competing objectives, where traditional polynomial models may offer only partial or local descriptions. In these cases, machine learning, Bayesian optimization, digital twins, and autonomous experimentation are valuable not because they are more fashionable, but because they can interrogate complexity that classical designs cannot efficiently resolve. However, their broader impact should not be overstated: the main bottlenecks are no longer merely computational, but organizational and regulatory. Progress will depend on whether the field can develop the interdisciplinary skills needed to use these tools critically, establish clearer regulatory expectations for hybrid and model-informed methods, and ensure rigorous validation, uncertainty assessment, documentation, and lifecycle management. In that sense, the future of formulation science will not be determined by artificial intelligence alone, but by whether advanced models can become credible, governable, and maintainable enough to support real pharmaceutical decision-making across the product lifecycle.