1. Introduction
Modeling has played an important role in the design, control, and optimization of processes over the past 130 years [
1]. Levenspiel [
2] pointed out that modeling is a major tool in chemical engineering. However, before establishing a model, a deep comprehension of the process mechanisms is usually required, which substantially extends the time of model development [
[3],
[4],
[5]]. Recently, engineers have combined modeling with simulations and experiments, using massive data as a toolkit to support predictions derived from experiments. Among the various models, artificial intelligence (AI) algorithms, which simulate human intelligence or behaviors, can efficiently cope with the massive data [
6]. Machine learning (ML) is an AI-derived concept through which a machine acquires knowledge from the user and inputs data to make automatic judgments and responses in the actual production. It can assist humans with problem-solving, reduce errors, improve efficiency, and involve the multidisciplinary specialty, covering probability theory, statistics, approximation theory, and complex algorithms (
Fig. 1(a)). This AI-derived ML algorithm has emerged in various fields, including neuroscience, computer science, statistics, social science, chemistry, robotics, image analysis, and transportation (
Fig. 1(b)) [
[7],
[8],
[9],
[10],
[11],
[12],
[13],
[14],
[15]]. ML can be divided into several categories: supervised learning, semi-supervised learning, unsupervised learning, and reinforcement learning (
Fig. 1(c)) [
[16],
[17],
[18],
[19]]. Proposed in 2006, deep learning refers to analytic learning and data interpretation by neural networks that simulate the human brain [
20]. ML algorithms have continuously evolved from linear regression models to convolutional neural networks (CNNs). The characteristics of ML algorithms in the evolution are presented in
Fig. 1(d).
Studies on data-driven ML models for process optimization or property prediction in chemistry, materials, and engineering have increased obviously [
21]. Dobbelaere et al. [
1] concluded the advances of ML in chemical engineering and emphasized the weaknesses, threats, opportunities, and strengths of ML models. They suggested that although ML possesses higher flexibility, accuracy, and execution speed than traditional modeling, its development is impeded by several limitations, such as the insufficient understanding of the underlying phenomenological principles. So, accurate real-time optimization is an important avenue for ML algorithms. Venkatasubramanian [
22] reviewed data-driven ML models and highlighted their insufficiencies in providing explanations of mechanisms, developing conceptual frameworks, and discovering domain-specific knowledge. Xiouras et al. [
23] summarized the applications of ML algorithms in the prediction of crystalline materials and simulation of the complex crystallization processes. They mentioned the remarkable contributions of ML to high-throughput automation, mathematics, and chemistry. Previously, we reviewed the advancements of AI-based image processing techniques in multiphase flow systems, covering fluidization, crystallization, dissolution, and emulsification [
24]. Data-driven analytical technology has delivered outstanding performance in image segmentation and visualization of crystallization processes.
ML modeling integrated with crystallization techniques can substantially accelerate the development of new products. More than 50% of the new materials, food, drugs, agricultural chemicals, and dyes produced by chemical industries are crystalline [
25]. Crystallization is a multi-objective and nonlinear processing technique that influences the purity, particle size distribution, and morphology of the product. Moreover, as crystallization involves molecules, particles, crystals, processes, and equipment on different spatial scales, it cannot be developed through theoretical investigation alone [
25]. ML strategies can predict crystallization behavior and guide processing control. In particular, ML models can promote green, automated, and intelligent manufacturing. Combining the results of previous reports with our current understanding, this work reviews the recent ML-based developments in molecular crystal design and crystallization control (
Fig. 2). Incorporating ML models can improve prediction accuracy and reduce the computational time of these endeavors.
2. Molecular crystal design
Molecular crystal drug design has been rigorously pursued in the pharmaceutical field. Drug polymorphisms have become increasingly important in fundamental research and intellectual property rights. Polymorphism threatens the generic safety of drugs and polymorphic tests increase dramatically with the expiry of numerous original drug patents [
26]. In most software for predicting polymorphisms based on molecular mechanisms, the molecular energy is calculated by the Polymorph module, often based on quantum mechanics or molecular mechanics [
27,
28]. Particularly, the recent emergence of ML has accelerated molecular crystal design. Liu et al. [
29] suggested that ML models can simulate crystal growth in multiple fields, resolving the difficulty of synthesizing high-quality single crystals. Here, the recent advances in ML models for molecular crystal design are presented, covering solvate screening and prediction, crystallographic structure prediction, crystal property prediction, and synthesis of co-crystals and colloidal nanocrystals.
2.1. Solvate screening and prediction
As the solvate influences the solubility, stability, morphology, powder flowability, and compressibility of a drug, accidental solvate formation can unpredictably change the properties of the drugs [
30]. ML can effectively screen different solvents and predict their solvate effects. Among numerous algorithms, random forest and support vector machines are commonly adopted in multivariate data analysis. Random forest is often applied in the classification or regression problems in chemistry, manufacturing, and biology [
[31],
[32],
[33]]. Takieddin et al. [
34] defined a knowledge-based model that forecasts hydrates and solvates from molecular formulae alone. They collected more than 19 000 datasets of organic, non-ionic, and nonpolymeric molecules from the Cambridge Structural Database and verified the accuracy of model predictions in water, chloroform, dichloromethane, methanol, and ethanol. Takieddin et al. [
34] fitted logistic regression models using the corresponding molecular descriptors of the molecule, to evaluate the solvate probability, with more than 80% accuracy rate. Xin et al. [
31] predicted the solvate formation probabilities of drug molecules with an accuracy of 86% through the random forest model. ML algorithms can also predict inclusion complexes. Ma et al. [
35] predicted the formation probabilities of cyclodextrin inclusion complexes in aqueous solutions using support vector machines, logistic regression, and artificial neural network models. All three models delivered good prediction performance.
Although the existing ML models can effectively predict solvate formation, their prediction accuracy and computational time should be further improved. Unclear correlations between the experimental results and crystal forms restrict the further development of ML algorithms. Therefore, ML models should not be established based on existing databases alone. Experimental results must be combined to excavate the intrinsic correlations between the technical variables and crystal products. The descriptor design should additionally consider the molecular structure and crystal properties of the product.
2.2. Crystallographic structure prediction
Crystallographic structures are predicted from chemical diagrams based on statistics and computational science [
36]. Traditional first-principle prediction requires highly accurate energy calculations. Solid-state density functional theory (DFT) is a high-precision computing tool that incurs high computational costs. Molecular dynamics simulations effectively track the trajectories of particles in phase space to explain the physical phenomena [
37]. Pèpe et al. [
38] forecasted the crystallographic structure of molecules in different solvents using experimentally assisted molecular modeling. After obtaining the chemical formulae of the given molecules, they analyzed the crystallographic structures under the minimum-energy principle. Previously, we analyzed the intermolecular interactions and charge distributions using the Hirshfeld surface and the molecular electrostatic potential surface, and simulated solute–solvent interactions with the solvation-free energy model [
39,
40]. The radial distribution function can model the hydrogen-bond interactions among molecules. However, these calculation tools are restricted by high computational costs and long runtimes.
ML-based algorithms simplify complex calculations and shorten the time from discovery to application of a product. When used in conjunction with experiments, ML replaces numerous calculations with probabilistic predictions. ML algorithms can predict the crystallographic structure and explore the chemical properties of a given molecule. Egorova et al. [
36] replaced the expensive hybrid functional DFT with a statistical ML model and successfully predicted the crystal properties of oxalic acid, maleic hydrazide, and urazole. Bhardwaj et al. [
32] predicted the three-dimensional (3D) crystal fillers and crystal forms of olanzapine using a random forest model. Doi et al. [
41] used an ML scheme to extract the effective order parameters for classifying the crystallographic structure. Wengert et al. [
42] optimized traditional ML algorithms and designed a data-efficient ML routine to forecast molecular structures, which accelerated the screening of crystals by considering the subtle interplay among the molecules.
ML can potentially improve the accuracy of targeted parameters, especially those derived solely from human insight. While, when predicting crystallographic structures, ML algorithms are less successful due to the requirement of massive training sets and specialized knowledge for encoding and algorithm deployment [
27]. As no ML algorithm can predict the crystallographic structures of all molecules, an exhaustive search of the parameter combinations is necessary.
2.3. Crystal property prediction
In crystal property analyses, DFT calculations provide the electronic band structures, but their further applicability is limited by poor accuracy and high computational costs [
[43],
[44],
[45]]. ML can achieve high-throughput prediction; especially, it can map correlations between data when the physical mechanisms are unclear [
46]. Increasingly, the design of crystalline materials has relied on the integration of ML with prior knowledge [
47]. The entire ML workflow, from establishing the mathematical descriptors to selecting specific ML algorithms, has been already developed [
48]. High-throughput, automated synthesis, and testing techniques can now generate large material databases for algorithm training, allowing ML models to predict the properties of crystalline materials and design novel materials [
49,
50]. As shown in
Fig. 3 [
51], property prediction has already evolved through three generations. First-generation prediction calculated the physical properties using the Schrödinger equation or by optimizing the locations of atomic forces. In the second generation, the chemical-component inputs were mapped to the outputs of structural predictions containing the adopted combinations of elements after global optimization. However, the first and second generations relied on the physical insight of human experts [
52]. The third generation predicts crystallographic structures or properties using ML models and optimizes the prediction process with training data. Pilania et al. [
53] discovered the properties of crystalline materials using the kernel ridge regression model. ML models can forecast the crystal plasticities, thermal conductivities, and configurational energies [
50,
[54],
[55],
[56]]. Artificial neural networks are used for predicting chemical properties at the atomic level, such as formation energy [
57], band gap, Fermi energy [
58], and optimal conditions [
59].
However, property prediction is a difficult task within the complex space of molecular structures. Mastering the features of crystalline materials and improving the prediction accuracy are especially challenging. To optimize complex chemical parameters, ML algorithms must be combined with design theories of crystalline materials. The rapid development of quantum chemicals and calculations has accelerated material discovery and provided abundant data for ML models.
2.4. Co-crystal formation
Co-crystal screening is a critical and challenging task in drug development. Traditional crystal-design routes have adopted solvent-mediated or solid-based approaches. Solvent-mediated approaches include antisolvent, reaction, and evaporation crystallization, whereas the solid-based approach refers to solvent-assisted grinding [
60,
61]. Previous prediction strategies mainly depended on the melting point difference between the co-crystal and its pure components, which requires numerous and accurate potential calculations. The internal correlations between the co-crystal and co-formers have been explored through various statistical analyses and algorithms, but no complete prediction model has appeared to date until the existence of the ML algorithms. Wicker et al. [
62] reported that ML algorithms can guide the selection of co-formers with simple descriptors, boosting the prediction probability. Mswahili et al. [
63] extracted the molecular descriptors of the starting compounds and compared the prediction performance of different ML models. They reported a higher accuracy and sensitivity of the artificial neural network than of other models. Wang et al. [
64] also accurately predicted the synthesis of captopril–proline and captopril–sarcosine using ML. Chabalenge et al. [
65] synthesized 54 co-crystals through the hot-melt extrusion technique and integrated them into an open-sourced decision tree model for investigating the key parameters of co-crystal formation and enriching the database.
ML models can accelerate the progress and lower the experimental effort of designing molecular crystals. Similarly, co-crystal prediction requires the selection of suitable descriptors. Moreover, statistical analyses coupled with data mining can sufficiently reveal the properties of co-crystal compositions and simplify complex calculations. Data-driven ML techniques are widely prospective for molecular crystal design, predicting the crystallographic structures, properties, and formations of solvates and co-crystals [
66,
67]. Margraf [
68] reviewed data-driven ML algorithms for novel material design and emphasized the importance of model selection on property prediction. Ashraf et al. [
69] determined an important role for AI in the discovery of new crystal molecules. Li et al. [
70] suggested that ML can be combined with quantum mechanics computation and experimental datasets to forecast molecular energies, crystallographic structure, and properties.
2.5. Synthesis of colloidal nanocrystals
AI strategies have been embraced not only by the crystal engineering field but also in the design and synthesis of colloidal nanocrystals. The unique physical properties, ability to assemble into large structures and size-dependent optical properties of colloidal nanocrystals, have been exploited in electrochemical, biomedical, and optical applications [
71,
72], such as light-emitting diodes [
73], electronic devices [
74], and luminescent labels [
75]. Chen et al. [
76] summarized the synthesis of colloidal nanocrystals, prospecting the emerging applications and prospects of these fields.
However, the complex growth process raises the difficulty of regulating the properties or structures of colloidal nanocrystals and correlating them with the operational parameters. Recently, AI integration with robotic synthesis techniques has substantially reduced labor requirements [
77,
78]. Zhao et al. [
79] designed a robotic platform that controls the morphologies of colloidal nanocrystals. The first step of this platform excavates the data and parameters of materials from the literature. The following step automatically and controllably synthesizes the desired morphologies. The final step imports ML algorithms that identify the relations between the morphologies and structure-guiding agents after training on an experimental database. This new data-driven robotic synthesis framework effectively reduces the trial-and-error costs, promising the digital synthesis of nanocrystals. Chan et al. [
80] established an automated platform that synthesizes colloidal nanocrystals with high-throughput optimization. The robotic platform can precisely control the reaction conditions and complete the complex synthesis process. The accuracy and utility of the platform were verified by the small coefficient of variation of the mean diameters (0.2%) of the nanocrystals. The size, crystal phase, and polydispersity of the nanocrystals were precisely controlled, substantially improving the unconverted luminescence compared with the traditional experimental methods. This automated synthesis platform greatly accelerates the design of colloidal nanomaterials. Overall, combined robotic and AI techniques promise the synthesis of colloidal nanocrystals with controllable morphology and size while reducing time and labor costs.
3. Crystallization development
Besides molecular crystal design, ML algorithms have demonstrated potential in process design and robust control. Herein, the application scenarios of ML models in the design, optimization, and control of crystallization are presented.
3.1. Crystallization behavior
3.1.1. Crystallization propensities
Industrial crystallization urgently requires cheaper and cleaner production technologies providing safer and more efficient solutions. Crystallization is widely applied in high-purity chemical production and target crystal product design. However, selecting the appropriate crystallographic structure, thermodynamic, and kinetic parameters for crystallization incurs considerable time costs [
[81],
[82],
[83]]. ML models provide guidance for the prediction of crystallization propensity and behavior.
Venkatram et al. [
84] developed a data-driven ML model that predicts the crystallinity of polymers based on experimental and theoretical group-contribution strategies. Adopting a multi-fidelity information fusion approach, they accurately predicted the crystallization tendency at a low cost (
Fig. 4(a)) [
84]. Ghosh et al. [
85] evaluated the crystallization propensities of small organic compounds using support vector machine regression, neural networks, and random forest regression, integrating molecular descriptors, training sets, and experimental conditions to optimize the prediction accuracy. On a small training set, the three algorithms achieved similar accuracies but on a training set with more than 150 members, random forest regression outperformed the other algorithms. Ghosh et al. [
85] then compared the prediction performances of an active pharmaceutical ingredient (API)-only model (
Fig. 4(b)) and an API + solvent model (
Fig. 4(c)). The prediction performance of both models improved after excluding chemical degradations and impurities, and the API + solvent model is more outstanding on larger training sets. Applying ML algorithms, Pereira [
86] predicted the crystallization propensity from the fingerprints of two-dimensional (2D) and 3D chemical descriptors. ML algorithms have proven their worth in crystallization propensity prediction, especially in pharmaceutical projects.
3.1.2. Solubility and the metastable zone
Solubility is an important parameter in drug development as it determines the synthesis, process design, and formulation of a crystal product [
87,
88]. Drug solubility determines the formation of co-crystals, solvates, and the efficacy of drug delivery [
40,
89]. Therefore, approaches that forecast drug solubility in different solvents can save appreciable time and cost [
[90],
[91],
[92],
[93]].
Previously, we trained random decision forests and artificial neural networks on the solubility data of 120 APIs [
94]. The trained ML algorithms were then applied to dataset analysis and prediction model optimization. The ML algorithms outperformed traditional models in terms of accuracy and prediction ability. Multiple linear regression and stepwise regression were then integrated to analyze the key elements of solubility. Ge and Ji [
95] combined molecular thermodynamic simulations and predicted drug solubilities using a single-hidden-layer neural network. They described drug–drug and drug–solvent interactions using 16 molecular descriptors input to five ML algorithms, which accurately predicted drug solubility. Boobier et al. [
87] combined ML models with computational chemistry for solubility predictions in organic solvents and determined the physicochemical correlations between solubility and molecular properties.
The metastable zone width (MSZW) is another important parameter. The MSZW depends on the experimental conditions and raw material properties, which directly determine the operational regimes [
[96],
[97],
[98],
[99]]. We previously predicted the MSZW of a reaction crystallization process using an artificial neural network [
100]. Among several parameters (concentration, reaction volume, stirring speed, and temperature), temperature and concentration were strongly positively correlated with the MSZW.
3.1.3. Crystalline particle agglomeration prediction
Agglomeration directly impacts the particle size distribution, crystal shape, and purity of crystal products, thus influencing the downstream processing. For example, agglomeration is desired in the wet granulation process but undesired in the filter or drying process. Complex interactions between the solvent and solute increase the difficulty of quantifying or controlling the agglomeration degree [
101,
102], but image processing is useful for detecting and quantifying agglomerates [
103,
104]. Ochsenbein et al. [
105] identified agglomeration behaviors using a nonlinear support vector machine and image analysis strategy, defining different dimensions, such as one-dimensional (1D) particle size distribution of agglomerates and 2D particle size and shape distributions of primary crystals, to evaluate the particle properties and crystal growth behavior. Lins et al. [
106] applied ML to the evaluation of crystalline particle properties. Deep learning-based image processing can effectively describe particle agglomeration and detailed descriptions of the agglomeration level. Sinha et al. [
107] proposed a sticky zone-based agglomeration model (SZAM) (
Fig. 5(a)) that predicts the degree of particle agglomeration by coupling the agglomeration risk zone and sticky zone with the discrete element method. The bed is classified into various 3D Cartesian bins or voxels, and each is supposed in a microenvironment. Combined with ML models, the agglomeration degree can be described as a functional of input variables, such as the material properties and processing conditions.
Particle agglomeration leads to spherical crystal formation. Commonly, spherical crystals possess larger specific surface areas, higher bulk densities, and higher fluidities than needle- and plate-shaped forms [
40,
89]. Previously, a spherical crystallization technique was designed based on liquid–liquid phase separation theory and ML models [
108]. The model involves three steps (
Fig. 5(b)) [
108]. First, 149 API structures and three solvent systems (water, ethanol, and water–ethanol) are selected as model compounds, and 21 descriptors are extracted from chemical-structure descriptions and solute–solvent interactions to evaluate the particle behaviors. Next, the liquid–liquid phase separation processes are predicted by three ML algorithms: logistic regression, artificial neural network, and support vector machine. The algorithms are evaluated in terms of the accuracy and recall metrics. Finally, the ML algorithms for designing spherical crystallization are successfully validated on vanillin, cholecalciferol, and sarcosine.
In summary, relevant parameters and descriptors should be selected based on experimental results, to improve the comprehensibility and generalization performances of ML models [
[109],
[110],
[111]]. However, it is challenging to optimize various parameters of precision, recall, and accuracy in the ML model for a single algorithm. Additionally, it may introduce errors in the sample classification when lying near the decision boundary [
64,
86]. Hence, ML-based design strategies must consider the requirements and application scenarios of the targeted crystallization process.
3.2. ML-based online crystal-image processing
In the pharmaceutical and fine chemical industries, online monitoring of particle shape and size distribution is challenged by complex processes and the lack of adequate
in situ sensors. The emergence of real-time imaging hardware and process analysis technology (PAT) has sparked the development of advanced online control techniques [
112]. As highlighted in several studies, image processing techniques are necessary for online control of crystallization, which required timely extraction of the crystal information.
Large images usually increase the difficulty of analysis and processing in real-time crystallization monitoring. ML algorithms can feasibly accelerate image recognition. Doan et al. [
113] combined multivariate image analysis and AI algorithms for analyzing solution crystallization. Image processing techniques suitable for object detection include image enhancement, edge detection, morphology operations, and feature extraction techniques. Previously, we proposed a robust nucleation tracking technology for monitoring the nucleation of
L-glutamic acid [
114]. Combined with image analysis tools and ML models, we successfully tracked
in situ crystallization and detected the product information of crystal habit, polymorphism, and particle size distribution [
115]. Compared with traditional analysis techniques, such as Raman and focus beam reflection measurement, deep learning-based image analysis techniques can enhance the accuracy of segmentation and classification, and monitor individual particles or crystals.
Table 1 summarizes the main differences between image analysis and instrumental measurements using lasers, ultrasonic irradiation, and other sources. Image analysis techniques can obtain more information on the crystal products and can adapt to more complex environments than instrumental techniques.
We have reviewed high-efficiency image segmentation via deep learning strategies involving image classification, object detection, semantic segmentation, and instance segmentation, and concluded the main characteristics of artificial neural network algorithms [
24]. Image recognition strategies that employ CNN algorithms have proven useful for analyzing sustainable emulsion manufacturing and crystallization processes (
Fig. 6(a)) [
116]. Mask region-based convolutional neural network (Mask R-CNN) is a modified CNN algorithm with high universality, good flexibility, and fast segmentation ability, containing the following procedures: database establishment, labelling, training, image processing, mask processing, and process analysis (
Fig. 6(b)).
Table 2 [
[117],
[118],
[119],
[120],
[121],
[122],
[123],
[124],
[125],
[126],
[127],
[128]] lists recent cases of ML-based image processing in crystallization development. ML-based image processing techniques effectively recognize the object characteristics and monitor the crystallization process. Compared with other algorithms, neural network models are more often combined with image processing techniques for crystallization monitoring.
Table 3 summarizes the main differences between deep learning-based and other algorithms employed in image processing. Deep learning-based models increase the processing capacity, accuracy, and processing speed from those of other algorithms.
Although ML-based algorithms can accurately classify images and extract the crystal size information, they cannot easily identify agglomerations and long-needle crystals when lied in highly concentrated solution. It is also challenging to extract the 3D information of products in complex crystallization systems. These limitations would be mitigated by an advanced imaging device and an image recognition database covering information on crystals and particles. For example, the camera angles could be optimized to maximally capture the 3D particle information [
24].
3.3. ML-based control of crystallization processes
The monitoring and precise control of crystallization processes is restricted by complex mechanisms, nonlinear and stochastic crystallization dynamics, insufficient evidence of crystal nucleation, and a lack of real-time crystal information [
[129],
[130],
[131],
[132]]. PAT tools provide product-analysis and online-monitoring support, efficiently resolving the insufficiency of real-time information during crystal growth [
132,
133]. Data-driven monitoring and control are important for optimizing crystallization processes.
3.3.1. Crystallization control strategies
Process analysis techniques are widely adopted in crystallization control, process optimization, and industrial automation. The development of PAT technology has remarkably advanced the online monitoring of crystallization, allowing accurate measurements of solution properties, characterization of crystal quality, simulations of crystallization, and process control. The guidelines of drug crystal development have changed from “quality by test” to “quality by design” and are moving toward “quality by control” with the emergence of intelligent manufacturing (
Fig. 7(a)) [
134]. Similarly, the production mode has changed from batch to continuous and finally to smart manufacturing. Process control defines the regulation of technical variables to obtain the desirable outputs in real-time while ensuring safe and stable operation. Crystallization control can be divided into model-based control, model-free control, or hybrid control strategies (
Fig. 7(b)). Model-based control, including open-loop optimal control and model predictive control, is restricted by the complexity of crystallization processes and obscure kinetic mechanisms. The main model-free control strategies are supersaturation and direct nucleation control [
135,
136]. Various PAT tools, such as focused beam reflectance measurements, particle video microscopes, and attenuated total reflectance–Fourier transform infrared (ATR-FTIR) spectroscopy, can be integrated into crystallization [
137].
Fig. 7(c) [
138] shows the monitoring of polymorphic concentration via online tools. The polymorphic concentration can be directly detected from the Raman and ultraviolet/visible spectra and applied as feedback control. Traditional control models are time-consuming and easily affected by disturbances. AI-based models can improve the performance of process control. Dutta and Upreti [
139] depicted a map of keywords in which neural networks and process control are the two most notable labels and are highly connected. Particle swarm optimization, machine learning, and fuzzy control form another notable group of keywords. Among the various algorithms, an artificial neural network is commonly used in complex crystallization processes.
3.3.2. ML-based control of crystallization
Crystallization can be divided into batch and continuous operations. Continuous crystallization is more easily controlled and achieves higher productivity and better consistency than batch processes, but is comparatively inflexible and requires a complex operational environment. Batch crystallization, commonly used in the pharmaceutical industry, is a labor-intensive process. Control strategies can be integrated with AI algorithms to improve the efficiency of crystallization processes. AI can direct the control process and optimize the operation with low disturbance [
22].
Table 4 [
[140],
[141],
[142],
[143],
[144],
[145],
[146]] summarizes typical AI algorithms adopted in chemical engineering. Artificial neural networks and reinforcement learning algorithms are more adaptable to disturbances than expert systems and fuzzy logic. Scientists have realized that hybrid algorithms can effectively avoid the limitations of single AI models [
139]. The main hybrid algorithms are evolutionary reinforcement learning, hybrid neuro-fuzzy systems, hybrid neural networks/fuzzy logic, and nature-inspired algorithms [
[147],
[148],
[149]]. All these data-driven control strategies can efficiently regulate crystallization [
[150],
[151],
[152]].
(1)
Concentration-based regulators. An AI-based concentration-control model can efficiently adjust the supersaturation level of the solution environment. Zhang et al. [
135,
136] proposed a feedback-control strategy that regulates the feed flow rate of semi-batch crystallization to modulate the supersaturation level. In our previous work, a supersaturation control strategy is proposed to optimize the crystal morphology of
p-aminobenzoic acid and reduce the length-to-diameter ratio of the crystals [
115]. The main technical variables are the feeding modes, solution temperature, and flow rate of the antisolvent. Kamaraju and Chiu [
153] designed a novel concentration-control strategy that measures the process variables of semi-batch crystallization in real-time. They simulated the solution concentration with just-in-time-learning modeling and predicted the product quality using nonlinear multiway partial least squares.
Fig. 8 [
154] displays a fuzzy logic-based feedback controller in which the solution concentration and cord length counts are measured by ATR-FTIR and LasenTec. The temperature and flow rate of the antisolvent are regulated based on the solution supersaturation [
[154],
[155],
[156]].
AI-based supersaturation control has become a promising pathway in crystallization processes. In particular, PAT tools can improve the sensitivity of the supersaturation determination in real-time. Paengjuntuek et al. [
157] regulated the batch crystallization of potassium sulphate as a model compound under neural network-based optimal control. Because the control framework is integrated into the neural network model, the supersaturation can be regulated by tuning the operating temperature. Damour et al. [
158] developed an artificial neural network for nonlinear predictive control of crystallization processes. They controlled the suspension density by regulating the feeding process. Georgieva and de Azevedo [
159,
160] discussed the use of artificial neural networks in the modeling and optimization of a batch crystallization process. They designed an AI-based control module, by integrating an artificial neural network as a computational tool, for batch crystallization. Combined with the nonlinear dynamic process modeling and model-based predictive control, the operational parameter feed flow can be urged along the optimal supersaturation trajectory. Guo et al. [
161] optimized the temperature and supersaturation level in a semi-batch crystallization process. They combined dynamic time warping with a CNN to optimize fault detection and diagnosis in the unsteady batch chemical process.
(2)
Image-based analysis. With the exception of supersaturation control, image recognition-based ML modeling can support the control and optimization of crystallization processes. Manee et al. [
162] designed an AI-based imaging-process control sensor that monitors crystallization and recognizes crystal properties in real-time. Their model can detect crystals in high-density slurries (
Fig. 9(a)). A reinforcement learning strategy successfully controls the crystalline particle size in the antisolvent crystallization [
163]. Manee et al. [
122] applied ML strategies to the closed-loop control process, combining a CNN with a reinforcement learning framework to optimize the process control. This AI-based sensor monitors the crystal size distribution and reduces the imaging processing time. In addition, the reinforcement learning model can successfully design the crystallization under disturbances. The
in situ analysis and image-based control system is shown in
Fig. 9(b) [
24]. Based on the dimensions of the crystalline particles obtained from the images, crystallization can be regulated and the operational parameters can be optimized. Öner et al. [
164] measured the temperature dependence of chord length distribution during batch crystallization in real-time using a network model with a radial basis function. Even in the absence of comprehensive experimental data, the proposed networks can optimize crystallization by manipulating the operational temperature. Wang et al. [
165] applied deep learning-based image analysis to the feedback control of crystallization (
Fig. 9(c)). They designed a deep learning-based image processing to control the particle size distribution. Improving the accuracy and efficiency of online process control is vitally important. In addition, timely handling of crystallization data and provision of accurate feedback are also important. Future research should focus on advanced online-monitoring devices and their integration into efficient ML algorithms for improved optimization and control of crystallization. The advantages and disadvantages of supervised/unsupervised ML algorithms for crystallization, and several representative examples are summarized in
Table 5 [
31,
65,
[166],
[167],
[168],
[169],
[170],
[171],
[172],
[173],
[65],
[174],
[175],
[176],
[31],
[177],
[178],
[179],
[180],
[181],
[182],
[183],
[184],
[185],
[186],
[187],
[188]].
4. Conclusions and outlook
ML has been widely utilized in the design of novel functional materials and predictive models for crystallization optimization. ML algorithms can predict the properties of products, reveal structure–function correlations, and shorten the time from discovery to application. Herein, we summarized the recent progress of ML in molecular crystal design and crystallization development. ML has modified the traditional design methods based on first-principles calculations and achieved robust process control of crystalline products.
We first discussed the use of ML in the design of multicomponent crystalline products, covering the formation of co-crystals and solvates, crystallographic structure and property predictions, and the synthesis of colloidal nanocrystals. Although multicomponent crystalline products are promising agents in drug development, their complex interactions are poorly understood and efficient screening strategies are lacking. Therefore, the design of such materials is limited in scope. ML-based molecular design strategies greatly reduce the uncertainty and operational costs of traditional approaches based on experiments and simulation calculations. Next, we reviewed applications of ML algorithms in crystallization development. ML models can predict drug solubilities, the MSZW, particle agglomeration behaviors, and spherical crystal products. ML-based online image processing can extract information about crystal products and track crystallization in situ using PAT tools. The features of ML-based image analysis and comparisons with other algorithms were also given. Finally, AI-based process control strategies were summarized. AI-based concentration control can detect supersaturation of a solution and image-based control strategies can capture the information of particles. Both feedback control routes effectively regulate the crystal product properties by changing the operational parameters. In further studies, the following issues should be paid attention.
(1) Data-driven ML algorithms are based on probability and statistics. They are black box models without sufficient professional knowledge. Although ML is potentially suitable for multiscale nonlinear mapping, huge-data association mining, and decision-making, ML models are incapable of deep logical reasoning and making physical connections. Future ML models must be constructed based on physical constraints and experimental results.
(2) Researchers often select the best-performing ML models for drug discovery and materials-science testing. However, the best regression or classification algorithm for a given application scenario is difficult to construct in a single ML model. To improve the predictive performance of ML models, developing specific ML-based routes and coupling efficient algorithms are required.
(3) ML-based online crystal-image processing may be unsuitable for complex systems containing particle aggregations, needle-like crystals, or bubble flow solutions. Therefore, designing advanced online-monitoring devices and expanding the sizes of databases are also important.
CRediT authorship contribution statement
Shengzhe Jia: Writing – original draft, Validation, Methodology, Investigation. Yiming Ma: Validation, Investigation. Yuechao Cao: Validation, Investigation, Conceptualization. Zhenguo Gao: Writing – review & editing, Supervision, Project administration, Conceptualization. Sohrab Rohani: Writing – review & editing, Methodology, Conceptualization. Junbo Gong: Writing – review & editing, Supervision, Conceptualization. Jingkang Wang: Writing – review & editing, Resources, Conceptualization.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was financially supported by the National Natural Science Foundation of China (22008173, 21938009, and 21676179), and the Major Key Technology Project of Shandong Provincial Key Research and Development Program (2021CXGC010514). Yiming Ma acknowledges the support of the China Scholarship Council.
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