Intelligent Agent for Guiding the Development of Composite Products

Abstract

The present disclosure is directed to systems and methods that enable an intelligent agent to optimize a black-box objective function over a sufficiently large search space. More particularly, the intelligent agent may be employed to provide guidance in the design, development, and / or formulation (or reformulation) of new (or existing) products. The intelligent agent provides guidance using machine learning and statistical techniques. A user and the intelligent agent may communicate via a "smart spreadsheet" enabled by embodiments.

Description

Technical Field

[0001] Priority Application This application claims the benefit of U.S. Provisional Patent Application No. 63 / 389,517, filed Jul. 15, 2022, the entire disclosure of which is incorporated herein by reference.

[0002] The present disclosure generally relates to the development of composite products. More specifically, the present disclosure relates to providing automated guidance and intelligent guidance to assist in the development of products manufactured by combining multiple components whose resulting properties are not known in advance.

Background Art

[0003] Many products such as food, beverages, cosmetics, fragrances, pharmaceuticals, etc. are manufactured by combining a "subset" of "components" from a set of available components in various relative ratios. Combining components in various ratios often results in synergistic effects, such that properties related to human perception (e.g., taste, flavor, smell, color, texture, viscosity, etc.) can often not be easily inferred from a "recipe" that describes the components and their relative ratios. Therefore, experts, artisans, and engineers tasked with developing new products often have to painstakingly create new recipes that satisfy the emerging styles, sensibilities, and preferences of the intended consumers while simultaneously accommodating market constraints such as manufacturing costs, dietary restrictions, and government regulations through trial-and-error based efforts.

[0004] Through such trial-and-error attempts, in some industries, "rules of thumb" and other heuristic mechanisms have emerged that provide some guidance when designing new products. However, with consumers continuing to demand novelty in products, rapidly changing market constraints (e.g., cost), and the continuous addition of additional components to the set of available components, the applicability of such heuristics may not be easily measurable.

Summary of the Invention

Means for Solving the Problem

[0005] Aspects and advantages of embodiments of the present disclosure are described in part in the following description, can be learned from the description, or can be learned by implementing the embodiments.

[0006] One exemplary aspect of the present disclosure is directed to a computer-implemented method for predicting mixture properties. The method may include receiving a representation of a set of potential formulations for a target product. Also, a representation of target values of a set of relevant properties of the target product may be received. An objective function may be generated over a first domain. The objective function may be associated with the set of relevant properties. The target values for the set of relevant properties may optimize the objective function over the first domain. A set of estimation functions may be determined. The set of estimation functions may enable estimation (e.g., its variance) of the objective function over a second domain. The second domain may be associated with the set of potential functions. Determining the set of estimation functions may be based on first characteristic data encoding values of the set of relevant properties. The values of the set of relevant properties encoded by the first characteristic data may be associated with a first subset of the set of potential formulations. The set of estimation functions may be iteratively updated based on additional characteristic data. The additional characteristic data may encode additional values for the set of relevant properties. The additional values for the set of relevant properties encoded by the additional characteristic data may be associated with an additional subset of the set of potential formulations. A target formulation can be selected from the set of potential formulations. Based on the updated set of estimation functions, the target formulation may substantially optimize the objective function over the second domain.

[0007] Another exemplary aspect of the present disclosure is directed to another computer-implemented method for predicting mixture properties. Other methods may include receiving, via a user interface (UI) provided by a computing system, first product data regarding the properties of a target product. The first property data may correspond to a first potential formulation of a set of potential formulations for the target product. A second potential formulation may be selected from the set of potential formulations. Selecting the target formulation may be based on processing a first evaluation of an objective function at the computing system. The objective function may be defined for the set of potential formulations. The objective function may be based on a target value of a property. The first evaluation of the objective function may be based on the first property data and may be associated with the first potential formulation. A second property of the properties of the target product may be received via the UI. The second property data may correspond to the second potential formulation. A second evaluation of the objective function may be processed at the computing system. The second evaluation of the objective function may be based on the second property data and may be associated with the second potential formulation. The target formulation may be from the set of potential formulations. Selecting the target formulation may be based on processing the second evaluation of the objective function. The target formulation may be provided via the UI.

[0008] Regardless of whether or not specifically and distinctly described herein as separate combinations, any two or more of the features described herein, including this summary section, can be combined to form embodiments of the present disclosure.

[0009] Other aspects of the present disclosure are directed to various systems, devices, non-transitory computer-readable media, user interfaces, and electronic devices.

[0010] These and other features, aspects, and advantages of the various embodiments of the present disclosure will be better understood with reference to the following description and the appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the present disclosure and, together with the description, serve to explain the relevant principles.

[0011] A detailed description of embodiments with reference to the accompanying drawings, directed to those skilled in the art, is set forth herein.

Brief Description of the Drawings

[0012]

Figure 1

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Figure 2

[0014]

Figure 3A

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Figure 3B

Modes for Carrying Out the Invention

[0016] Reference numerals repeated throughout the several figures are intended to identify the same features in various embodiments.

[0017] Summary Generally, the present disclosure is directed to systems and methods that enable an intelligent agent to optimize (e.g., minimize or maximize), at least approximately, a black-box objective function over a sufficiently large search space. More particularly, the intelligent agent can be used to provide guidance in the design, development, and / or formulation (or reformulation) of new (or existing) products. The product being formulated or reformulated can be referred to as a “target product”. The target product can be a composite product. Non-limiting examples of types of composite products include foodstuffs, foods, beverages, cosmetics, fragrances, pharmaceuticals, fuels, etc. Other non-limiting examples of types of composite products include consumer products such as pesticides, insect repellents, etc.

[0018] As discussed below, embodiments can model the formulation of a target product as a search problem over a high-dimensional (and sufficiently large) search space. Such a search space can be a vector space in which a set of potential formulation vectors encoding a set of potential formulations for the target product spans the vector space. A “search criterion” can be defined by an objective function to identify (within the search space) potential formulations that optimize, at least approximately, target values of a set of relevant characteristics of the target product. The search can be an interactive and iterative search over the space. The two-way nature of the search can be between the intelligent agent and a user (e.g., a stakeholder with an interest in the formulation of the target product). For each iteration of the search, the intelligent agent can provide guidance by knowingly recommending to the user a set of points in the search space to “experimentally sample”. The user can experimentally sample the recommended points and provide the experimental results to the intelligent agent. Based on the experimental results, the intelligent agent can recommend a next set of sampling points. This process can be repeated until the search converges to identify a point in the space (e.g., a point that optimizes, at least approximately, the objective function) that at least approximately satisfies the search criterion.

[0019] More specifically, the guidance provided by the intelligent agent may include iterative recommendations of one or more points sampled empirically (or experimentally) in the space of potential formulations. Sampling a point in the space of potential formulations may include manufacturing or creating a target prototype version corresponding to the sampling point (e.g., manufacturing a prototype product based on the potential formulation corresponding to the sampling point). Once the prototype product is manufactured, its unpredictable (and relevant) characteristics may be measured or observed empirically (or experimentally).

[0020] The process of manufacturing a prototype product through a potential formulation and empirically observing the value of its corresponding unpredictable (and relevant) characteristics may be referred to as an "experiment" regarding the potential formulation or an "experimental" observation of the corresponding potential formulation. The intelligent agent may empirically evaluate the objective function at each of the sampling points based on the empirically measured unpredictable characteristics and any predictable characteristics of interest (e.g., relevant characteristics). The space of potential formulations (e.g., the search space) may sometimes be simply referred to as the "formulation space" or the "space of formulations". A vector in the formulation space may be referred to as a "potential formulation vector" or simply a "formulation vector".

[0021] As with other search problems, an objective function is used to quantify how well a particular point in the search space meets the objectives of the search criteria. For embodiments, the search criteria can include values of relevant characteristics associated with responses from potential formulations that match (as closely as possible) the target values of a set of relevant characteristics of a target product. The search over the search space can be constrained by a set of design constraints. For example, in sampling the space of potential formulations and optimizing the objective function, one or more secondary regions of the space that violate one or more of the design constraints in the set of design constraints may not be considered.

[0022] A scalar objective function can be defined over the space of potential formulations. When constructing such a space of potential formulations, the intelligent agent can automatically remove any regions of the space corresponding to potential formulations that violate one or more design constraints. By such rejection of such regions, the intelligent agent is ensured not to recommend sampling points corresponding to potential formulations that violate the design constraints. The objective function can be a function of potential formulations for the target product. The objective function can indicate the match between the observed values for the set of relevant characteristics associated with a potential formulation and the target values for each relevant characteristic of the set of relevant characteristics for the target product (e.g., the intended or desired values). The objective function can be defined (e.g., in terms of the target values of the set of relevant characteristics), and points in the formulation space that at least approximately optimize (e.g., maximize or minimize) the objective function correspond to potential formulations that result in a target product having characteristics that at least partially match the target values of the set of relevant characteristics.

[0023] That is, the "objective" of the objective function is to select, from a set of potential formulations, at least to some extent an "optimized" formulation. The selected formulation enables the manufacture of a target product having characteristics that match the target values of the relevant characteristics of the target product. A formulation that is at least to some extent optimized may be referred to as a "target" formulation. Embodiments can model the formulation of a target product as a search for a target formulation within a large search space that includes a set of potential formulations.

[0024] The set of relevant characteristics can be defined by the user. Each characteristic of the set of relevant characteristics can be a characteristic that is controlled (e.g., selected as an objective or selected to be contrary) in the formulation of the target product. The set of relevant characteristics (and the values associated with each relevant characteristic) can define a "relevant characteristic space". Each dimension in the relevant characteristic space can correspond to a relevant characteristic in the set of relevant characteristics. The basis vectors (and associated metrics) associated with the dimensions in the space can correspond to the quantification of the corresponding relevant characteristics. The relevant characteristic space may sometimes simply be referred to as the "characteristic space". Thus, the quantification of the set of relevant characteristics corresponding to a potential formulation can be encoded in a characteristic vector embedded in the characteristic space. As discussed below, the target values presented by the user for the set of relevant characteristics can be encoded in a target characteristic vector (or set of target characteristic vectors) of the characteristic space. Thus, the search problem can be defined as a search for potential formulations associated with vector embeddings in a characteristic space that "resemble" the target characteristic vector.

[0025] In at least one embodiment, the intelligent agent may encode a target value for a set of relevant characteristics of a "target characteristic vector" embedded in the characteristic space. Each formulation vector in the formulation space may correspond to a characteristic vector in the characteristic space via the value of the relevant characteristic generated by the potential formulation. More specifically, the potential formulation may generate a prototype product of the values of the relevant characteristics corresponding to the points in the characteristic space. Thus, there may be a mapping between the points in the formulation space and the points in the characteristic space. It should be noted that this mapping is not a one-to-one mapping in that there may be one or more points in the characteristic space that cannot be reached via the potential formulations in the formulation space. Further, there may be multiple potential formulations corresponding to the same point in the characteristic space; for example, multiple potential formulations may result in products having equivalent (or at least similar) characteristics.

[0026] Since the objective function is a function of both a point in the formulation space and a target value for a set of relevant characteristics, this mapping may be useful for evaluating the objective function. However, since one or more of the relevant characteristics may be unpredictable, the mapping from the formulation space to the characteristic space may not be achievable via prediction means. Empirical or experimental means may be required to generate the mapping from the formulation space to the characteristic space for the target product. Thus, empirical means may be required for evaluating the objective function.

[0027] As described above, the objective function may be based on a target value for a set of relevant characteristics, e.g., a vector embedding (s) of the target value for the set of relevant characteristics. Also, as described above, at least some of the relevant characteristics may be unpredictable. Since at least some of the target / relevant characteristics are unpredictable, the objective function may be a black-box function. That is, it may be infeasible to generate a mapping of the formulation to the value of the corresponding relevant characteristic based on first principles, modeling, or other prediction means. Thus, the objective function may be a "black-box function". Evaluation of such a black-box objective function at a generalized point in the formulation space may be infeasible from predictive analysis.

[0028] Rather, an empirical (or experimental) mechanism may be required to evaluate the objective function at a point in the formulation space. Thus, optimization of the objective function may require empirical sampling of the objective function at a finite set of sampling points to generate an estimated value of the objective function over the formulation space. The target formulation (e.g., a potential formulation that at least approximates and optimizes the objective function) may be selected via empirical evaluation at the sampled points and / or an estimated value of the objective function over the formulation space.

[0029] Such empirical evaluation of the objective function can be costly in both time and financial resources. Thus, an intelligent agent provides intelligent guidance (or proposals) by repeatedly recommending one or more sets of sampling points to sample in the formulation space. When the sampling points are intelligently selected by the intelligent agent, efficient convergence of the estimation of the objective function can be achieved by performing repeated empirical evaluation of the objective function at the recommended sampling points. When its estimate converges, the objective function can be at least approximately optimized and a target formulation that matches the target value of the set of relevant characteristics can be selected. By performing empirical observations at the sampling points recommended by the intelligent agent, it is possible to significantly improve efficiency not only in optimizing the objective function but also in the convergence of the estimation of the objective function compared to conventional trial-and-error or heuristic-based methods. That is, the embodiments enable formulating a target product in a manner that is significantly more efficient than conventional methods.

[0030] An intelligent agent can use machine learning and / or statistics-based methods to determine a set of recommended points for sampling in the space of formulations. In at least one embodiment, the intelligent agent can use one or more black-box optimization techniques to generate one or more sets of recommended sampling points. Such adoptable black-box optimization techniques include, but are not limited to, techniques of Bayesian optimization and / or Gaussian process regression.

[0031] The formulation process (e.g., optimization of the black box objective function) can be an iterative process. For example, in the formulation of a target product, stakeholders can sample an initial set of sampling points by empirically observing the values of the relevant characteristics of the prototype products associated with the potential formulations corresponding to the initial set of sampling points. In such embodiments, the stakeholders can provide the initial set of sampling points and the empirically observed values of the relevant characteristics at each of the initial sampling points. The intelligent agent can evaluate the objective function at these initial sampling points based on the empirically observed values of the characteristics being provided. Based on the evaluation of the objective function in the initial set of sampling points, the intelligent agent can use black box function optimization techniques and the initial set of sampling points to generate statistical bounds (such as variance) on a set of potential functions that approximate the objective function to at least a specific confidence level. The set of potential functions can be regarded as statistical estimates of the objective function. Using the statistical bounds of the set of potential functions, the next set of sampling points is selected (and recommended), which improves the estimated value of the objective function. The stakeholders may perform an empirical evaluation of the relevant characteristics in the recommended set of sampling points. Next, the stakeholders can provide the intelligent agent with the empirical observations of the values of the relevant characteristics at the recommended next set of sampling points. This process can be iteratively continued until the estimation of the objective function converges to a convergence level that allows at least partial optimization of the objective function. Such optimization of the objective function enables the agent to select the target formulation from the set of potential formulations.

[0032] Intelligent agents and stakeholders (e.g., users) can communicate iteratively during the formulation process via a user interface (UI) provided by the intelligent agent. In non-limiting embodiments, the UI interface may be a graphical user interface (GUI). In at least one embodiment, the GUI may be a "smart spreadsheet" that includes an interactive table. The table may include a set of rows and a set of columns that form a set of cells. Each cell may be uniquely indexed by the corresponding row and column. Each row may correspond to a potential sampling point in the formulation space. At least a portion of the columns may be used to store values that encode potential formulations (recommended and / or sampled). Another portion of the columns may correspond to storing values that encode a feature vector representing a set of relevant features of the potential formulation that was the subject of the "experimental observation" of the sampling. For example, a user who has performed an experimental observation of a prototype product (manufactured via the corresponding potential formulation) can input the experimentally observed values of the relevant features into the cells corresponding to the rows and columns of that experiment. In this way, the user can provide the intelligent agent with the "experimental results" related to the sampling.

[0033] Another portion of the columns may be used to store values that encode potential formulations, such as formulation vectors. The intelligent agent can recommend sampling points to the user by "filling" the "formulation encoding cells" of the rows corresponding to the recommended sampling points in the formulation. In at least one embodiment, the intelligent agent may highlight the rows corresponding to the recommended sampling points. At least one column may be used to store values indicating the empirical evaluation of the objective function. In such an embodiment, the intelligent agent can automatically provide the value of the objective function evaluated at the sampling point and the cell corresponding to the corresponding column.

[0034] The intelligent agent can provide the user with formulations to recommend via the GUI. Similarly, the user can provide potential formulations to the intelligent agent via the GUI. The user can provide the intelligent agent with a set of potential formulations, a set of relevant characteristics, target values of the set of relevant characteristics, and a set of design constraints via the GUI. The user can also provide the intelligent agent with the experimental results of sampling (e.g., empirical observations of the quantification of relevant characteristics) via the GUI. The intelligent agent can provide the user with an empirical evaluation of the objective function and recommended sampling points via the GUI. Thus, the GUI can function as an interactive interface between the intelligent agent and the stakeholders interested in the formulation of the target product.

[0035] As described above, at least due to the unpredictability of some characteristics, formulating or reformulating new or existing products by conventional methods can be costly, difficult, time-consuming, and require trial-and-error-based efforts. Even when the formulation process is fulfilled with conventional rules of thumb, heuristics, and other types of empirical (or experimental) knowledge, developing (or redeveloping) a product that meets consumers' expectations and preferences via conventional methods can be cumbersome, expensive, and mostly unsuccessful. Embodiments overcome such limitations associated with conventional methods by providing an enhanced machine learning and statistics-based approach for such formulation or reformulation attempts. In addition to overcoming such conventional limitations, embodiments provide many technical effects and technical benefits as described throughout.

[0036] For the purposes of the present disclosure, a composite product can be any tangible or virtualized object composed of a plurality of other types of objects, articles, elements, components, compounds, alloys, chemicals, molecules, and / or atoms. That is, a composite product is any (tangible or virtual) object composed of two or more secondary objects or secondary components. Composite products can include, but are not limited to, consumables such as foodstuffs, foods, beverages, cosmetics, fragrances, pharmaceuticals, fuels, etc. Other non-limiting examples of composite products include consumer products such as pesticides, insect repellents, etc. Unless stated to the contrary, the terms "composite product", "product", "composite", and "compound" are used interchangeably and may refer to a composite product.

[0037] As used herein, the term "component" of a product may refer to a particular secondary object or secondary component contained in the product. The components of a product can include any object, article, element, component, compound, alloy, chemical, molecule, and / or atom contained in the product. In a non-limiting example of a soft drink-based product, sugar is one component of the soft drink. As used herein, the term "set of components" or "list of components" for a product can be used to refer to a set of information indicating the set of components for the product. In the example of a soft drink, the set of components for the soft drink can include, but is not necessarily limited to, {carbonated water, sugar, caramel color, phosphoric acid, caffeine, flavor_1, flavor_2}.

[0038] As used herein, the term "formulation" for a product can be used to refer to a set of ingredients for the product, as well as a set of information indicating the absolute and / or relative amounts of each ingredient of the set of ingredients required for the manufacture, fabrication, and / or production of the product. The formulation of a product can encode the molecular or chemical composition (e.g., chemical formula) of the product. In the example of a soft drink, the formulation of the soft drink can include information such as {(carbonated water, amt1), (sugar, amt2), (caramel coloring, amt3), (phosphoric acid, amt4)), (caffeine, amt5), (flavor_1, amt6), (flavor_2, amt7)}, where amt x represents the absolute or relative amount (or ratio) of the corresponding ingredient required for the manufacture of the soft drink. In at least one embodiment, the formulation of a product can encode or include information indicating instructions for combining (or assembling) the ingredients in a way that enables at least partially the manufacture or production of the product. That is, the formulation of a product can enable the manufacture or production of the product. Thus, the formulation of a product can encode at least some effective instructions for its manufacture or production. The terms "recipe", "parts list", "BOM", "blueprint", "source code", "design", or "genotype" for a product can be used interchangeably to refer to the formulation of the product. As described throughout, the formulation of a product can be encoded in a data structure. In at least one embodiment, the formulation can be encoded in a multi-dimensional data object or structure such as, but not limited to, a vector, 1D array, or n-tuple. In some embodiments, the formulation can be encoded in a higher-dimensional data object or structure such as, but not limited to, a rank-2 tensor (e.g., matrix), a higher-rank tensor, and / or an array of objects.

[0039] The term "characteristics" of a product can include any observable, perceptible, measurable, and / or quantifiable aspect, property, or feature of the product. By loose analogy, if the formulation (or recipe) of a product is analogized as the "genotype" for making and / or manufacturing the product, the characteristics of the product can be analogized as the "phenotype" of the manufactured / or made product. Thus, similar to the case where the formulation of a product is called the "genotype" of the product, the characteristics of the product may be called the "phenotype" of the product. By another loose analogy, if the product is a software application and its formulation is its source code, the characteristics of the product can be the features (or bugs) of the compiled application. Examples of product characteristics include, but are not limited to, human perceptions associated with the consumption of the product, such as taste, flavor, odor, color, texture, viscosity, etc. Other exemplary characteristics of a product can include the effectiveness of the intended purpose of the product (e.g., an insect repellent does not attract insects), the (relative or absolute) cost of the formulation of the product, or whether the formulation complies with one or more regulations, dietary / nutritional restrictions, and other such constraints. As yet another example, product characteristics can include nutritional information (e.g., the amount of energy, macronutrients, and / or micronutrients), mass, volume, etc.

[0040] Some (but not necessarily all) characteristics may be quantifiable for various levels of solution. For example, some characteristics can be quantified by binary classification (e.g., whether a product formulation contains (or does not contain) a specific ingredient, whether the formulation complies with specific regulations, or whether an insect repellent attracts insects or not). Some exemplary characteristics can be quantified by scalar values that are unbounded (or bounded) and / or continuous (or discrete) (e.g., the cost of a formulation, the cardinality of the set of components of a formulation, or the degree to which an insect repellent does not attract insects). Still other exemplary characteristics can be quantified using higher-dimensional objects such as (1D or multi-dimensional) arrays, n-tuples, vectors, matrices, higher-order tensor objects, etc. For example, the taste of a product can be quantifiable via a vector, 1D array, or n-tuple, where different tastes (or taste domains) (e.g., sweetness, sourness, saltiness, bitterness, and umami) correspond to the individual dimensions or components of the vector, array, or n-tuple. Note that in encoding a set of relevant characteristics of a product, not all characteristics of the product need to be encoded. For example, the encoding may encode only a subset of the relevant characteristics (e.g., target values for the set of relevant characteristics).

[0041] Some characteristics may follow (at least in part) objective quantification, such as the cost of a formulation, nutritional information, the pungency of a product (e.g., spiciness or "heat") (e.g., Scoville value), or whether a formulation contains (or does not contain) a specific ingredient. The quantification of other characteristics can be more subjective. For example, the taste, flavor, or aroma of a product is subjective and can vary depending on an individual's opinion regarding the characteristic. The "nose" or "scent" characteristics associated with wine are examples of product characteristics that tend to be more subjective and less objective than other characteristics.

[0042] Some product characteristics may be (at least to some extent) predictable, estimable, or otherwise determinable, based at least in part on knowledge of the product's formulation and / or other characteristics. That is, some characteristics may be at least somewhat predictable from the formulation before manufacturing or fabricating at least a prototype version of the product, taking into account theory, first principles, primary (or linear) effects, prior knowledge (e.g., experience), heuristics (e.g., rules of thumb), and / or models that are readily applicable to the product's formulation. For example, the cost, nutritional information, and mass / volume of a product that is a soft drink may be predictable or estimable from the product's formulation. Other characteristics may be less predictable or estimable from the product's formulation. Some product characteristics may be at least somewhat unpredictable, at least prior to manufacturing or fabricating at least a prototype of the product, due to unknown interactions, synergistic effects, non-linear relationships, and other unpredictable and / or uncontrollable interactions between components. The unpredictability of at least some characteristics may be due at least in part to subjectivity inherent in the characteristics, e.g., the variance or variation in the ways a panel of tasters may subjectively evaluate the taste of a product. Characteristics associated with large variance (or dispersion) may be classified as unpredictable characteristics. Some characteristics may be at least somewhat unpredictable because they are due at least in part to unmodeled interactions between components, second-order (or higher-order) effects between components, or other such unknown mechanisms. Some unpredictable or estimable characteristics may be "emergent," in that the "emergent characteristic" itself does not exist until the components are aggregated or combined as encoded in the product's formulation.

[0043] The terms "empirical," "unpredictable," "inestimable," or "emergent" may be used interchangeably to refer to characteristics that are not readily predictable or inferable through product formulation, theory, first principles, prior knowledge (e.g., experience), heuristics (e.g., rules of thumb), and / or models that are readily applicable to potential product formulations. Characteristics that are readily predictable or estimable by first principles, theoretical considerations, experience, heuristics, models, etc. may simply be referred to as "predictable" characteristics or "estimable" characteristics. It should be noted that the characterization of a particular characteristic as a predictable or unpredictable characteristic itself may be an unpredictable characteristic of the product's characteristics. For example, due to unknown or unmodeled interactions between components, it may be impossible to predict whether a particular characteristic is unpredictable or predictable until at least a prototype of the product is manufactured or produced. The predictability of whether one or more characteristics of a product are unpredictable is sometimes referred to as a "meta-characteristic" (or simply a characteristic) of the characteristic. Characteristics of unpredictable meta-characteristics may be classified as unpredictable.

[0044] Exemplary Devices and Systems FIG. 1 shows a block diagram of an exemplary computing system 100 that enables the formulation of a target product according to an exemplary embodiment of the present disclosure. System 100 includes a user computing device 102 and a server computing system 130 communicatively coupled via a network 180.

[0045] User computing device 102 can be any type of computing device, such as, for example, a personal computing device (e.g., a laptop or desktop), a mobile computing device (e.g., a smartphone or tablet), a game console or controller, a wearable computing device, an embedded computing device, or any other type of computing device.

[0046] The user computing device 102 includes one or more processors 112 and a memory 114. The one or more processors 112 can be any suitable processing device (e.g., a processor core, a microprocessor, an ASIC, an FPGA, a controller, a microcontroller, etc.), and can be a single processor or multiple processors operably connected. The memory 114 can include one or more non-transitory computer-readable storage media such as RAM, ROM, EEPROM, EPROM, flash memory devices, magnetic disks, and combinations thereof. The memory 114 can store data 116 and instructions 118 that are executed by the processor 112 to cause the user computing device 102 to perform operations.

[0047] More specifically, the machine-learned prediction model can be trained to take in molecular data and mixture data and output a prediction of the properties of the mixture described by the mixture data. In some embodiments, the molecular data may be embedded by an embedding model before being processed by the prediction model.

[0048] The user computing device 102 can also include one or more user input components 122 that receive user input. For example, the user input component 122 can be a touch sensing component (e.g., a touch sensing display screen or a touch pad) that senses the touch of a user input object (e.g., a finger or a stylus). The touch sensor component functions to implement a virtual keyboard. Other exemplary user input components include a microphone, a conventional keyboard, or other means by which a user can execute the user's input.

[0049] Server computing system 130 includes one or more processors 132 and a memory 134. The one or more processors 132 can be any suitable processing device (e.g., a processor core, a microprocessor, an ASIC, an FPGA, a controller, a microcontroller, etc.), and can be a single processor or multiple processors operably connected. The memory 134 can include one or more non-transitory computer-readable storage media such as RAM, ROM, EEPROM, EPROM, flash memory devices, magnetic disks, etc., and combinations thereof. The memory 134 can store data 136 and instructions 138 that are executed by the processor 132 to cause the server computing system 130 to perform operations.

[0050] In some embodiments, server computing system 130 includes or is implemented by one or more server computing devices. When server computing system 130 includes multiple server computing devices, such server computing devices can operate according to a sequential computing architecture, a parallel computing architecture, or a combination thereof.

[0051] Server computing system 130 can include an intelligent agent engine 140 that is capable of providing guidance in the development of complex products as discussed herein. That is, intelligent agent engine 140 provides intelligent agent services that enable the execution of various embodiments discussed herein. A user of a user computer device may access the services of the intelligent agent via communication network 180. That is, user computing device 102 can be a client of intelligent agent engine 140 implemented by server computing system 130. Other embodiments may not employ such a client / server architecture. For example, a user computing device may implement intelligent agent engine 140, and as a result, a user of user computing device 102 may access the services of the intelligent agent.

[0052] Various embodiments of intelligent agent engine 140 are described in conjunction with at least FIG. 2. However, briefly described here, an intelligent agent (e.g., implemented by intelligent agent engine 140) can be enabled to optimize (e.g., minimize or maximize) a black-box objective function over a sufficiently large search space. More specifically, an intelligent agent can be used (e.g., by a user of user computing device 1023) to provide guidance in the design, development, and / or formulation (or reformulation) of a new (or existing) product. A product that is formulated or reformulated may be referred to as a "target product." As discussed below, embodiments may model the formulation of a target product as a search problem over a high-dimensional (and sufficiently large) search space, e.g., a first vector space spanned by a set of potential formulation vectors that encode a set of potential formulations for the target product.

[0053] Network 180 can be any type of communication network, such as a local area network (e.g., intranet), a wide area network (e.g., Internet), or a combination thereof, and can include any number of wired or wireless links. Generally, communication on network 180 can be performed via any type of wired and / or wireless connection using a variety of communication protocols (e.g., TCP / IP, HTTP, SMTP, FTP), encodings or formats (e.g., HTML, XML), and / or protection schemes (VPN, secure HTTP, SSL, etc.). FIG. 1 shows an example of a computing system that can be used to implement the present disclosure. Other computing systems can be used as well.

[0054] Exemplary intelligent agent engine FIG. 2 shows a block diagram of an exemplary intelligent agent engine 200 implemented according to an exemplary embodiment of the present disclosure. Intelligent agent engine 200 can be equivalent and / or similar to intelligent agent 140 of FIG. 1. Thus, intelligent agent engine 200 can implement an intelligent agent. Whether implemented on user computing device 102 of FIG. 1 or on server computing device 130, the intelligent agent can provide intelligent agent services to the user of user computing device 102. As shown in the non-limiting embodiment of FIG. 2, intelligent agent engine 200 can include a user interface (UI) manager 202, a formulation encoder 203, and a feature encoder 206. Intelligent agent engine 200 can further include an objective function evaluator 208, an objective function optimizer 210, and a constraint encoder. Objective function optimizer 210 can include a Bayesian optimizer 212 and a Gaussian process regressor 214. Note that in other embodiments of intelligent agent engine 200, additional and / or alternative components, modules, and / or other structures can be included.

[0055] The operations and functions of non-limiting exemplary components of the intelligent agent engine 200 will be described below. However, briefly explained here, the UI manager 202 is generally responsible for providing one or more UIs to the user computing device 102 and managing various interactions with the user computing device 102. The UI may include a "smart spreadsheet" that enables interaction between the user and the intelligent agent. The formulation encoder 204 is generally responsible for encoding potential formulations of a formulation vector corresponding to a point in the formulation space. The feature encoder 206 is generally responsible for encoding values (e.g., empirically observed values and / or target values) for a set of relevant features in a feature vector. The constraint encoder 216 is generally responsible for encoding a set of design constraints. The objective function evaluator 208 is generally responsible for generating and evaluating an objective function given an encoding of target values for a set of relevant features, a formulation vector, and / or an empirically observed feature vector. The objective function optimizer 210 is generally responsible for optimizing the objective function. To fulfill its role, the objective function analyzer 210 may include a Bayesian optimizer 212 and a Gaussian process regressor 214. The Bayesian optimizer 212 is generally responsive to performing a Bayesian optimization process used to optimize the objective function. The Gaussian process regressor 214 generally plays the role of performing a Gaussian process, which process may be a subprocess of the Bayesian optimization process of the Bayesian optimizer 212.

[0056] An intelligent agent (implemented by the intelligent agent engine 200) enables the optimization (e.g., minimization or maximization), at least approximately, of a black-box objective function over a sufficiently large search space. More specifically, the intelligent agent may be used to provide guidance in the design, development, and / or formulation (or reformulation) of a new (or existing) target product. The intelligent agent may model the formulation of a target product as a search problem over a high-dimensional (and sufficiently large) search space, e.g., a first vector space spanned by a set of potential formulation vectors encoding a set of potential formulations for the target product. The guidance provided by the intelligent agent may include iterative recommendations of one or more points to empirically (or experimentally) sample in the space of potential formulations. Sampling points in the space of potential formulations may include manufacturing or fabricating a target prototype version corresponding to the sampling point and empirically (or experimentally) measuring or observing the characteristics of the prototype product. As with other search problems, the objective function is used to quantify how well a particular point in the search space satisfies the goal of the search. The search over the search space may be constrained by a set of design constraints. For example, in sampling the space of potential formulations and optimizing the objective function, one or more secondary regions of the space represented by the set of design constraints may not be considered.

[0057] More specifically, the intelligent agent can be used to provide guidance when attempting to introduce, increase, eliminate, or decrease one or more relevant characteristics of a new or existing target product. That is, the embodiments can be employed such that when attempting to formulate (or reformulate) a target product, the formulation at least approximately and maximally achieves the target (or intended) values of the set of relevant characteristics of the target product. For such purposes, stakeholders (e.g., users of the intelligent agent) (e.g., developers, designers, fabricators, manufacturers, distributors, publishers, customers, consumers, etc.) who are interested in formulating (or reformulating) the target product can define (via the UI) the target values of the set of relevant characteristics of the target product. The set of relevant characteristics of the target product can include any characteristic that is introduced, increased, eliminated, or decreased in the formulation (or reformulation) of that target product. That is, the set of relevant characteristics can include any characteristic that is constrained, controlled, selected as a goal, selected to be contrary, or otherwise targeted in the target product. Note that the set of relevant characteristics may not cover all the characteristics of the target product. Rather, the relevant characteristics among the set of relevant characteristics can only be those characteristics that are at least partially maximized, minimized, or selected as a goal (or selected to be contrary) in the formulation (or reformulation) of the target product.

[0058] For one or more of the set of relevant characteristics, a target value of the relevant characteristic (e.g., a desired quantification) can be provided by the user. The target value of the relevant characteristic (e.g., the target value) can include the intention to optimize (e.g., maximize or minimize) the relevant characteristic. The relevant characteristic (and / or its target value) can be an "intended" or "desired" characteristic (and / or the intended quantification of the relevant characteristic) for the target product. The guidance of the agent (e.g., the recommended sampling points) ensures that, at the time of manufacture or fabrication, the achieved formulation at least approximately maximally achieves the target values for the set of relevant characteristics. In a non-limiting example, the target product can be an insect formulation. In a non-limiting example, the target product can be an insect repellent. The set of relevant characteristics of the insect repellent can include {repellency, cost}. Repellency can be a measurable scalar value indicating how effectively the insect repellent keeps insects away. Cost can be a scalar value indicating the cost of the set of ingredients included in the formulation of the insect repellent. In some embodiments, the formulation of the insect repellent can include attempting to at least approximately maximize the repellency of the insect repellent, while at the same time suppressing the cost below a cost threshold.

[0059] The value of a set of related characteristics (e.g., either empirically observed or a given target value) may be encoded in a data structure or data object, such as a vector, 1D array, n-tuple, etc. In such an encoding, each dimension (or component) of the vector (or array or n-tuple) corresponds to a related characteristic, and the value of that component may be set to the value of the related characteristic (e.g., empirically observed or a given target value). Other vector encoding schemes for sets of characteristics may be used by various embodiments. The vector encoding scheme used for the value of the set of related characteristics may define a "characteristic vector space" (or space of characteristic vectors) of the target product and / or the set of related characteristics of the target product. In at least one embodiment, this vector space may be referred to as the characteristic space of the target product. In non-limiting embodiments, each potential characteristic may correspond to a dimension of the characteristic vector space. The basis vectors (and axes) of each dimension in the characteristic vector space may correspond to the quantification of the characteristic corresponding to the axis. Note that each point in the characteristic vector space may not be achievable by a potential formulation. In the above example of the insect repellent, the portion of the characteristic vector space corresponding to high repellency and low cost may not be achievable by some formulations of the insect repellent that are possible.

[0060] The quantification of at least some of the relevant properties may be predictable without the need to manufacture or produce at least a prototype instance of the product. Other relevant properties may be unpredictable. Due to such unpredictable relevant properties, at least a prototype instance of the product may be manufactured or produced. When manufactured or produced via a potential formulation, the unpredictable properties may be measured, observed, or otherwise quantified. In the above example of the insect repellent, the repellency of the potential formulation may be unpredictable, but the cost of the potential formulation is predictable by the combination of the costs of the individual components of the set of components of the potential formulation. To measure the repellency associated with a potential formulation, a prototype of the insect repellent may be manufactured and the associated repellency may be measured. In such a scenario, the quantification of the repellency property is evaluated or measured empirically and / or experimentally.

[0061] In addition to the target values of the set of relevant properties, a stakeholder may define a set of design constraints for the target product. The constraint encoder 216 may encode the set of design constraints in a data structure that the objective function evaluator 208 may evaluate or otherwise analyze. The design constraints in the set of design constraints may be constraints on the formulation of the target product and / or the set of relevant properties. Non-limiting examples of such design constraints include that the formulation must (or must not) include a particular component, that the nutritional information must be limited by one or more thresholds, or that the market cost of the set of components must not exceed a cost threshold. In the above example of the insect repellent, the design constraints in the set of design constraints may include ensuring that the cost of the set of components is less than a cost threshold. The guidance of the agent ensures that the reached formulation (and the values of the associated set of relevant properties) complies with the set of design constraints.

[0062] Embodiments may use various combinations of machine learning and statistics-based techniques to enable an agent to provide guidance in the generation, determination, development, formulation, and / or reformulation of one or more possible formulations for a new or existing target product. Such machine learning and statistics-based techniques may include, but are not necessarily limited to, Bayesian optimization techniques and Gaussian process regression techniques. In some embodiments, the agent uses a Bayesian optimization and / or Gaussian process regression regressor that recommends sampling points in the potential formulation space via an empirical evaluation of a set of relevant characteristics.

[0063] The formulation (or reformulation) of a new (or existing) target product may include target values for a set of relevant characteristics and / or a set of design constraints. The target values for the set of relevant characteristics are defined to "improve the product" in one or more domains of product evaluation (e.g., price, consumer taste profile, product effectiveness, government regulations, etc.). Such improvement scenarios may include, but are not limited to, exploring updated formulations to reduce manufacturing costs, including one or more newly available ingredients in the formulation, or adapting to changes in consumer trends and / or regulatory policies. For example, if the cost of one or more ingredients in an existing formulation suddenly increases due to supply chain-related issues, embodiments may be used to explore alternative ingredients that provide similar or enhanced characteristics of the product.

[0064] The user of the user computing device 102 in FIG. 1 can define a set of potential formulations, target values of a set of related characteristics, a set of design constraints for a target product, and a set of design constraints via the UI manager 202 through interactions with the UI manager 202. In at least one embodiment, the user can define an objective function. In other embodiments, the intelligent agent can automatically define and / or generate an objective function based on a set of potential formulations, a set of related characteristics, target values for the set of related characteristics, and / or design constraints provided by the user. The user can define these objects via any suitable encoding schema. In at least one embodiment, the user can define a set of potential formulations by providing each of the potential components. In some embodiments, the user can further define the set of potential formulations by providing (absolute or relative) quantitative limits (e.g., upper and / or lower bounds) for each potential component. As described throughout, the formulation encoder 204 can convert a potential formulation (and thus a set of potential formulations) from the native data schema used by the user to a common encoding (e.g., vector encoding) recognized by other components of the intelligent agent engine 200. Similarly, the characteristic encoder 206 and the constraint encoder enable the data supplied by the user to be converted to a common data encoding recognized by other components of the intelligent agent engine 200.

[0065] The information contained in each of these user-based definitions will be described in more detail below. However, briefly stated here, the set of potential formulations can include each possible formulation for the target product that can be considered by an intelligent agent. Through the vector encoding generated by the formulation encoder 204, a vector space of potential formulations can be defined from the definition of the set of potential formulations. The set of relevant characteristics can include a list of each characteristic that is controlled and / or restricted in the formulation of the target product. That is, the characteristics included in the set of relevant characteristics are the characteristics that are optimized, selected as an objective, or selected to be contrary by an intelligent agent. The target value of the set of relevant characteristics can be a quantification of the intended (or desired) value for each of the relevant characteristics of the formulation. In some embodiments, the target value of a particular relevant characteristic can be an indication that the value associated with the particular relevant characteristic is optimized (e.g., maximized or minimized) in the formulation of the target product.

[0066] Through the vector encoding generated by the feature encoder 206, the vector space of features can be defined from the definition of a set of related features. The objective function can be a scalar objective function defined for the vector space of potential formulations. The objective function can be a function of potential formulations for the target product. The objective function can indicate a match between the value for a set of related features associated with a potential formulation and a target value for the set of related features. The objective function can be defined (e.g., in terms of the target value of the set of related features) such that at least an approximate optimization (e.g., maximization or minimization) of the objective function yields a target product having features that at least partially match the target value of the set of related features. That is, the "objective" of the objective function is to select, from the set of potential formulations, a "optimized" formulation to some extent as the objective. As described above, in some embodiments, the intelligent agent can automatically generate the objective function. In other embodiments, the user can at least partially define the objective function. For example, the user can provide a distance or similarity metric used by the objective function when attempting to control related features. The set of design constraints can include one or more constraints on potential formulations and on features associated with products manufactured from the set of potential formulations.

[0067] Each potential formulation included in the set of potential formulations is a "possible", "potential", or "candidate" formulation for the target product. Each potential formulation can include a set of components and an absolute or relative quantification of the amount of each component in the set of potential components of the formulation. For some potential components, the quantification can be binary (e.g., whether the potential component is included or not included in the potential formulation). For other potential components, the quantification can include a rational number indicating the absolute or relative amount of the component included in the potential formulation. What is inherent in the concept of the set of potential formulations is the set of potential components for the target product. Each potential component in the set of potential components is a component included in at least one potential formulation of the set of potential formulations. Note that in order to be included in the set of potential components, a potential component can be included in multiple potential formulations of the set of potential formulations, but it is not necessary to be included. In various embodiments, the set of potential components is a finite set, and thus there are a finite number of components included in the set of potential components.

[0068] As described above, each potential component in a potential formulation may include an absolute or relative quantification of the amount of the potential component included in the potential formulation. The potential (or possible) range of such quantification may be a finite range. For example, for any potential component, the potential range of quantification is limited by a lower threshold and an upper threshold. In some embodiments, the absolute (or relative) lower limit (or threshold) of a potential component may be 0.0. For example, if the quantification of the amount of a potential component for a potential formulation is set to 0.0, the potential component is not included in the corresponding potential formulation. The upper limit (or threshold) of a potential component may depend on the absolute or relative scale used for the formulation. For example, if relative quantification is used, the upper limit of any potential component may be set to 1.0, indicating that the target product should be composed of only that potential component. Thus, a set of potential formulations can be defined by a set of potential components and the upper / lower thresholds of each potential component.

[0069] In some embodiments, a set of potential formulations may be encodable in a finite vector space, where each potential component in the set of potential components is associated with a distinct dimension of the vector space. The formulation encoder 204 may generally be responsive to generating such an encoding. The dimension of the vector space may correspond to the cardinality of the set of potential components. The axis of each dimension of the vector space may be limited by the upper threshold and the lower threshold of the corresponding potential component. Thus, the finite vector space for the set of potential formulations may be an N-dimensional hyper-rectangle or hyper-box, where N is a positive integer corresponding to the cardinality of the set of potential components. This finite vector space may be referred to as the "space of potential formulations" (or potential formulation space) for the target product. The space may also be referred to as a formulation vector space or simply a formulation space.

[0070] In some embodiments, a metric of distance can be imposed on the space of potential formulations that enables measurement of distances and angles in a vector space. That is, the metric can be defined such that the inner product of a pair of vectors and / or distances are appropriately defined across the space. In at least one embodiment, the metric can be encoded with a symmetric 2-tensor (e.g., a matrix). In some embodiments, the metric matrix can be a diagonal matrix. The metric matrix can be the identity matrix for the dimension of the vector space (e.g., the Euclidean metric). Various embodiments may employ other metrics, such as the Manhattan, Minkowski, Hamming, and other such distance metrics.

[0071] Via the formulation encoder 204, each potential formulation of the set of potential formulations for the target product can be encoded as a vector embedding in the space of potential formulations. Each component of the vector embedding can be associated with a potential component of the set of potential components. The quantification of the potential component can be assigned to the corresponding component in the vector embedding of the potential formulation. In some embodiments, one or more of the axes for the dimensions of the space of potential formulations can be discretized by binning of the axis. In other embodiments, each axis can be a continuous axis of real-valued numbers. Other vector embeddings of potential formulations are possible and embodiments are not limited to the vector embeddings discussed herein.

[0072] In various embodiments, other vector encodings of sets of relevant characteristics may be used, such as vector embeddings of potential formulations. As noted above, the set of relevant characteristics of a target product can include any characteristic that is introduced, increased, eliminated, or decreased in the formulation (or reformulation) of that target product. That is, the set of relevant characteristics can include any characteristic that is constrained, controlled, selected as a goal, selected to oppose, or otherwise targeted in the target product. Note that the set of relevant characteristics may not cover all characteristics of the target product. Rather, the relevant characteristics among the set of relevant characteristics can only be those characteristics that are at least partially maximized, minimized, or selected as a goal (or selected to oppose it) in the formulation (or reformulation) of the target product. Values for the set of relevant characteristics (e.g., target values, predicted values, and / or empirically observed values) may be encoded by the formulation encoder 206.

[0073] The objective function evaluator 208 is capable of evaluating an objective function when given a target characteristic vector, a characteristic vector encoding empirically observed values for a particular point in the formulation space, and a set of design constraints. The objective function may be undefined for points in the formulation space or characteristic vectors that violate one or more of the design constraints in the set of design constraints. For example, the objective function evaluator 208 may return an undefined indication when given a condition (e.g., a potential formulation or value for a set of relevant characteristics that violates one or more design constraints).

[0074] In such an embodiment, if the cardinality of the set of relevant characteristics is finite and at least a portion of the relevant characteristics are quantifiable, the values for the set of relevant characteristics may be encoded in a data structure or object. The feature encoder 206 may encode the set of relevant features in a common data structure recognized by other components of the intelligent agent engine 200, such as, for example, a vector, a 1D array, an n-tuple, etc. In a non-limiting example of the encoding used by the feature encoder 206, each dimension (or component) of the vector (or array or n-tuple) corresponds to a relevant feature, and the value of the component is set for the quantification of the relevant feature. The feature encoder 206 may use other vector encoding schemes for the set of relevant features. The feature encoder 206 may convert the set of relevant features received via the UI manager 202 into a common encoding scheme.

[0075] The vector encoding scheme used by the feature encoder 206 may define a "feature vector space" (or space of feature vectors) for the target product and / or the set of relevant characteristics of the target product. In at least one embodiment, this vector space may be referred to as the feature space of the target product. In a non-limiting embodiment, each potential feature may correspond to a dimension of the feature vector space. The axis of each dimension in the feature vector space may correspond to the quantification of the feature corresponding to the axis. Note that each point in the feature vector space may not be achievable by a potential formulation. In the above example of the insect repellent, the portion of the feature vector space corresponding to high repellency and low cost may not be achievable by a realizable formulation of the insect repellent.

[0076] In some embodiments, a metric of distance can be imposed on a characteristic vector space that enables measurement of distances and angles in a vector space. That is, the metric can be defined such that the inner product and / or distance of a pair of vectors are well-defined. In at least one embodiment, the metric may be encoded by a symmetric 2-tensor (e.g., a matrix). In some embodiments, the metric matrix can be a diagonal matrix. The metric matrix can be an identity matrix with respect to the dimension of the vector space (e.g., Euclidean metric). Various embodiments may employ other metrics, such as Manhattan, Minkowski, Hamming, and other such distance metrics.

[0077] The quantification of at least some relevant characteristics may be predictable without the need to manufacture or fabricate at least a prototype instance of the product. Other relevant characteristics may be unpredictable. Due to such unpredictable relevant characteristics, at least a prototype instance of the product can be manufactured or fabricated. Once manufactured or fabricated via a potential formulation, the unpredictable characteristics can be quantified by measurement, observation, or other means. That is, the characteristics of a prototype version of the product can be empirically observed. In the above example of the insect repellent, the repellency of a potential formulation may be unpredictable, but the cost of a potential formulation can be predicted by the set of components of the potential formulation. To measure the repellency associated with a potential formulation, a prototype of the insect repellent may be manufactured and the associated repellency can be measured.

[0078] The user can provide, via the UI manager 202, the results of any such empirical observations of the characteristics of the "experimental" or "prototype" version of the target product to the intelligent agent engine 200. The characteristic encoder 206 can generate an encoding of such empirically observed characteristics. In addition to the target values of the set of relevant characteristics, the user can define, via the UI manager 202, a set of design constraints for the target product.

[0079] The objective function optimizer 210 can use various combinations of machine learning and statistics-based techniques that enable an agent to iteratively optimize the objective function. In the non-limiting embodiment of FIG. 2, the objective function optimizer 210 includes a Bayesian optimizer 212 and a Gaussian process regressor 214. As discussed in more detail in connection with FIGS. 3A-3B, the Bayesian optimizer 212 may perform a Bayesian optimization process to optimize the objective function. The Bayesian optimizer 212 can use the Gaussian process regressor 214 to enable the optimization process. The Gaussian process regressor 214 may implement Gaussian process regression techniques to enable the Bayesian optimization process.

[0080] Exemplary method FIG. 3A shows a flowchart diagram of an exemplary method 300 for providing guidance in formulating a target product, according to an exemplary embodiment of the present disclosure. Although FIG. 3A shows steps performed in a particular order for purposes of illustration and discussion, the methods of the present disclosure are not limited to the specifically illustrated order or arrangement. The various steps of method 300 can be omitted, rearranged, combined, and / or adapted in various ways without departing from the scope of the present disclosure. An intelligent agent implemented by an intelligent agent engine (e.g., the intelligent agent engine 140 of FIG. 1 and / or the intelligent agent engine 200 of FIG. 2) can perform at least some of the steps of method 300. The intelligent agent engine can be implemented by a computing system such as, but not limited to, the system 100 of FIG. 1.

[0081] At 302, the intelligent agent can receive a set of potential formulations, a set of related characteristics, target values of the set of related characteristics, and a set of design constraints of the target product. The intelligent agent can receive any of the set of potential formulations, the set of related characteristics, the target values of the set of related characteristics, and the set of design constraints through a user using an interactive user interface (UI). The interactive UI can include a "smart spreadsheet" with an interactive table. The table can be interactive in that a user of a computing device can access the table and the intelligent agent. The user can provide information to the intelligent agent by entering values into one or more cells of the table. Similarly, the intelligent agent can provide information to the user by entering values into other cells of the table. The UI can be provided to the user via a UI manager (e.g., the UI manager 202 of FIG. 2).

[0082] At block 304, based on the set of potential formulations, the set of related characteristics, and the set of design constraints, a formulation space and a characteristic space can be generated. The formulation space and the characteristic space can each be a vector space. A target characteristic vector can be generated based on the target values of the set of related characteristics. The target characteristic vector can be an embedding vector of the characteristic space that encodes the target values of the set of related characteristics. A characteristic encoder (e.g., the characteristic encoder 206 of FIG. 2) can generate the target characteristic vector. Each potential formulation of the set of potential formulations can be embedded into the formulation space via a vector encoding of the potential formulation. A formulation encoder (e.g., the formulation encoder 204 of FIG. 2) can generate the vector embedding of the potential formulation.

[0083] In at least one embodiment, the formulation space may be updated or modified to “cut out” (or remove) portions of the formulation space that correspond to vector embeddings of potential formulations that violate one or more of the design constraints of a set of design constraints. The set of relevant characteristics may be embedded in the characteristic space via vector encoding. A characteristic encoder (e.g., characteristic encoder 206 of FIG. 2) may generate a vector embedding (or scalar embedding for a single relevant characteristic) of the set of relevant characteristics. Similar to the design constraint-based cutting out of the formulation space, one or more portions of the characteristic space may be cut out from the characteristic space corresponding to vector embeddings of characteristics that violate one or more design constraints.

[0084] In block 306, the objective function may be generated based on the values of the set of relevant characteristics. An objective function evaluator (e.g., objective function evaluator 208 of FIG. 2) may generate the objective function based on target values for the set of relevant characteristics, e.g., a vector (or scalar) encoding of a target characteristic vector. The objective function may be a scalar function defined over the formulation space. More specifically, the objective function may be a function of the vector (or scalar) embedding of the set of relevant characteristics corresponding to a potential formulation. Thus, the objective function may be a scalar function implicitly defined over the characteristic space. For example, evaluation of the objective function may produce more extreme scalar values (e.g., values closer to the maximum or minimum value of the objective function) when points corresponding to characteristic embeddings (e.g., scalar or vector) that are “similar” or “close” to the vector embedding of the target value of the set of relevant characteristics, such as a target characteristic vector, are evaluated. Such distances or similarities may be measured via various metrics such as Euclidean distance, cosine similarity, inner product, etc. That is, the objective function may be a function of the comparison between the vector embedding of the target value of the set of relevant characteristics and the vector embedding of the set of relevant characteristics (empirically observed) corresponding to a potential formulation.

[0085] At block 308, for each initial sampling point in the set of initial sampling points, values of the set of relevant characteristics of the target product can be received. The set of sampling points and the values of the set of relevant characteristics of the target product can be provided to the intelligent agent via the UI. The set of initial sampling points can be points (or vector embeddings) in the formulation space. At least some of the characteristics in each set of relevant characteristics may have been empirically (or experimentally) measured by manufacturing (e.g., conducting experiments) a prototype product based on the corresponding potential formulation of the point. A characteristic encoder (e.g., the characteristic encoder 206 of FIG. 2) can encode the received values regarding the sampling points of the vector embedding in the characteristic space.

[0086] At block 310, for each initial sampling point in the set of initial sampling points, the objective function can be evaluated at the sampling point based on the received values of the set of relevant characteristics corresponding to the sampling point. The evaluation of the objective function can be an empirical or experimental evaluation of a function based on the values empirically observed for the set of relevant characteristics. In at least one embodiment, the evaluation of the objective function can be based on a comparison between the vector embedding of the target values of the set of relevant characteristics and the vector embedding of the corresponding received values of the set of relevant characteristics. In some embodiments, the comparison can be based on the difference between the two vector embeddings. In at least one embodiment, the comparison can be based on the distance between the two vector embeddings, the inner product of the two vector embeddings, or the similarity (e.g., cosine similarity) of the two vector embeddings. In some embodiments, an objective function evaluator (e.g., the objective function evaluator 208 of FIG. 2) can evaluate the objective function. The values for the evaluated function can be provided to the user via the UI. In other embodiments, the user can evaluate the objective function. The user can provide, via the UI, the values of the intelligent agent for the evaluated function.

[0087] In block 312, the objective function can be iteratively optimized based on the evaluation of the objective function at each of the initial sampling points in the set of initial sampling points. Various embodiments of iteratively optimizing the objective function are described in relation to at least the method 320 of FIG. 3B. Briefly here, however, one or more optimization techniques can be repeatedly employed to optimize the objective function. In some embodiments, a Bayesian optimization process can be used. In at least one embodiment, a Gaussian process regressor can be used as a sub-process of the Bayesian optimization process.

[0088] In block 314, a target formulation for the target product can be selected and / or specified within the formulation space. The selection of the target formulation can be based on the optimized objective function. The target formulation can be provided to the user via the UI. In block 316, the target product can be manufactured and / or fabricated based on the selected target formulation.

[0089] FIG. 3B shows a flowchart diagram of an exemplary method 320 for iteratively optimizing an objective function according to an exemplary embodiment of the present disclosure. Although FIG. 3B shows steps performed in a particular order for purposes of illustration and discussion, the methods of the present disclosure are not limited to the particularly illustrated order or arrangement. The various steps of method 320 can be omitted, rearranged, combined, and / or adapted in various ways without departing from the scope of the present disclosure. A knowledge agent implemented by a knowledge agent engine (e.g., the knowledge agent engine 140 of FIG. 1 and / or the knowledge agent engine 200 of FIG. 2) can perform at least some of the steps of method 320. The knowledge agent engine may be implemented by a computing system such as, but not limited to, the system 100 of FIG. 1. Method 320 can be a secondary method of method 300 of FIG. 3A. For example, method 320 may be called in block 312 of method 300.

[0090] Method 320 can implement a Gaussian optimization process to optimize an objective function. For the purposes of this description, the objective function ) may be referred to as f(x). In the formula, x ∈ R d is a point in a d-dimensional formulation space (R d ), and d is a positive integer. Such embodiments are non-limiting, and x can be a variable (or type of variable) that extends beyond real (or rational) numbers. For example, x can include a categorical categorical variable that encodes a decision, or can represent a set of vertices and edges that represent a molecular structure (e.g., a graph data structure). Method 320 is such that f(x T ) selects a target formulation (x T ) from the formulation space such that f(x) is at least approximated and optimized (e.g., maximized or minimized) for all points in the formulation space. In various embodiments, the objective function can be a black-box function because at least some of the relevant characteristics are unpredictable characteristics.

[0091] When using the Gaussian optimization process, method 320 can model the black-box objective function as a random function (e.g., a generalization of statistical random variables). Method 320 can employ Bayes' theorem and thus can consider the prior distribution of the function (e.g., the distribution of candidate functions approximating the objective function) for the objective function. Similar to other applications of Bayes' theorem, the prior distribution of the function represents a set of "beliefs" about the "true" representation of the objective function. The objective function can be empirically (or experimentally) evaluated at sampling points. Through such empirical evaluations and the application of Bayes' theorem to the prior distribution, the set of beliefs is updated by calculating the posterior distribution of the candidate functions. An acquisition function can be calculated from the posterior distribution. The acquisition function gives a score or usefulness associated with the acquisition of an empirical observation of the objective function at that point. The acquisition function can be used to determine another set of points in the formulation space to sample. Evaluating the objective points at this next set of sampling points updates the model at these new points and obtains a new posterior distribution. This process can be iteratively continued until the posterior distribution converges sufficiently.

[0092] In at least one embodiment, a Gaussian process regressor is used to iteratively update the prior / posterior distribution. Briefly, a Gaussian process regressor can include a probabilistic technique for estimating a function based on empirical observations of the evaluation of the function at sampling points. In contrast to linear regression techniques, a Gaussian process regressor models each random variable as being distributed via a multivariate normal distribution, and each variable has an independent mean value and variance parameter. The mean value and variance of each random variable are iteratively updated through iterative empirical evaluations of the objective function at a set of iteratively generated sampling points. This iterative estimation of the multivariate normal distribution is sometimes referred to as the training of the Gaussian process regressor.

[0093] At block 322, for each sampling point in the set of sampling points, corresponding values of the set of relevant characteristics of the target product can be received. The intelligent agent can be provided with values for the set of sampling points via a user who employs an interactive user interface (UI). The interactive UI can include a "smart spreadsheet" with an interactive table. The table can be interactive in that a user of a computing device can access the table and the intelligent agent. The user can provide information to the intelligent agent by entering values into one or more cells of the table. Similarly, the intelligent agent can provide information to the user by entering values into other cells of the table. The UI can be provided to the user via a UI manager (e.g., UI manager 202 of FIG. 2). Various embodiments for receiving values of the set of sampling points are described in conjunction with at least block 308 of method 300.

[0094] The set of sampling points can be points (or vector embeddings) in a formulation space. At least some of the characteristics in each set of relevant characteristics may have been empirically (or experimentally) measured by manufacturing a prototype product based on the corresponding potential formulation of the point. Each received set of relevant characteristics can be encoded in a vector embedding into a characteristic space. A characteristic encoder (e.g., characteristic encoder 206 of FIG. 2) can generate a vector encoding for each received set of relevant characteristics. The set of sampling points at block 322 can be an initial set of sampling points (e.g., see block 308 of method 300).

[0095] At block 324, for each sampling point in the set of sampling points, the objective function can be evaluated at the sampling point based on the set of associated characteristics corresponding to the sampling point. The evaluation of the objective function may be an empirical or experimental evaluation of the function based on the set of empirically observed associated characteristics. In at least one embodiment, the evaluation of the objective function can be based on a comparison between a vector embedding of the target values of the set of associated characteristics and a vector embedding of the corresponding set of associated characteristics. In some embodiments, the comparison can be based on the difference between the two vector embeddings. In at least one embodiment, the comparison can be based on the distance between the two vector embeddings, the inner product of the two vector embeddings, or the similarity between the two vector embeddings (e.g., cosine similarity). The various embodiments for evaluating the objective function are described in conjunction with at least block 310 of method 300.

[0096] At block 326, the training of the Gaussian process regressor can be updated based on the (empirical) evaluation of the objective function at the sampling points. In at least one embodiment, a Gaussian process regressor (e.g., Gaussian process regressor 214 of FIG. 2) can be used to train the Gaussian process regressor. At block 328, the acquisition function can be updated based on the updated Gaussian process regressor. In various embodiments, a Bayesian optimizer (e.g., Bayesian optimizer 213 of FIG. 2) can be used to update the acquisition function. At block 330, the convergence criterion can be evaluated based on the updated acquisition function. At decision block 332, based on the convergence criterion, it is determined whether to terminate the iterative (and empirical) sampling of the objective function. If the sampling process ends, the method proceeds to block 242. Otherwise, if sampling continues, process 320 proceeds to 334.

[0097] In block 334, the set of next sampling points in the formulation space is identified (or selected) based on the updated acquisition function and the set of design constraints. In at least one embodiment, if the updated acquisition function identifies a sampling point that violates one or more of the design constraints in the set of design constraints, the violating points can be removed from the set of next sampling points. A Bayesian optimizer may be used to determine the set of next sampling points. In block 336, the UI can be updated. For example, the UI can be updated to show the objective function evaluations of block 310 of method 300 and / or block 324 of method 320. The UI can be updated to show the identified set of next sampling points. A UI manager (e.g., UI manager 202 of FIG. 2) can be used to update the UI. In block 338, the set of next sampling points is provided. Providing the set of next sampling points may be performed by providing the updated UI to the user. A UI manager may be used to provide the set of next sampling points and / or the updated UI. In block 340, for each sampling point in the set of next sampling points, an observation of the set of relevant characteristics can be received. The various embodiments of receiving the values of the relevant characteristics are described in conjunction with at least block 308 of method 300 and block 322 of method 320. Method 320 returns to block 324 and can evaluate the objective function at each of the sampling points in the set of next sampling points.

[0098] In block 342, the objective function is optimized based on the trained Gaussian regressor. An objective function optimizer or a Bayesian optimizer can be used to optimize the objective function. In block 344, the UI can be updated to show the objective function. In block 346, the optimized objective function and the updated interface can be provided. When block 346 is executed, method 320 can proceed to block 314 of method 300.

[0099] Formulation of an Exemplary Target Composite Product In a non-limiting embodiment, an exemplary target product to be formulated is a mosquito repellent. The target product is a composite product, and the set of ingredients includes three molecules, {vanillin, dimethyl carbonate, dimethyl phthalate}. The three potential ingredients can be combined in various ratios. In one embodiment, a vector encoding of potential formulations can be shown, {x v ,x dc ,x dp}, where x v represents the amount of vanillin in a potential formulation, x dc represents the amount of dimethyl carbonate in a potential formulation, and x dp represents the amount of dimethyl phthalate in a potential formulation. The set of basis vectors {{1,0,0},{0,1,0},{0,0,1}} can span the formulation space. In one embodiment, the amounts may be relative amounts, such that the boundary condition between vector components x v + x dc + x dp = 1 (or other such relationship) defines the "edge" of the formulation space. In other embodiments, the amounts indicated by the vector components are absolute amounts and the formulation space is not restricted.

[0100] The set of relevant characteristics may include a single relevant characteristic, namely, the repellency of a mosquito repellent. Repellency indicates the time-dependent ability of the repellency to keep mosquitoes away from a food source. The experimental quantification of repellency is defined below. Sampling points in the formulation space may involve synthesizing (or manufacturing) a prototype insect repellent based on a potential formulation in the vector embedding corresponding to the sampling point. An experiment may be conducted to empirically measure the repellency associated with the potential formulation. The experiment may be a control experiment in that the experiment may include two experimental groups of mosquitoes, namely, a control group and a treatment group. Each experimental group may be given a separate food source. The food source of the treatment group may have been treated with the prototype insect repellent, while the food source of the control group may not have been treated with the prototype insect repellent.

[0101] Each mosquito in each experimental group is monitored, and in particular, whether the mosquito feeds on its food source and the time at which the mosquito feeds are recorded. The feeding (or non-feeding) of each mosquito is treated as a random variable assuming a Bernoulli distribution. The cumulative distribution of the feeding times of each experimental group is modeled as a sigmoid function (e.g., a logistic function) characterized by two parameters. t m is the average feeding time of the mosquitoes within the group, and k is the feeding rate. The logistic function is defined as follows.

Number

[0102] The feeding times of the mosquitoes in each group are measured, and the logistic function for each group is determined based on the measured feeding times. A Gaussian process can be used to regress the values of the two parameters for each of the experimental groups. More specifically, for the mosquitoes in the control group, y c = 1 or 0 indicates whether the mosquito feeds. The probability that the i-th mosquito in the control group feeds can be calculated as follows.

Number

Equation

Equation

[0103] Based on the above definition, the maximum value of the repellency is 1.0. Therefore, the target value of the repellency can be set to 1.0. In at least one embodiment, the objective function can be defined such that the repellency is maximized.

[0104] Additional Disclosure In the technology described herein, reference is made to servers, databases, software applications, other computer-based systems, and the actions performed and the information transmitted and received between such systems. Because computer-based systems have inherent flexibility, a wide variety of configurations, combinations, and divisions of tasks and functions between components are possible. For example, the processes described herein can be implemented using a single device or component, or multiple devices or components operating in combination. The database and the application can be implemented in a single system or distributed across multiple systems. The distributed components can operate sequentially or in parallel.

[0105] Although the subject matter of the present invention has been described in detail with respect to various specific exemplary embodiments, each example is presented for illustrative purposes and is not intended to limit the disclosure. Those skilled in the art, upon understanding the foregoing, can readily generate modifications, variations, and equivalents to such embodiments. Accordingly, the disclosure is not intended to preclude such modifications, variations, and / or additions to the subject matter that would be readily apparent to those skilled in the art. For example, features illustrated or described as part of one embodiment can be used with another embodiment to obtain yet another embodiment. Accordingly, the disclosure is intended to cover such modifications, variations, and equivalents.

[0106] The headings are provided for the convenience of the reader and are not intended to limit the claimed subject matter.

Claims

1. A computer-implemented method for manufacturing a target product, comprising: receiving, by a computing system including one or more computing devices, a display of a set of potential formulations of the target product and a display of target values of a set of related characteristics of the target product; generating, by the computing system, an objective function over a first domain associated with the set of related characteristics, wherein the target values for the set of related characteristics optimize the objective function over the first domain; determining, by the computing system, a set of estimation functions for estimating the objective function over a second domain associated with a set of potential functions, wherein determining the set of estimation functions is based on first characteristic data encoding values of the set of related characteristics associated with a first subset of the set of potential formulations; iteratively updating, by the computing system, the set of estimation functions based on additional characteristic data encoding additional values for the set of related characteristics associated with an additional subset of the set of potential formulations; selecting, by the computing system, a target formulation from the set of potential formulations, wherein based on the updated set of estimation functions, the target formulation substantially optimizes the objective function over the second domain; and providing, by the computing system, a display of the target formulation.

2. The method according to any of the preceding claims, wherein the target product is an insect repellent.

3. The method according to any of the preceding claims, wherein the target product includes food or beverages.

4. The method according to any of the preceding claims, wherein the target product includes at least one of fragrance products, cosmetics, or pharmaceuticals.

5. The method according to any of the preceding claims, wherein updating the set of estimation functions includes employing a Bayesian optimization process.

6. The method according to claim 5, wherein the Bayesian process employs a Gaussian process regressor method.

7. The method according to any of the preceding claims, wherein values for at least a subset of the set of relevant characteristics are unpredictable based on the set of ingredients included in the potential formulation. **Claim 8** The method according to any of the preceding claims, wherein the set of relevant characteristics includes at least one of taste, flavor, odor, color, or texture of the target product. **Claim 9** The method according to any of the preceding claims, wherein the set of relevant characteristics includes the cost as a set of ingredients included in the potential formulation. **Claim 10** The method according to any of the preceding claims, wherein one or more potential formulations are excluded from the set of potential formulations based on a set of design constraints. **Claim 11** A computer-implemented method for manufacturing a target product, comprising: Receiving, via a user interface (UI) provided by a computing system, first product data regarding characteristics of the target product, wherein the first characteristic data corresponds to a first potential formulation of a set of potential formulations for the target product; Selecting, by the computing system, a second potential formulation from the set of potential formulations based on processing a first evaluation of an objective function defined for the set of potential formulations and a target value for the characteristic, wherein the first evaluation of the objective function is based on the first characteristic data and is associated with the first potential formulation; Receiving, via the UI, second characteristics regarding the characteristics of the target product, wherein the second characteristic data corresponds to the second potential formulation; Processing, by the computing system, a second evaluation of the objective function, wherein the second evaluation of the objective function is based on the second characteristic data and is associated with the second potential formulation; and Selecting a target formulation from the set of potential formulations based on processing the second evaluation of the objective function. The method, comprising: providing the target formulation via the UI. **Claim 12** A computing system configured to execute the method according to any one of claims 1 to 11. **Claim 13** One or more non-transitory computer-readable media that, when executed by a computer system, collectively store instructions that cause the computer system to execute the method according to any one of claims 1 to 11.

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