Predicting the stability of vitamin supplements

Abstract

Systems, methods, and computer programs disclosed herein relate to predicting the temporal stability of vitamin supplements using a trained machine learning model.

Description

[0001] Predicting the stability of vitamin supplements

[0002] FIELD OF THE DISCLOSURE

[0003] Systems, methods, and computer programs disclosed herein relate to predicting the temporal stability of vitamin supplements using a trained machine learning model.

[0004] BACKGROUND

[0005] Vitamins, minerals, and other nutrients play an important role in human health. They are mostly chemical substances that the human body cannot produce itself or cannot produce in sufficient quantities and must therefore be supplied in the form of food and / or nutritional supplements. In particular, athletes, women in pregnancy, elderly and / or sick people may have an increased need for vitamins and / or minerals and / or other nutrients that are not supplied through food (see, e.g.: I. Hamrick, S. Counts: Vitamin and Mineral Supplements. Primary Care Clinics in Office Practice, 2008, 35(4): 729-747).

[0006] For this purpose, vitamin preparations, mineral preparations, nutrient preparations, or combination preparations are available in the form of tablets, powders, granules, pellets, capsules, liquids, confectionery like and / or other dosage forms.

[0007] Such Vitamin and / or Mineral Supplement (VMS) products are usually stored under different conditions. Typical storage conditions are described, e.g., in ICH (International Council for Harmonisation) guidelines that allow the scientist to propose a shelf-life for the finished products depending on the region of the world where the product is sold. Over time, the ingredients of such vitamin supplements may degrade (see, e.g., L. T. Abe-Matsumoto et al. '. Stability of antioxidant vitamins in commercial vitamin supplements, Brazilian Journal of Pharmaceutical Sciences, 2018, 54(4): el7700). The storage conditions, including temperature, humidity, light, and duration of storage can influence the speed of degradation of the ingredients.

[0008] When a new dosage form of a VMS products and / or a new VMS product with a new combination of ingredients is developed, experimental studies are usually carried out to determine storage stability (R. Coad, L. Bui: Stability of Vitamins Bl, B2, B6 and E in a Fortified Military Freeze-Dried Meal During Extended Storage, Foods 9, 2020, No. 1: 39.). The storage stability determined experimentally in this way can be used to determine the shelf-life of a VMS product.

[0009] Assessing storage stability and shelf-life is time-consuming and can result in increased development costs and potentially delay product launches.

[0010] SUMMARY

[0011] It would therefore be desirable to be able to predict storage stability and / or shelf-life of VMS products.

[0012] This could avoid or reduce expensive and / or time-consuming investigations, shorten time to market and / or prevent overruns of shelf-life.

[0013] This task is solved by the subject matter of the independent claims of the present disclosure. Preferred embodiments are defined in the dependent claims, the description, and the drawings.

[0014] In a first aspect, the present disclosure relates to a computer-implemented method comprising: providing a trained machine learning model, o wherein the trained machine learning model is a probabilistic prediction model, o wherein the trained machine learning model is configured to determine a temporal stability of one or more ingredients of a vitamin supplement based on compositional information of the vitamin supplement and based on model parameters, wherein the temporal stability comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur, o wherein the machine learning model has been trained in a supervised learning process using training data, the training data comprising, for each reference vitamin supplement of a plurality of reference vitamin supplements, (i) compositional information of the reference vitamin supplement as input data, and (ii) information on the temporal stability of one or more ingredients of the reference vitamin supplement as target data, o wherein the training of the machine learning model comprises:

[0015] ■ inputting the input data into the machine learning model,

[0016] ■ receiving a predicted temporal stability of the one or more ingredients of the reference vitamin supplement from the machine learning model,

[0017] ■ reducing deviations between the predicted temporal stability and the target data, receiving compositional information of a candidate vitamin supplement, inputting the received compositional information into the trained machine learning model, receiving a predicted temporal stability for one or more ingredients of the candidate vitamin supplement from the trained machine learning model, wherein the predicted temporal stability comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur, outputting the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement and / or storing the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement in a data memory and / or transmitting the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement to a separate computer system.

[0018] In another aspect, the present disclosure provides a computer system comprising: a processor; and a memory storing an application program configured to perform, when executed by the processor, an operation, the operation comprising: providing a trained machine learning model, o wherein the trained machine learning model is a probabilistic prediction model, o wherein the trained machine learning model is configured to determine a temporal stability of one or more ingredients of a vitamin supplement based on compositional information of the vitamin supplement and based on model parameters, wherein the temporal stability comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur, o wherein the machine learning model has been trained in a supervised learning process using training data, the training data comprising, for each reference vitamin supplement of a plurality of reference vitamin supplements, (i) compositional information of the reference vitamin supplement as input data, and (ii) information on the temporal stability of one or more ingredients of the reference vitamin supplement as target data, o wherein the training of the machine learning model comprises:

[0019] ■ inputting the input data into the machine learning model,

[0020] ■ receiving a predicted temporal stability of the one or more ingredients of the reference vitamin supplement from the machine learning model,

[0021] ■ reducing deviations between the predicted temporal stability and the target data, receiving compositional information of a candidate vitamin supplement, inputting the received compositional information into the trained machine learning model, receiving a predicted temporal stability for one or more ingredients of the candidate vitamin supplement from the trained machine learning model, wherein the predicted temporal stability comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur, outputting the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement and / or storing the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement in a data memory and / or transmitting the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement to a separate computer system.

[0022] In another aspect, the present disclosure provides a non-transitory computer readable storage medium having stored thereon software instructions that, when executed by a processor of a computer system, cause the computer system to execute the following steps: providing a trained machine learning model, o wherein the trained machine learning model is a probabilistic prediction model, o wherein the trained machine learning model is configured to determine a temporal stability of one or more ingredients of a vitamin supplement based on compositional information of the vitamin supplement and based on model parameters, wherein the temporal stability comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur, o wherein the machine learning model has been trained in a supervised learning process using training data, the training data comprising, for each reference vitamin supplement of a plurality of reference vitamin supplements, (i) compositional information of the reference vitamin supplement as input data, and (ii) information on the temporal stability of one or more ingredients of the reference vitamin supplement as target data, o wherein the training of the machine learning model comprises:

[0023] ■ inputting the input data into the machine learning model,

[0024] ■ receiving a predicted temporal stability of the one or more ingredients of the reference vitamin supplement from the machine learning model,

[0025] ■ reducing deviations between the predicted temporal stability and the target data, receiving compositional information of a candidate vitamin supplement, inputting the received compositional information into the trained machine learning model, receiving a predicted temporal stability for one or more ingredients of the candidate vitamin supplement from the trained machine learning model, wherein the predicted temporal stability comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur, outputting the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement and / or storing the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement in a data memory and / or transmitting the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement to a separate computer system.

[0026] BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Fig. 1 shows schematically and exemplarily a process of training a machine learning model.

[0028] Fig. 2 shows an example of a method of training a machine learning model in form of a flowchart.

[0029] Fig. 3 shows schematically and exemplarily the use of a trained machine learning model for prediction.

[0030] Fig. 4 shows an embodiment of the computer-implemented method of the present disclosure in form of a flowchart.

[0031] Fig. 5 shows schematically and exemplarily a computer system according to the present disclosure.

[0032] Fig. 6 shows the result of a prediction with a trained machine learning model and a comparison with measured values.

[0033] DETAILED DESCRIPTION

[0034] The invention will be more particularly elucidated below without distinguishing between the aspects of the invention (method, computer system, computer-readable storage medium). On the contrary, the following elucidations are intended to apply analogously to all the aspects of the invention, irrespective of in which context (method, computer system, computer-readable storage medium) they occur.

[0035] If steps are stated in an order in the present description or in the claims, this does not necessarily mean that the invention is restricted to the stated order. On the contrary, it is conceivable that the steps can also be executed in a different order or else in parallel to one another, unless one step builds upon another step, this absolutely requiring that the building step be executed subsequently (this being, however, clear in the individual case). The stated orders are thus preferred embodiments of the present disclosure.

[0036] As used herein, the articles “a” and “an” are intended to include one or more items and may be used interchangeably with “one or more” and “at least one.” As used in the specification and the claims, the singular form of “a”, “an”, and “the” include plural referents, unless the context clearly dictates otherwise. Where only one item is intended, the term “one” or similar language is used. Also, as used herein, the terms “has”, “have”, “having”, or the like are intended to be open-ended terms. Further, the phrase “based on” is intended to mean “based at least partially on” unless explicitly stated otherwise. Further, the phrase “based on” may mean “in response to” and be indicative of a condition for automatically triggering a specified operation of an electronic device (e.g., a controller, a processor, a computing device, etc.) as appropriately referred to herein.

[0037] Some implementations of the present disclosure will be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all implementations of the disclosure are shown. Indeed, various implementations of the disclosure may be embodied in many different forms and should not be construed as limited to the implementations set forth herein; rather, these example implementations are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0038] The present disclosure describes means for predicting the temporal stability of one or more ingredients of a vitamin supplement. A “vitamin supplement” is a manufactured product intended to supplement the diet. Synonyms for the term vitamin supplement are, for example, nutritional supplement, dietary supplement, and vitamin preparation.

[0039] A vitamin supplement can provide nutrients extracted from food sources and / or nutrients that are synthetic in order to increase the quantity of their consumption.

[0040] The class of nutrients includes vitamins, minerals, fiber, fatty acids, and amino acids. Vitamin supplements can also contain substances that have not been confirmed as being essential to life, but are marketed as having a beneficial biological effect, such as plant pigments and / or polyphenols. Animals can also be a source of supplement ingredients, such as collagen from chickens or fish for example. These are also sold individually and in combination and may be combined with other nutrient ingredients.

[0041] The vitamin supplement comprises one or more vitamins.

[0042] “Vitamins” are organic molecules (or a set of closely related molecules called vitamers) that are essential to an organism in small quantities for proper metabolic function. Essential nutrients cannot be synthesized in the organism in sufficient quantities for survival, and therefore must be obtained through the diet. The term "vitamin" also includes precursors of a vitamin. A “precursor” is a chemical compound that is converted into a vitamin in a person's body. For example, beta-carotene is converted into vitamin A in the human body.

[0043] The vitamin supplement may contain one or more of the following vitamins: vitamin A, beta-carotene, vitamin Bl (thiamin), vitamin B2 (riboflavin), vitamin B3 (niacin, nicotinic acid) vitamin B5 (pantothenic acid), vitamin B6 (pyridoxal, pyridoxine, pyridoxamine), vitamin B7 (biotin), vitamin B9 (folic acid, folate), vitamin B12, vitamin C (ascorbic acid), choline, vitamin DI (ergocalciferol, lumisterol), vitamin D2 (ergocalciferol), vitamin D3 (cholecalciferol), vitamin D4 (22- dihydroergocalciferol), vitamin D5 (sitocalciferol), vitamin E (alpha-tocopherol), vitamin KI (phylloquinone), vitamin K2 (menaquinone).

[0044] In an embodiment of the present disclosure, the vitamin supplement is a multivitamin supplement, i.e., it comprises more than one vitamin, e.g., 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 or more than 20 vitamins. In an embodiment of the present disclosure, the vitamin supplement contains more than 10, preferably more than 20 ingredients.

[0045] Preferably, the vitamin supplement comprises one or more of the following vitamins: vitamin A, beta- carotine, vitamin E, vitamin KI, vitamin C, vitamin D3, folic acid, biotin, vitamin Bl, vitamin B2, vitamin B3, vitamin B5, vitamin B6, vitamin B12.

[0046] Preferably, the vitamin supplement comprises the following vitamins: vitamin A, beta-carotine, vitamin E, vitamin KI, vitamin C, vitamin D3, folic acid, biotin, vitamin Bl, vitamin B2, vitamin B3, vitamin B5, vitamin B6, vitamin B12.

[0047] The prediction of temporal stability can be made for one or more ingredients of the vitamin supplement.

[0048] Preferably, the prediction is made for several ingredients. Preferably, the prediction is made for some or all vitamins contained in the vitamin supplement.

[0049] “Temporal stability” is a measure that provides information on the extent to which the composition of a vitamin supplement changes or remains the same over time.

[0050] The predicted temporal stability comprises an expected value of the temporal stability and an information about how likely it is that the expected temporal stability value will occur.

[0051] The predicted temporal stability may be a predicted temporal stability distribution. The predicted temporal stability may comprise an expected value of the temporal stability and a prediction interval.

[0052] A “prediction interval” provides a range around a point estimate (such as the expected value of the temporal stability) that is likely to contain the true value of what is being predicted. This interval captures the uncertainty of the prediction, taking into account the noise in the data and any limitations of the model itself. Prediction intervals are different from confidence intervals, which are more about the uncertainty in estimating model parameters. Prediction intervals account for both the uncertainty in the model parameters and the inherent noise in the data.

[0053] For example, the machine learning model may be configured and trained to output a degradation curve of one or more ingredients of the vitamin supplement with quantiles. The quantiles can be, e.g., the 25% quantile and the 75% quantile, or the 5% quantile and the 95% quantile, or any other statistical quantity.

[0054] Temporal stability can be, for example, a shelf-life. Shelf-life can be defined as the period of time that a vitamin supplement can be stored under defined conditions without significant quality degradation.

[0055] Temporal stability is preferably understood as the amount of an ingredient that is present in the vitamin supplement after a certain storage time under certain conditions.

[0056] The amount may be expressed, for example, as a percentage relative to the amount originally contained in the vitamin supplement.

[0057] The storage time can be, for example, one week or several weeks or one month or several months or one year or several years or any other time period.

[0058] Preferably, a prediction is made not only for one time period but for several time periods.

[0059] Preferably, a degradation curve is predicted for one or more ingredients of the vitamin supplement. Such a degradation curve may indicate, for each point in time of a finite or infinite time period, the amount and / or percentage of an ingredient (still) contained in the vitamin supplement as a function of time.

[0060] Preferably, a probability distribution of the amount of an ingredient (still) present in the vitamin supplement is predicted for one or more time periods. In this way, not only an expected value for the amount (still) present in the vitamin supplement for the one or more time periods can be determined, but also information about the probability with which this expected value occurs and / or the uncertainty associated with this expected value.

[0061] The prediction is done using a trained machine learning model.

[0062] The term “machine learning” refers to the development of algorithms and statistical models used by computer systems to perform a specific task without explicit instructions, relying instead on patterns and inference. Machine learning is seen as a subset of artificial intelligence. Machine learning algorithms build a mathematical model based on sample data, known as “training data”, in order to make predictions or decisions without being explicitly programmed to perform the task.

[0063] The term “machine learning model”, as used herein, may be understood as a computer implemented data processing architecture. The machine learning model can receive input data and provide output data based on that input data and on parameters of the machine learning model. The machine learning model can learn a relation between input data and output data through training. In training, parameters of the machine learning model may be adjusted in order to provide a desired output for a given input.

[0064] The process of training a machine learning model involves providing a machine learning algorithm (that is the learning algorithm) with training data to learn from. The term “trained machine learning model” refers to the model artifact that is created by the training process. The training data must contain the correct answer, which is referred to as the target. The learning algorithm finds patterns in the training data that map input data to the target, and it outputs a trained machine learning model that captures these patterns. In the training process, training data are inputted into the machine learning model and the machine learning model generates an output. The output is compared with the (known) target. Parameters of the machine learning model are modified in order to reduce the deviations between the output and the (known) target to a (defined) minimum.

[0065] For point predictions, a loss function can be used for training, where the loss function can quantify the deviations between the output and the target. Such a loss function may be chosen in a way that it rewards a wanted relation between output and target and / or penalizes an unwanted relation between an output and a target. Such a relation can be, e.g., a similarity, or a dissimilarity, or another relation.

[0066] If, for example, the output and the target are numbers, the loss function may be the difference between these numbers. In this case, a high absolute value of the loss function can mean that a parameter of the model needs to undergo a strong change.

[0067] In the case of vector-valued outputs, for example, difference metrics between vectors such as the root mean square error, a cosine distance, a norm of the difference vector such as a Euclidean distance, a Chebyshev distance, an Lp-norm of a difference vector, a weighted norm or any other type of difference metric of two vectors can be chosen. These two vectors may for example be the desired output (target) and the actual output.

[0068] In the case of higher dimensional outputs, such as two-dimensional, three-dimensional or higherdimensional outputs, for example an element-wise difference metric can be used. Alternatively or additionally, the output data may be transformed, for example to a one -dimensional vector, before computing a loss.

[0069] The modification of model parameters and the reduction of the loss can be done in an optimization procedure, for example gradient descent optimization, particle swarm optimization, genetic algorithm optimization, Levenberg -Marquardt optimization and / or other optimization procedure.

[0070] In a preferred embodiment, a gradient descent optimization procedure is used, in particular a natural gradient descent optimization procedure or stochastic gradient descent optimization procedure.

[0071] The loss function or training algorithm may include weights to balance under- and over-represented data.

[0072] The machine learning model of the present disclosure is a probabilistic prediction model.

[0073] A “probabilistic prediction model” is a type of machine learning model that provides not only a point estimate of the target variable but also captures the uncertainty associated with the prediction, e.g. by outputting a probability distribution over the possible values of the target variable. In other words, the probabilistic prediction model does not just provide a single prediction, but rather a range of potential predictions along with the likelihood of each prediction being correct.

[0074] Probabilistic prediction models provide a measure of uncertainty and / or confidence in the predictions, which can be crucial in decision-making processes. This allows for a more informed understanding of the potential variability in the predicted outcomes.

[0075] Probabilistic prediction models enable decision-makers to take into account the entire range of potential outcomes and their associated probabilities, which can be particularly useful in scenarios where risk assessment and risk management are important.

[0076] By capturing the entire distribution of potential outcomes, probabilistic prediction models are often more robust to outliers and noise in the data, providing a more comprehensive understanding of the underlying patterns.

[0077] When training a probabilistic prediction model, the goal may be to predict a probability distribution over the possible values of the target variable . This means that the model is not only providing a point estimate but also capturing the uncertainty associated with the prediction. The training process for a probabilistic model may involve learning the parameters of the probability distribution, such as mean and variance, for example, rather than just optimizing for a single point estimate.

[0078] In point predictions, the predictions are compared with the observed data (target) with a loss function (see above). The analog in probabilistic regression may be a scoring rule that compares the estimated probability distribution with the observed data.

[0079] A proper scoring rule may take as input a predicted probability distribution and one observation (outcome) and assign a score to the prediction such that the true distribution of the outcomes gets the best score in expectation. An optimization procedure such as a gradient descent approach can be used to find the model parameters that minimize the scoring rule. Preferably, the natural gradient is calculated, i.e., the direction of the steepest descent in Riemannian space.

[0080] The probabilistic prediction model of the present disclosure may be a probabilistic regression model. A probabilistic regression model is a type of machine learning model used for predicting a continuous target variable while also providing a probability distribution over the possible values of the target variable.

[0081] The probabilistic prediction model of the present disclosure may be an ensemble of multiple machine learning models. An “ensemble” of machine learning models refers to a technique in which multiple individual models are combined to make predictions. The individual models, often referred to as “base models” can be of the same type (homogeneous ensemble) or different types (heterogeneous ensemble).

[0082] Each base model in the ensemble may be trained to produce probabilistic predictions, meaning that instead of providing a single point estimate, they output a probability distribution over the possible values of the target variable. These individual models can be any type of probabilistic model, such as Gaussian processes, Bayesian neural networks, or probabilistic decision trees.

[0083] Once the individual models are trained, their probabilistic predictions can be combined or aggregated to form a collective prediction. This can be done using various ensemble techniques such as averaging the predicted distributions, weighted averaging, or more complex methods like stacking or boosting.

[0084] The aggregated probabilistic predictions from the ensemble may then be used to construct the final probability distribution over the target variable. This distribution represents the collective uncertainty- aware prediction produced by the ensemble.

[0085] Ensembles can take various forms, such as bagging (e.g., Random Forest), boosting (e.g., AdaBoost, Gradient Boosting Machines), and stacking, each with its own approach to combining the predictions of individual models.

[0086] It is possible to use an ensemble of point predictors to predict a probability distribution. An ensemble of point prediction models can be adapted to predict a probability distribution by using the variability in the predictions of the ensemble members to estimate the uncertainty of the prediction, for example. This approach is based on the idea that while each individual model may provide a single point estimate, the collection of point estimates from multiple models can be used to infer a distribution that reflects the consensus and the differences in their predictions.

[0087] Multiple point prediction models may be trained on different subsets of the data (as in bagging) or sequentially with a focus on different aspects of the prediction task (as in boosting).

[0088] For prediction, each trained model in the ensemble may be used to make predictions on the same input data, resulting in a set of point predictions for each instance in the dataset. The set of predictions for each instance can be treated as samples from an underlying probability distribution. There are several ways to estimate this distribution: Kernel Density Estimation (KDE) may be used to estimate the probability density function from the ensemble predictions; a histogram of the predictions may be generated, which may be normalized to form a probability distribution. ; a parametric form for the distribution may be assumed (e.g., Gaussian) and the mean and standard deviation of the ensemble predictions may be used to define it.

[0089] Further information on machine learning models of the present disclosure is provided later in this description.

[0090] The machine learning model is trained on training data to predict a temporal stability of one or more ingredients of a vitamin supplement.

[0091] The training data comprise, for each reference vitamin supplement of a plurality of reference vitamin supplements, (i) compositional information of the reference vitamin supplement as input data, and (ii) information on the temporal stability of one or more ingredients of the reference vitamin supplement as target data.

[0092] The term “plurality” preferably means more than ten, even more preferably more than one hundred.

[0093] The term “reference” is used in this disclosure to distinguish the training phase from the inference phase. The term “reference” otherwise has no limiting meaning.

[0094] Thus, a “reference vitamin supplement” is a vitamin supplement from which data is used to train the machine learning model. In turn, the vitamin supplement for which temporal stability of one or more contained ingredients is predicted using the trained machine learning model is called a “candidate vitamin supplement”. Statements made in this description with respect to a “vitamin supplement” apply equally to reference vitamin supplements and candidate vitamin supplements.

[0095] The plurality of reference vitamin supplements may be pure chemical substances and / or mixtures.

[0096] “Compositional information” includes information about the ingredients contained in a vitamin supplement and their respective amounts.

[0097] Compositional information preferably includes information on all ingredients present in the vitamin supplement, at least those ingredients present in a minimum quantity. The minimum quantity may be, for example, 1 weight percent or 0.5 weight percent or 0. 1 weight percent or 0.05 weight percent or 0.01 weight percent or some other value.

[0098] Examples of ingredients include vitamins, minerals and / or other nutrients, binders, carriers, colorants, flavors, aromas, preservatives, solvents and / or other / further substances.

[0099] The compositional information may also include information about what the composition is, such as a liquid or solid composition, a suspension or emulsion, or a mixture or other formulation.

[0100] A machine learning model typically requires numbers as inputs.

[0101] Categorical variables, such as the name of an ingredient or the type of a composition or formulation, can be converted into numerical variables, e.g., by arbitrarily assigning a number to each category (see, e.g., W.D Fisher: On Grouping for Maximum Homogeneity, Journal of the American Statistical Association, 1958, Volume 53, Issue 284; A. Di Ciaccio: Categorical Encoding for Machine Learning, 2020, https: / / research.uniromal.it / pubblicazioni / 52965)

[0102] It is also possible to use one-hot encodings for categorical variables. “One-hot encoding” is a method to quantify categorical data. In short, this method produces a vector with length equal to the number of categories in the data set. If a data point belongs to the zthcategory then components of this vector are assigned the value 0 except for the zthcomponent, which is assigned a value of 1. A nutritional supplement can be composed of a defined number of ingredients, where the ingredients are selected from a defined number of available materials. If a number N of materials is available, then a number n can be selected from these N materials, which are then combined as ingredients of the nutritional supplement, wherein N and n are integers greater than or equal to 1, and n is equal to or smaller than N. The materials can be represented by an index i that can take the values from 1 to N. The composition of a nutritional supplement can be represented by a number of n vectors (a set of vectors), each vector representing one material which is an ingredient of the nutritional supplement. If the material with index i is used as an ingredient in the nutritional supplement, there is a vector for which the components of this vector are assigned the value 0 except for the zthcomponent, which is assigned a value of 1.

[0103] In an analogous way, one-hot encodings can be used for other categorical variables.

[0104] The amount (quantity) of each ingredient can be encoded by another dimension added to the set of vectors. For example, the amount can be specified in terms of weight percent, volume percent, mole percent, concentration or some other form.

[0105] One or more ingredients of a vitamin supplement can also be represented by molecular graph(s). A molecular graph is a representation of the structural formula of a chemical compound in terms of graph theory. A molecular graph can be a labeled graph whose vertices correspond to the atoms of the compound and edges correspond to chemical bonds. Its vertices can be labeled with the kinds of the corresponding atoms and edges can be labeled with the types of bonds.

[0106] Molecular graphs can be represented by strings. Examples of graphs in the form of strings are SMILES, InChi or WLN representations. The simplified molecular-input line-entry system (SMILES) is a specification in the form of a line notation for describing the structure of chemical species using short ASCII strings. The IUPAC International Chemical Identifier (InChi) is a textual identifier for chemical substances. Wiswesser line notation (WLN) was one of the first line notations capable of precisely describing complex molecules.

[0107] Molecular graphs can also be represented by matrices, such as an adjacence matrix.

[0108] Another possibility to represent the molecular structure of ingredients is offered, for example, by the Chemical Markup Language. Chemical Markup Language (CML) is an approach to managing molecular information using tools such as XML (Extended Markup Language) and Java.

[0109] Ingredients of a vitamin supplement can also be represented by (molecular) fingerprints, such as Morgan fingerprint, also known as extended-connectivity fingerprint ECFP4, MinHashed fingerprint MHFP6, MAP4, RDKit AP, Molecular ACCess Systems keys fingerprint (MACCS), and PubChem Fingerprints (PubChemFP), AtomPairs2DFingerprint (APFP), GraphOnlyFingerprint (GraphFP), Natural Compound Molecular Fingerprint (NC-MFP) and / or others (see, e.g., A. Capecchi et al.: One molecular fngerprint to rule them all: drugs, biomolecules, and the metabolome, J Cheminform, 2020, 12:43; M. Seo et al.: Development of Natural Compound Molecular Fingerprint (NC-MFP) with the Dictionary of Natural Products (DNP) for natural product-based drug development, J Cheminform, 2020, 12:6).

[0110] In addition to the compositional information, further information can be used to specify vitamin supplements. That is, further information about the reference vitamin supplements can be used as further input data to train the machine learning model, and further information about the candidate vitamin supplement can be used to predict temporal stability for one or more ingredients of the candidate vitamin supplement using the trained machine learning model.

[0111] Such further information can be, for example, physical and / or chemical properties of one or more ingredients and / or of the respective vitamin supplement. Such physical and / or chemical properties can be, for example, molecular weight, water solubility, partition coefficient (e.g., for octanol / water), melting point (e.g., at standard conditions), proportion of polar / apolar functional groups, pKa / pKb values, pH of the vitamin supplement and / or an ingredient in an aqueous solution and / or other / further physical and / or chemical properties.

[0112] The physical and / or chemical properties can be measured values. The physical and / or chemical properties can be read from one or more databases and / or determined from the literature. Examples of databases that store physical and / or chemical properties include PubChem (https: / / pubchem.ncbi.nlm.nih.gov / ), NIST Chemistry WebBook (https: / / webbook.nist.gov / chemistry / ), and CRC Handbook of Chemistry and Physics (https: / / hbcp.chemnetbase.com / ). The physical and / or chemical properties can be determined experimentally. The physical and / or chemical properties may be calculated values. For example, the physical and / or chemical properties can be calculated based on the molecular structure of an ingredient. There are numerous methods for calculating physical and / or chemical properties based on molecular structure. These can be found in the literature under the name QSPR (Quantitative Structure Property Relationship), among others. There are also commercially and freely available computer programs for calculating physical and / or chemical properties of substances based on their molecular structure (e.g..: QSAR-Co: J. Chem. Inf. Model. 2019, 59, 6, 2538-2544; Molgen-QSPR: https: / / www.researchgate.net / publication / 266470632; RDKit: https: / / www.rdkit.org).

[0113] For example, a procedure for calculating the decadic logarithm of the partition coefficient for n- octanol / water is described in: A. J. Leo: Calculating log Poct from structures, Chem. Rev. 1993, 93, 4, 1281-1306. A method for calculating the melting point is described, for example, in: H. Modarresi et al:. QSPR Correlation of Melting Point for Drug Compounds Based on Different Sources of Molecular Descriptors, J. Chem. Inf. Model. 2006, 46, 2, 930-936. For example, a method for calculating aqueous solubility is described in: N. Meftahi et al. : Predicting aqueous solubility by QSPR modeling, Journal of Molecular Graphics and Modelling, Volume 106, July 2021, 107901. Additional methods for calculating physical and / or chemical properties can be found in: A.R. Katritzky et al QSPR as a means of predicting and understanding chemical and physical properties in terms of structure, Pure and Applied Chemistry 69(2):245-248).

[0114] It is also possible to represent one or more ingredients of a vitamin supplement (e.g., solely) by their physical and / or chemical properties. For example, instead of a name in the form of a categorical variable, instead of a one-hot encoding, instead of a graph, and / or instead of a molecular fingerprint, it is possible to represent one or more ingredients of a vitamin supplement by its physical and / or chemical properties.

[0115] Further information used for training and prediction can be, for example, information about the dosage form of the vitamin supplement. For example, it may be specified whether the vitamin supplement is in the form of tablets, lozenges, capsules (soft capsule, hard capsule), granules, powder, gel, suspension, crystal suspension, emulsion, solution, syrup, juice, concentrate, Effervescent or in another form.

[0116] Further information used for training and prediction can be, for example, information about the packaging of the vitamin supplement. For example, it may be specified whether the vitamin supplement is contained in a bottle or in a bag or in a blister or in a tube or in a pouch or in another packaging. The material of the packaging may be specified, in particular the material of the packaging that comes into contact with the vitamin supplement. Typical packaging materials are polyethylene (e.g., high density polyethylene (HDPE)), polypropylene (PP), polyester (e.g., polyethylene terephthalate (PET)), glass, aluminum. Further information about the packaging may be specified, such as opening size (e.g., in case of bottles), volume, color (e.g., in case of transparent packaging), blister thickness, closure (e.g., foil, cap) and / or others.

[0117] It is also possible that the further information will include information on the conditions under which the vitamin supplement is stored. Storage conditions may include temperature, humidity, barometric pressure, and / or intensity of electromagnetic radiation (e.g., of a certain wavelength or a range of wavelengths). The values can be mean values (e.g., arithmetically averaged values over a defined period of time, e.g., one day) and / or maximum values and / or minimum values.

[0118] It is also possible that the machine learning model is trained to predict temporal stability under certain (invariant) conditions, e.g., standard conditions. In such a case, the trained machine learning model is able to predict the temporal stability of one or more ingredients of a vitamin supplement under consideration for these defined conditions only. These defined conditions are then reflected in the target data. However, if the machine learning model is to be trained to predict temporal stability under different conditions, training data for different conditions must also be available, and the model must be told by the appropriate input data for which conditions to make a prediction. Of course, a trained machine learning model can also be used to predict scenarios that are not covered by the training data; however, in such a case, the less the prediction scenario matches the scenarios of the training data, the lower the prediction quality will usually be.

[0119] “Standard conditions” are sets of conditions for experimental measurements that allow comparisons to be made between different sets of data. The most used standards are those of the International Union of Pure and Applied Chemistry (IUPAC) and the National Institute of Standards and Technology (NIST). Other organizations have established a variety of alternative definitions for their standard reference conditions.

[0120] In chemistry, IUPAC defined standard temperature as a temperature of 273.15 K (0° C, 32° F) and standard pressure as a pressure of 1 bar (100 kPa).

[0121] Standard conditions may also be the storage conditions as described in the ICH (International Council for Harmonisation) guidelines, such as 25°C / 60% relative humidity or 30°C / 65% relative humidity or 40°C / 75% relative humidity.

[0122] It is possible that the input data is aggregated and / or scaled and / or otherwise pre-processed before being fed to the (trained and / or untrained) machine learning model.

[0123] It is possible to perform dimensional reduction of input data, e.g., using a principal component analysis and / or uniform manifold approximation and projection and / or other / further techniques (see, e.g.: U. Mclnnes et al. : UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction, arXiv: 1802.03426v3, 2020).

[0124] It is also possible to combine input data and use the combined data as input data together with the original data or instead of the original data.

[0125] Preprocessing steps can also be performed in whole or in part by the machine learning model and may have trainable parameters.

[0126] In addition to the aforementioned input data, target data is also required to train the machine learning model. The target data includes, for each reference vitamin supplement of the plurality of reference vitamin supplement, a temporal stability. The target data represents what the machine learning model should learn. Preferably, therefore, the target data comprise a degradation curve of one or more ingredients of each reference multitude under defined conditions as the temporal stability.

[0127] The temporal stability of the reference vitamin supplements is usually measured data. It is possible that a reference vitamin supplement is stored under the defined conditions for a defined period of time or for several defined periods of time. After a defined period of time has elapsed, a sample of the reference vitamin supplement may be analyzed. It is possible to examine for one or for several ingredients how much of the amount originally contained in the reference vitamin supplement is still present. Such investigations are known to the person skilled in the art of analytics and are described in the state of the art (see, e.g., I. Pencheva et al. : Analysis of water-soluble vitamins in supplement mixtures byHPLC / UV, Pharmacia 61, 2014, pages 3-8; C. J. Bates: Vitamin analysis, Ann Clin Biochem 34, 1997, 599-626; A. Mateeva et al. '. Simultaneous analysis of water-soluble and fat-soluble vitamins through RP- HPLC / DAD in food supplements and brewer’s yeast, Heliyon, Volume 9, Issue 1, 2023, el2706,).

[0128] Measured data may be pre-processed before being used as training data. Pre-processing of measured data includes, for example, scaling to relative amounts as an alternative to absolute amounts.

[0129] The process of training the machine learning model is exemplarily and schematically shown in Fig.l. The machine learning model MUM is trained on training data TD. The training data TD comprises, for each reference vitamin supplement of a plurality of reference vitamin supplements, (i) compositional information CIRof the reference vitamin supplement, and (ii) information TSRabout the temporal stability of one or more ingredients of the reference vitamin supplement. In Fig. 1, only one data set of one reference vitamin supplement is shown.

[0130] The compositional information CIRis used as input data. The information TSRabout the temporal stability is used as target data. The training data TD further comprises further data FIR. The further data FIRis also used as input data. As described herein, the further data FIRcan be information about physical and / or chemical properties of one or more ingredients of the reference vitamin supplement, information about the type of composition, information about the dosage form, information about the packaging and / or information about the conditions under which the temporal stability of the reference vitamin supplement was determined.

[0131] In the example shown in Fig. 1 , the information TSRabout the temporal stability comprises a degradation curve of one ingredient of the reference vitamin supplement. The degradation curve indicates the quantity Q of the ingredient as a function of time t.

[0132] The compositional information CIRand further information FIRis input into the machine learning model MLM.

[0133] The machine learning model MLM is configured to determine a predicted temporal stability TSR* based on the input data and based on model parameters MP.

[0134] The predicted temporal stability TSR* is compared with the target data, i.e., the information TSRabout the temporal stability of the respective ingredient of the reference vitamin supplement. Deviations between the predicted temporal stability TSR* and the temporal stability TSRof the target data TD can be quantified using a loss function or a scoring rule LF. The deviations can be minimized by modifying the model parameters in an optimization procedure such as a gradient descent procedure or any other optimization procedure as described herein.

[0135] The process shown in Fig. 1 is performed one or more times for all data sets of the plurality of reference vitamin supplements. The training can be terminated if one or more stop criteria are met.

[0136] Such stop criteria can be for example: a predefined maximum number of training steps has been performed, the deviations can no longer be reduced by modifying model parameters MP, a predefined minimum of the loss function or scoring rule LF is reached, and / or an extreme value of another performance value is reached. The trained machine learning model may be stored in a data memory and / or transmitted to a separate computer system and / or used to predict the temporal stability of one or more ingredients of a candidate vitamin supplement.

[0137] Fig. 2 shows an example of the method of training the machine learning model in form of a flowchart.

[0138] The training method (100) comprises the steps:

[0139] (110) providing training data, the training data comprising, for each reference vitamin supplement of a plurality of reference vitamin supplements, (i) input data and (ii) target data, the input data comprising compositional information of the reference vitamin supplement, and the target data comprising a temporal stability of one or more ingredients of the reference vitamin supplement,

[0140] (120) providing a machine learning model, wherein the trained machine learning model is a probabilistic prediction model, wherein the machine learning model is configured to determine a predicted temporal stability of one or more ingredients of a reference vitamin supplement based on the input data and based on model parameters, wherein the predicted temporal stability comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur,

[0141] (130) training the machine learning model, wherein the training of the machine learning model comprises: for each reference vitamin supplement:

[0142] (131) inputting the input data into the machine learning model,

[0143] (132) receiving a predicted temporal stability of the one or more ingredients of the reference vitamin supplement from the machine learning model, wherein the predicted temporal stability comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur,

[0144] (134) quantifying deviations between the predicted temporal stability and the target data,

[0145] (133) reducing the deviations by modifying model parameters,

[0146] (140) storing the trained machine learning model and / or outputting the trained machine learning model and / or using the trained machine learning model for predicting a temporal stability of one or more ingredients of a candidate vitamin supplement.

[0147] The use of the trained machine learning model for prediction is exemplified and schematically shown in Fig. 3. The trained machine learning model MLMTis fed with composition information CIcand further information FICof a candidate vitamin supplement. The trained machine learning model MLMTmay have been trained as described with reference to Fig. 1 and / or Fig. 2.

[0148] The candidate vitamin supplement may be a vitamin supplement that has a different composition than the reference vitamin supplements and / or is packaged in a different form and / or is in a different dosage form and / or has been tested for stability over time under different conditions and / or differs from the reference vitamin supplements in one or more other respects.

[0149] The trained machine learning model MLMTis configured and trained to predict and output a predicted temporal stability TSC* of one or more ingredients of the candidate vitamin supplement based on the input data. The predicted temporal stability TSC* comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur.

[0150] The predicted temporal stability TSC* can be outputted (e.g., displayed on a monitor and / or printed by a printing device) and / or stored in a data memory and / or transmitted to a separate computer system.

[0151] It is possible that the prediction results will be confirmed experimentally.

[0152] Fig. 4 shows an embodiment of the computer-implemented method of the present disclosure in form of a flowchart.

[0153] The method (200) comprises the steps:

[0154] (210) providing a trained machine learning model, o wherein the trained machine learning model is a probabilistic prediction model, o wherein the trained machine learning model is configured to determine a temporal stability of one or more ingredients of a vitamin supplement based on compositional information of the vitamin supplement and based on model parameters, wherein the temporal stability comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur, o wherein the machine learning model has been trained in an at least semi-supervised learning process using training data, the training data comprising, for each reference vitamin supplement of a plurality of reference vitamin supplements, (i) compositional information of the reference vitamin supplement as input data, and (ii) information on the temporal stability of one or more ingredients of the reference vitamin supplement as target data, o wherein the training of the machine learning model comprises:

[0155] ■ inputting the input data into the machine learning model,

[0156] ■ receiving a predicted temporal stability of the one or more ingredients of the reference vitamin supplement from the machine learning model,

[0157] ■ reducing deviations between the predicted temporal stability or the predicted temporal stability distribution and the target data, (220) receiving compositional information of a candidate vitamin supplement,

[0158] (230) inputting the received compositional information into the trained machine learning model,

[0159] (240) receiving a predicted temporal stability of one or more ingredients of the candidate vitamin supplement from the trained machine learning model, wherein the predicted temporal stability comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur,

[0160] (250) outputting the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement and / or storing the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement in a data memory and / or transmitting the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement to a separate computer system.

[0161] The machine learning model can be or comprise an artificial neural network, for example.

[0162] An “artificial neural network” (ANN) is a biologically inspired computational model. An ANN usually comprises at least three layers of processing elements: a first layer with input neurons (nodes), a kthlayer with at least one output neuron (node), and k-2 inner layers, where k is a natural number greater than 2.

[0163] In such a network, the input neurons serve to receive the input data. If the input data constitute or comprise an w-dimcnsional vector (e.g., a feature vector), with n being an integer equal to or greater than 1, there is usually one input neuron for each component of the vector. The output neurons serve to output at least one value (e.g., a temporal stability of one ingredient after storage over one period time). The processing elements of the layers are interconnected in a predetermined pattern with predetermined connection weights therebetween. Each network node represents a pre-defined calculation of the weighted sum of inputs from prior nodes and a non-linear output function. The combined calculation of the network nodes relates the inputs to the outputs.

[0164] When trained, the connection weights between the processing elements in the ANN contain information regarding the relationship between the input data and the output data which can be used to predict new output data from new input data.

[0165] Training estimates network weights that allow the network to calculate output values close to the target values. The network weights can be initialized with small random values or with the weights of a prior trained network. The training data inputs are applied to the network and the output values are calculated for each training sample. The network output values are compared to the target values. A backpropagation algorithm can be applied to correct the weight values in directions that reduce the error between targeted and calculated outputs. The process is iterated until one or more stop criteria are met, e.g., until no further reduction in error can be made or until a predefined prediction accuracy has been reached.

[0166] A cross-validation method can be employed to split the data into training and hold-out data sets. The training data set is used in the backpropagation training of the network weights. The hold-out data set is used to verify that the trained network generalizes to make good predictions. The best network weight set can be taken as the one that best predicts the outputs of the hold-out data.

[0167] Such cross-validation can also be used for training other machine learning models and is not limited to ANNs.

[0168] Hyperparameters of the machine learning model can also be optimized. Hyperparameters are, for example, in the case of ANNs: the number of network hidden nodes, learning rate, number of epochs, and or others.

[0169] The machine learning model can be or comprise a gradient boosted model, such as a gradient boosted tree model. “Gradient boosting” is a machine learning technique used in regression and classification tasks, among others. It gives a prediction model in the form of an ensemble of weak prediction models, which are typically decision trees. When a decision tree is the weak learner, the resulting algorithm is called gradient-boosted trees. A gradient-boosted trees model is built in a stage-wise fashion as in other boosting methods, but it generalizes the other methods by allowing optimization of an arbitrary differentiable loss function.

[0170] Gradient Boosting is a powerful boosting algorithm that combines several weak learners into strong learners, in which each new model is trained to minimize the loss function such as mean squared error or cross-entropy of the previous model using gradient descent. In each iteration, the algorithm computes the gradient of the loss function with respect to the predictions of the current ensemble and then trains a new weak model to minimize this gradient. The predictions of the new model are then added to the ensemble, and the process is repeated until a stopping criterion is met.

[0171] The gradient boosted model can be an extreme Gradient Boosting (XGBoost) model as described, e.g., in: T. Chen, C. Guestrin: XGBoost: A Scalable Tree Boosting System, arXiv: 1603.02754v3) or it can be a LightGBM model as described, e.g., in: G. Ke et al. '. LightGBM: A Highly Efficient Gradient Boosting, Advances in Neural Information Processing Systems 30 (NIPS 2017) or any other gradient boosted model.

[0172] Natural Gradient Boosting (NGBoost) algorithm enables predictive uncertainty estimation with Gradient Boosting through probabilistic predictions. The NGBoost algorithm is a supervised learning procedure that uses gradient boosting to estimate the parameters of a conditional probability distribution as a function of the input data. In other words: the NGBoost algorithm generalizes gradient boosting to predicting conditional distributions.

[0173] Details of the NGBoost algorithm can be found in the prior art (see, e.g., T. Duan et al. '. NGBoost: Natural Gradient Boosting for Probabilistic Prediction, arXiv: 1910.03225v4).

[0174] Another example of a probabilistic prediction model is xgboost-distribution (see, e.g., https: / / github.com / CDonnerer / xgboost-distribution).

[0175] Another example of a probabilistic prediction model is a quantile regression model (see, e.g., R. Koenker and K.F. Hallock: Quantile Regression, Journal of Economic Perspectives, Volume 15, Number 4, 2001, 143-156; Y. Romano et al.: Conformalized Quantile Regression, 2019, arXiv: 1905.03222).

[0176] The probabilistic prediction model can also be a Bayesian neural network (see, e.g., D. J. C. MacKay: Bayesian neural networks and density networks, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 1995, Vol 354 (1), 73- 80) or any other Bayesian model, such as a Gaussian process.

[0177] There are also several methods by which “non-probabilistic models” can be made probabilistic.

[0178] So, another example of a probabilistic prediction model is an ensemble of multiple machine learning models, such as a bootstrap ensemble (e.g., a random forest ensemble), a cross validation ensemble, a stacked ensemble, or a combination of such machine learning models or any other ensemble (see, e.g., Z.-H. Zhou: Ensemble Methods, Chapman and Hall / CRC 2012, ISBN: 9780429151095; M. N. Wright, A. Ziegler: ranger: A Fast Implementation of Random Forests for High Dimensional Data in C+ + and R, 2018, arXiv: 1508.04409v2).

[0179] In case the machine learning model is or comprises an artificial neural network, Monte-Carlo dropout may be used to generate an ensemble of multiple machine learning models (see, e.g., Y. Gal, Z. Ghahramani: Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning, 2016, arXiv: 1506.02142v6).

[0180] In case the machine learning model is or comprises an artificial neural network, different initializations can be used to generate an ensemble, (see, e.g., T. Pearce et al.: High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach, Proceedings of the 35th International Conference on Machine Learning, PMLR 80:4075-4084, 2018).

[0181] If for instance, Markov-Chain Monte-Carlo, variational inference (see, e.g., A. Kucukelbir et al:. Automatic Differentiation Variational Inference , Journal of Machine Learning Research 18, 2017, 1-45) or the Laplace approximation (see, e.g., https: / / mc-stan.org / docs / reference-manual / laplace- approximation.html) is applicate to a maximum-likelihood estimator, the model can be made a probabilistic model.

[0182] The probabilistic prediction model may be a generalized additive model (see, e.g., S. N. Wood: Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models , Journal of the American Statistical Association, Vol. 99, No. 467, 2004, 673-686).

[0183] The probabilistic prediction model may be a distributional forests model (see, e.g.: L. Schlosser et al. : Distributional regression forests for probabilistic precipitation forecasting in complex terrain, Ann. Appl. Stat. 13(3), 2019, 1564-1589).

[0184] In addition to an expected value for the temporal stability of one or more ingredients of the candidate vitamin supplement, the machine learning model of the present disclosure may be used to determine a prediction interval around the expected value. As shown in Fig. 1 and Fig. 3, the output of the machine learning model can be a degradation curve with quantiles (dashed lines) specified in addition to the point estimates (solid line). The quantiles can be, e.g., the 25% quantile and the 75% quantile, or the 5% quantile and the 95% quantile, or any other statistical quantity.

[0185] The means described in this disclosure allow acceleration of the development of new vitamin supplements. Before a new vitamin supplement (e.g., the candidate vitamin supplement) is subjected to lengthy and expensive storage stability studies, temporal stability can be predicted for one or more ingredients. In addition to the expected temporal stability, a prediction interval around the expected value can also be determined. If the lower prediction bound is above the threshold, the formulation is considered stable. If the upper prediction interval bound is below the threshold, the formulation can be considered unstable. If the threshold cuts either bound, validation experiments are required.

[0186] Threshold values can be determined empirically and / or by experts.

[0187] The operations in accordance with the teachings herein may be performed by at least one computer system specially constructed for the desired purposes or general-purpose computer system specially configured for the desired purpose by at least one computer program stored in a typically non-transitory computer readable storage medium.

[0188] A “computer system” is a system for electronic data processing that processes data by means of programmable calculation rules. Such a system usually comprises a “computer”, that unit which comprises a processor for carrying out logical operations, and also peripherals.

[0189] In computer technology, “peripherals” refer to all devices which are connected to the computer and serve for the control of the computer and / or as input and output devices. Examples thereof are monitor (screen), printer, scanner, mouse, keyboard, drives, camera, microphone, loudspeaker, etc. Internal ports and expansion cards are, too, considered to be peripherals in computer technology.

[0190] Computer systems of today are frequently divided into desktop PCs, portable PCs, laptops, notebooks, netbooks and tablet PCs and so-called handhelds (e.g. smartphone); all these systems can be utilized for carrying out the invention.

[0191] The term “non-transitory” is used herein to exclude transitory, propagating signals or waves, but to otherwise include any volatile or non-volatile computer memory technology suitable to the application.

[0192] The term “computer” should be broadly construed to cover any kind of electronic device with data processing capabilities, including, by way of non-limiting example, personal computers, servers, embedded cores, computing system, communication devices, processors (e.g., digital signal processor (DSP)), microcontrollers, field programmable gate array (FPGA), application specific integrated circuit (ASIC), etc.) and other electronic computing devices.

[0193] The term “process” as used above is intended to include any type of computation or manipulation or transformation of data represented as physical, e.g., electronic, phenomena which may occur or reside e.g., within registers and / or memories of at least one computer or processor. The term processor includes a single processing unit or a plurality of distributed or remote such units.

[0194] Fig. 5 illustrates a computer system (1) according to some example implementations of the present disclosure in more detail.

[0195] Generally, a computer system of exemplary implementations of the present disclosure may be referred to as a computer and may comprise, include, or be embodied in one or more fixed or portable electronic devices. The computer may include one or more of each of a number of components such as, for example, a processing unit (20) connected to a memory (50) (e.g., storage device).

[0196] The processing unit (20) may be composed of one or more processors alone or in combination with one or more memories. The processing unit (20) is generally any piece of computer hardware that is capable of processing information such as, for example, data, computer programs and / or other suitable electronic information. The processing unit (20) is composed of a collection of electronic circuits some of which may be packaged as an integrated circuit or multiple interconnected integrated circuits (an integrated circuit at times more commonly referred to as a “chip”). The processing unit (20) may be configured to execute computer programs, which may be stored onboard the processing unit (20) or otherwise stored in the memory (50) of the same or another computer.

[0197] The processing unit (20) may be a number of processors, a multi-core processor or some other type of processor, depending on the particular implementation. For example, it may be a central processing unit (CPU), a field programmable gate array (FPGA), a graphics processing unit (GPU) and / or a tensor processing unit (TPU). Further, the processing unit (20) may be implemented using a number of heterogeneous processor systems in which a main processor is present with one or more secondary processors on a single chip. As another illustrative example, the processing unit (20) may be a symmetric multi -processor system containing multiple processors of the same type. In yet another example, the processing unit (20) may be embodied as or otherwise include one or more ASICs, FPGAs or the like. Thus, although the processing unit (20) may be capable of executing a computer program to perform one or more functions, the processing unit (20) of various examples may be capable of performing one or more functions without the aid of a computer program. In either instance, the processing unit (20) may be appropriately programmed to perform functions or operations according to example implementations of the present disclosure.

[0198] The memory (50) is generally any piece of computer hardware that is capable of storing information such as, for example, data, computer programs (e.g., computer-readable program code (60)) and / or other suitable information either on a temporary basis and / or a permanent basis. The memory (50) may include volatile and / or non-volatile memory, and may be fixed or removable. Examples of suitable memory include random access memory (RAM), read-only memory (ROM), a hard drive, a flash memory, a thumb drive, a removable computer diskette, an optical disk, a magnetic tape or some combination of the above. Optical disks may include compact disk - read only memory (CD-ROM), compact disk - read / write (CD-R / W), DVD, Blu-ray disk or the like. In various instances, the memory may be referred to as a computer-readable storage medium or data memory. The computer-readable storage medium is a non-transitory device capable of storing information, and is distinguishable from computer-readable transmission media such as electronic transitory signals capable of carrying information from one location to another. Computer-readable medium as described herein may generally refer to a computer- readable storage medium or computer-readable transmission medium.

[0199] In addition to the memory (50), the processing unit (20) may also be connected to one or more interfaces for displaying, transmitting and / or receiving information. The interfaces may include one or more communications interfaces and / or one or more user interfaces. The communications interface(s) may be configured to transmit and / or receive information, such as to and / or from other computer(s), network(s), database(s) or the like. The communications interface may be configured to transmit and / or receive information by physical (wired) and / or wireless communications links. The communications interface(s) may include interface(s) (41) to connect to a network, such as using technologies such as cellular telephone, Wi-Fi, satellite, cable, digital subscriber line (DSL), fiber optics and the like. In some examples, the communications interface(s) may include one or more short-range communications interfaces (42) configured to connect devices using short-range communications technologies such as NFC, RFID, Bluetooth, Bluetooth LE, ZigBee, infrared (e.g., IrDA) or the like.

[0200] The user interfaces may include a display (30). The display (screen) may be configured to present or otherwise display information to a user, suitable examples of which include a liquid crystal display (LCD), light-emitting diode display (LED), plasma display panel (PDP) or the like. The user input interface(s) (11) may be wired or wireless, and may be configured to receive information from a user into the computer system (1), such as for processing, storage and / or display. Suitable examples of user input interfaces include a microphone, image or video capture device, keyboard or keypad, joystick, touch-sensitive surface (separate from or integrated into a touchscreen) or the like. In some examples, the user interfaces may include automatic identification and data capture (AIDC) technology (12) for machine-readable information. This may include barcode, radio frequency identification (RFID), magnetic stripes, optical character recognition (OCR), integrated circuit card (ICC), and the like. The user interfaces may further include one or more interfaces for communicating with peripherals such as printers and the like.

[0201] As indicated above, program code instructions (60) may be stored in memory (50), and executed by processing unit (20) that is thereby programmed, to implement functions of the systems, subsystems, tools and their respective elements described herein. As will be appreciated, any suitable program code instructions (60) may be loaded onto a computer or other programmable apparatus from a computer- readable storage medium to produce a particular machine, such that the particular machine becomes a means for implementing the functions specified herein. These program code instructions (60) may also be stored in a computer-readable storage medium that can direct a computer, processing unit or other programmable apparatus to function in a particular manner to thereby generate a particular machine or particular article of manufacture. The instructions stored in the computer-readable storage medium may produce an article of manufacture, where the article of manufacture becomes a means for implementing functions described herein. The program code instructions (60) may be retrieved from a computer- readable storage medium and loaded into a computer, processing unit or other programmable apparatus to configure the computer, processing unit or other programmable apparatus to execute operations to be performed on or by the computer, processing unit or other programmable apparatus.

[0202] Retrieval, loading and execution of the program code instructions (60) may be performed sequentially such that one instruction is retrieved, loaded and executed at a time. In some example implementations, retrieval, loading and / or execution may be performed in parallel such that multiple instructions are retrieved, loaded, and / or executed together. Execution of the program code instructions (60) may produce a computer-implemented process such that the instructions executed by the computer, processing circuitry or other programmable apparatus provide operations for implementing functions described herein.

[0203] Execution of instructions by processing unit, or storage of instructions in a computer-readable storage medium, supports combinations of operations for performing the specified functions. In this manner, a computer system (1) may include processing unit (20) and a computer-readable storage medium or memory (50) coupled to the processing circuitry, where the processing circuitry is configured to execute computer-readable program code instructions (60) stored in the memory (50). It will also be understood that one or more functions, and combinations of functions, may be implemented by special purpose hardware-based computer systems and / or processing circuitry which perform the specified functions, or combinations of special purpose hardware and program code instructions.

[0204] EXAMPLE A machine learning model was trained on training data. The machine learning model was a cross- validation ensemble of 10 NGBoost models. The training data comprised more than 270,000 measured stability data of 157 formulations that differ in their composition and galenic forms . Data on composition and information on galenic form were used as input data.

[0205] After training, the trained machine learning model was used for prediction. The temporal stability of biotin, folic acid, vitamin A, vitamin Bl, vitamin B12, vitamin B5, vitamin B6, vitamin C and vitamin E in a multivitamin formulation was predicted. The above ingredients were present in the following mass ratios:

[0206] Biotin : Folic Acid : Vitamin A : Vitamin Bl : Vitamin B12 : Vitamin B5 : Vitamin B6 : Vitamin C : Vitamin E4.0 : 24.4 : 86.7 : 79.2 : 1.0 : 938.1 : 214.1 : 3227.4 : 860.1 A film-coated tablet was chosen as the galenic form of the multivitamin formulation. The following storage conditions were chosen for the prediction: relative humidity: 60%, temperature: 25°C. The following time periods were chosen: 6 months, 12 months, 18 months, 22 months.

[0207] Fig. 6 shows in a graphical representation the measured and the predicted percentage amount of the mentioned ingredients as a function of time. The time 0 indicates the quantity originally present in the formulation (100%). The measured values are represented by circles. The solid line reflects the predicted median value. The shaded area indicates the predicted 2.5% percentile and the predicted 97.5% percentile.

[0208] The trained machine learning model was able to predict the measured values very well.

Claims

CLAIMS1. A computer-implemented method comprising: providing a trained machine learning model, o wherein the trained machine learning model is a probabilistic prediction model, o wherein the trained machine learning model is configured to determine a temporal stability of one or more ingredients of a vitamin supplement based on compositional information of the vitamin supplement and based on model parameters, wherein the temporal stability comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur, o wherein the machine learning model has been trained in a supervised learning process using training data, the training data comprising, for each reference vitamin supplement of a plurality of reference vitamin supplements, (i) compositional information of the reference vitamin supplement as input data, and (ii) information on the temporal stability of one or more ingredients of the reference vitamin supplement as target data, o wherein the training of the machine learning model comprises:■ inputting the input data into the machine learning model,■ receiving a predicted temporal stability of the one or more ingredients of the reference vitamin supplement from the machine learning model,■ reducing deviations between the predicted temporal stability and the target data, receiving compositional information of a candidate vitamin supplement, inputting the received compositional information into the trained machine learning model, receiving a predicted temporal stability for one or more ingredients of the candidate vitamin supplement from the trained machine learning model, wherein the predicted temporal stability comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur, outputting the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement and / or storing the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement in a data memory and / or transmitting the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement to a separate computer system.

2. The method of claim 1, wherein the temporal stability of one or more ingredients of each reference vitamin supplement and / or the candidate vitamin supplement comprises an information about an amount of an ingredient that is present in the respective vitamin supplement after a predefined storage time under predefined storage conditions.

3. The method of claim 1 or 2, wherein the temporal stability of one or more ingredients of the reference vitamin supplement comprises degradation data of an ingredient of the reference vitamin supplement as a function of time.

4. The method of claim 3, wherein the predicted temporal stability comprises a predicted degradation curve of an ingredient of the candidate vitamin supplement.

5. The method of any one of claims 1 to 4, wherein the predicted temporal stability comprises a probability distribution of an amount of an ingredient present in the candidate vitamin supplement after a predefined storage time under predefined storage conditions.

6. The method of any one of claims 1 to 5, wherein the predicted temporal stability comprises the expected value of the temporal stability and a prediction interval around the expected value.

7. The method of any one of claims 1 to 6, wherein the predicted temporal stability comprises a degradation curve with quantiles.

8. The method of any one of claims 1 to 7, wherein the target data is measured data.

9. The method of any one of claims 1 to 8, wherein the compositional information comprises information about the ingredients contained in the candidate vitamin supplement and each reference vitamin supplement, and their respective amounts.

10. The method of any one of claims 1 to 9, wherein one or more ingredients are represented in the compositional information by molecular graphs and / or molecular fingerprints and / or by their physical and / or chemical properties.

11. The method of any one of claims 1 to 10, wherein the input data comprises further information, wherein the further information comprises: physical and / chemical properties of one or more ingredients, physical and / or chemical properties of the vitamin supplement, information about the dosage form of the vitamin supplement, information about the packaging of the vitamin supplement, and / or information about storage conditions under which the vitamin supplement is stored.

12. The method of any one of claims 10 or 11, wherein the physical and / or chemical properties comprises measured and / or calculated data.

13. The method of any one of claims 1 to 12, wherein the candidate vitamin supplement and each reference vitamin supplement comprises more than one vitamin.

14. The method of claim 13, wherein the temporal stability of one or more ingredients comprises a temporal stability of each vitamin.

15. The method of any one of claims 1 to 14, wherein the machine learning model is a probabilistic regression model.

16. The method of any one of claims 1 to 14, wherein the machine learning model is an ensemble of multiple machine learning models.

17. The method of any one of claims 1 to 14, wherein the machine learning model is or comprises a gradient boosted model.

18. The method of any one of claims 1 to 14, wherein the machine learning model is or comprise a quantile regression model.

19. The method of any one of claims 1 to 14, wherein the machine learning model is or comprises an artificial neural network.

20. A computer system comprising: a processor; and a memory storing an application program configured to perform, when executed by the processor, an operation, the operation comprising: providing a trained machine learning model, o wherein the trained machine learning model is a probabilistic prediction model, o wherein the trained machine learning model is configured to determine a temporal stability of one or more ingredients of a vitamin supplement based on compositional information of the vitamin supplement and based on model parameters, wherein thetemporal stability comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur, o wherein the machine learning model has been trained in a supervised learning process using training data, the training data comprising, for each reference vitamin supplement of a plurality of reference vitamin supplements, (i) compositional information of the reference vitamin supplement as input data, and (ii) information on the temporal stability of one or more ingredients of the reference vitamin supplement as target data, o wherein the training of the machine learning model comprises:■ inputting the input data into the machine learning model,■ receiving a predicted temporal stability of the one or more ingredients of the reference vitamin supplement from the machine learning model,■ reducing deviations between the predicted temporal stability and the target data, receiving compositional information of a candidate vitamin supplement, inputting the received compositional information into the trained machine learning model, receiving a predicted temporal stability for one or more ingredients of the candidate vitamin supplement from the trained machine learning model, wherein the predicted temporal stability comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur, outputting the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement and / or storing the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement in a data memory and / or transmitting the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement to a separate computer system.

21. A non-transitory computer readable storage medium having stored thereon software instructions that, when executed by a processor of a computer system, cause the computer system to execute the following steps: providing a trained machine learning model, o wherein the trained machine learning model is a probabilistic prediction model, o wherein the trained machine learning model is configured to determine a temporal stability of one or more ingredients of a vitamin supplement based on compositional information of the vitamin supplement and based on model parameters, wherein the temporal stability comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur, o wherein the machine learning model has been trained in a supervised learning process using training data, the training data comprising, for each reference vitamin supplement of a plurality of reference vitamin supplements, (i) compositional information of the reference vitamin supplement as input data, and (ii) information on the temporal stability of one or more ingredients of the reference vitamin supplement as target data, o wherein the training of the machine learning model comprises:■ inputting the input data into the machine learning model,■ receiving a predicted temporal stability of the one or more ingredients of the reference vitamin supplement from the machine learning model,■ reducing deviations between the predicted temporal stability and the target data, receiving compositional information of a candidate vitamin supplement, inputting the received compositional information into the trained machine learning model, receiving a predicted temporal stability for one or more ingredients of the candidate vitamin supplement from the trained machine learning model, wherein the predicted temporal stability comprises an expected temporal stability value and information about how likely it is that the expected temporal stability value will occur, outputting the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement and / or storing the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement in a data memory and / or transmitting the predicted temporal stability of the one or more ingredients of the candidate vitamin supplement to a separate computer system.

Images