SYSTEMS AND METHODS FOR GLOBAL OPTIMIZATION OF MATERIAL PROPERTIES

A machine learning system includes a processor and a memory communicably coupled to the processor. The memory stores an acquisition module, a mapping module, a machine learning module, a fitting module, and a minimization module that include instructions that when executed by the processor cause the processor to: select a training dataset, map the training dataset from an input space to an output space such that the mapped training dataset is convex; train a machine learning model to learn a convex function that approximates the mapped training dataset in the output space; learn a minimum of the convex function; map the minimum of the convex function to the input space; and predict, based at least in part on the minimum of the convex function mapped to the input space, an optimum material property value and a corresponding material composition.

TECHNICAL FIELD

The present disclosure relates generally to machine learning of material properties and particularly to machine learning of material properties and discovery of new material compositions.

BACKGROUND

The use of machine learning to assist in the discovery of new materials and/or identify properties of known materials through optimization, i.e., finding a set of inputs to an objective function that results in a maximum or minimum output from the objective function, is an ongoing field of research and development. And while finding an arbitrary local minimum or maximum can be relatively straight forward using known optimization methods, finding a global minimum or maximum of a function can be time and cost prohibitive since analytical methods are typically not available and numerical solution strategies often lead to excessive computation time and/or unacceptable error.

The present disclosure addresses issues related to machine learning and global optimization of material of material properties and discovery of new materials, and other issues related to machine learning.

SUMMARY

In one form of the present disclosure, a system includes a processor and a memory communicably coupled to the processor. The memory stores machine-readable instructions that, when executed by the processor, cause the processor to select a training dataset comprising a plurality of material compositions and tagged property values of a predefined material property and map the training dataset from an input space to an output space such that the mapped training dataset is convex. In some variations, the memory stores machine-readable instructions that, when executed by the processor, cause the processor to learn a convex function that approximates the mapped training dataset in the output space and learn a minimum of the learned convex function and map the minimum of the learned convex function to the input space. And in at least one variation, the memory stores machine-readable instructions that, when executed by the processor, cause the processor to predict, based at least in part on the minimum of the learned convex function mapped to the input space, an optimum material property value and a corresponding material composition.

In another form of the present disclosure, a machine learning system includes a processor and a memory communicably coupled to the processor. The memory stores an acquisition module with instructions that when executed by the processor cause the processor to select a training dataset from at least one of a candidate material dataset and a material properties dataset. Also, the training dataset includes a plurality of material compositions and a property value of at least one predefined material property for each of the plurality of material compositions. The memory also stores a mapping module, a machine learning module, a fitting module, and a minimization module with instructions that when executed by the processor cause the processor to: map the training dataset from an input space to an output space such that the mapped training dataset is convex; train a machine learning model to learn a Softmax-affine function that approximates the mapped training dataset in the output space; learn a minimum of the learned convex function using gradient descent; map the minimum of the learned convex function to the input space; and predict, based at least in part on the minimum of the learned convex function mapped to the input space, an optimum material property value and a corresponding material composition.

In still another form of the present disclosure, a method includes selecting a training dataset comprising a plurality of material compositions and tagged property values of a predefined material property and mapping the training dataset from an input space to an output space such that the mapped training dataset is convex. In some variations, the method further includes learning a convex function that approximates the mapped training dataset in the output space and learning a minimum of the learned convex function and map the minimum of the learned convex function to the input space. And in at least one variation the method includes predicting, based at least in part on the minimum of the learned convex function mapped to the input space, an optimum material property value and a corresponding material composition.

Further areas of applicability and various methods of enhancing the above technology will become apparent from the description provided herein. The description and specific examples in this summary are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.

DETAILED DESCRIPTION

The present disclosure provides a machine learning (ML) system and a ML method for predicting global optimization of at least one material property for a given material system and predicting at least one material composition based, at least in part, on the predicted global optimization. The ML system and ML method train a ML model to learn a convex function for at least one set of material property values mapped from an input space to an output space where the material property values exhibit a convex shape or form (also referred to herein simply as “convex”). The ML system and ML method train the ML model to learn a minimum of the convex function, e.g., using gradient descent, and the learned minimum is mapped back to the input space such that an optimized material property value and corresponding material composition are predicted based, at least in part, on the learned minimum. And in some variations of the present disclosure, the ML system and ML method generate or predict a new material composition with an optimized material property and/or optimum combination of two or more material properties. As used herein, terms such as “property” and phrases such as “material property”, “the property”, and “predicting the property” refer to a property exhibited by a material and a value for the property.

Referring toFIGS.1A-1B, plots of two non-limiting examples of material property values as a function of material composition for hypothetical A-B material system are shown. Particularly,FIG.1Ashows a plot illustrating a relatively heavily populated dataset without a particular, shape, form or trend with increase in B content (XB), andFIG.1Bshows a plot illustrating a relatively sparse dataset that appears to exhibit an increase in material property with increase in B content. And while the material property dataset inFIG.1Amay be used to determine an average material property value independent of B content, and the material property dataset inFIG.1Bmay be used to determine a linear increasing relationship between the material property and B content, it should be understood thatFIGS.1A-1Brepresent plots where either determination would not provide desirable confidence in a calculated material property value as a function of material composition. It should also be understood that the plots shown inFIGS.1A-1Bdo not lend themselves to discovering a material composition with an optimal material property value.

Referring now toFIG.2, a ML system10for predicting a global optimum of at least one material property within a material system is illustrated. The ML system10is shown including at least one processor100(referred to herein simply as “processor100”), and a memory120and a data store140communicably coupled to the processor100. It should be understood that the processor100can be part of the ML system10, or in the alternative, the ML system10can access the processor100through a data bus or another communication path.

The memory120is configured to store modules such as an acquisition module121, a mapping module122, a ML module123, a fitting module124, a minimization module125and an output module126, among others. The memory is a random-access memory (RAM), read-only memory (ROM), a hard-disk drive, a flash memory, or other suitable memory for storing the acquisition module121, mapping module122, ML module123, fitting module124, minimization module125and output module126(referred to herein collectively as “modules121-126”). Also, the modules121-126are, for example, computer-readable instructions that when executed by the processor100cause the processor to perform the various functions disclosed herein.

In some variations the data store140is a database, e.g., an electronic data structure stored in the memory120or another data store. Also, in at least one variation the data store140in the form of a database is configured with routines that can be executed by the processor100for analyzing stored data, providing stored data, organizing stored data, and the like. Accordingly, in some variations the data store140stores data used by the acquisition module121, the mapping module122, the ML module123, the fitting module124, the minimization module125and/or the output module126. For example, and as shown inFIG.2, in at least one variation the data store140stores a candidate material dataset142(also referred to herein simply as “candidate dataset142”) and a material properties dataset144. In some variations, the candidate dataset142includes a listing of a plurality of material compositions for at least one material system and the material properties dataset144includes a property value of at least one predefined property for at least a subset of the plurality of material compositions in the candidate dataset142. It should be understood that the property values and the at least one predefined property in the material properties dataset144are properly tagged and/or associated with the plurality of material compositions in the candidate dataset142.

Non-limiting examples of material systems in the candidate dataset142include materials such as polymers, metals, intermetallics, semiconductors, dielectrics, ionic liquids, solvents, electrolytes, and combinations thereof (e.g., ceramic matrix composites and metal matrix composites, among others). In some variations, the material properties dataset144includes a property value of a predefined material property for each of the plurality of material compositions in the candidate dataset142, while in other variations the material properties dataset144includes a property value for at least two different predefined material properties for each of the plurality of material compositions in the candidate dataset142. In at least one variation, the material properties dataset144includes a property value for at least three different predefined material properties for each of the plurality of material compositions in the candidate dataset142, for example, four or more, five or more, or six and more different predefined material properties for each of the plurality of material compositions in the candidate dataset142.

The acquisition module121can include instructions that function to control the processor100to select a training dataset from the candidate dataset142and the material properties dataset144. That is, the acquisition module121can include instructions that function to control the processor100to select a subset of material compositions from the candidate dataset142and corresponding property values for at least one predefined material property from the material properties dataset144. In at least one variation, the acquisition module121includes instructions that function to control the processor100to select the training dataset by applying a training function to the candidate dataset142. Non-limiting examples of the training function include instructions to select the training dataset based on a random selection and/or an expert analysis.

The mapping module122includes instructions that function to control the processor100to map the training dataset from an input space (e.g., seeFIGS.1A,1B) to an output space where the training dataset is convex, and map at least a portion of the output space back to the input space. Stated differently, the mapping module122includes one or more invertible functions that function to control the processor100to map a dataset from an input space to convex in an output space, and vice versa. Non-limiting examples of functions in the mapping module that map the training dataset from the input space to convex in the output space include autoencoders, e.g., variational autoencoders or adversarial encoders, and recurrent neural networks, among others.

The fitting module124includes instructions that function to control the processor100to learn a convex function that fits or approximates the mapped training dataset in the output space. Non-limiting examples of the convex function include logarithmically convex functions such as Softmax functions and Quadratic functions, i.e., methods/functions known for convex regression and convex combination, and combinations thereof such as Softmax Quadratic functions. In one variation of the present disclosure, the convex function is a Softmax-affine function.

The minimization module125includes instructions that function to control the processor to learn a minimum of the learned convex function. In at least one variation the minimization module125includes instructions that function to control the processor to learn a minimum of the learned convex function using gradient descent during each of one or more iterations. It should be understood that the term “gradient descent” as used herein refers to a first-order optimization algorithm for finding a local minimum of a differentiable function by taking repeated steps in the opposite direction of the gradient of the function at the current point until a minimum gradient is determined.

The output module126includes instructions that function to control the processor to generate at least one material composition within the material system of the training dataset that is not included in the candidate dataset based, at least in part, on the learned minimum of the learned convex function.

Training the ML model provides for predictions of at least one material composition with an optimized material property and/or an optimized combination of material properties. Particularly, and with reference toFIGS.3A and3B, the acquisition module121selects a training dataset from the candidate dataset142and material properties dataset144and the mapping module maps (i.e., instructs the processor100to map) the training dataset from an input space (e.g., seeFIG.1A) to an output space shown inFIG.3Asuch that the mapped training dataset is convex. The fitting module124learns (i.e., instructs the processor100to learn) a convex function ‘ƒ’ that approximates the mapped training dataset as shown inFIG.3B. As noted above, in some variations the convex function is the Softmax-affine function according to the equation:

where ƒSMA(x) is the material property, x is material composition, and α, bk, and akTare fitting parameters.

The minimization module125determines a minimum “Fmin” of the convex function ‘ƒ’ as shown inFIG.3Bsuch that mapping of Fminand the corresponding abscissa value or coordinate “F(XB*)” back to the input space provides an optimized property value and corresponding material composition. And whileFIGS.1A,3A and3Billustrate mapping, minimization, and optimization in two dimensions, it should be understood that the ML system10is configured for mapping, minimization, and optimization in n dimension where n is an integer greater than 2. For example, in at least one variation the acquisition module121includes instructions that function to control the processor100to select a subset of material compositions from the candidate dataset142and a property value of two different predefined properties from the material properties dataset144for each of the material compositions such that the training dataset has three dimension data points and can be or is plotted in a three dimension input space. That is, each data point in the training dataset has coordinates of material composition, a property value for a first predefined material property, and a property value for a second predefined property value. Also, the mapping module122includes instructions that function to control the processor100to map the training dataset to convex in a three dimension output space, learn a three dimension convex function of the mapped training dataset, learn a minimum of the convex function, and map the minimum of the convex function and the corresponding material composition back to the three dimension input space in order to predict or provide a material composition with an optimum combination of the two material properties.

Referring now toFIG.4, a flow chart for a ML method20is shown. The ML method20includes selecting a training dataset from a candidate dataset at200and mapping the training dataset from an input space to an output space such that the mapped training dataset is convex at210. The ML20then trains a ML model to learn a convex function that approximates the mapped training dataset at220and learns a minimum of the convex function, e.g., using gradient descent, at230. And the minimum of the convex function and a corresponding material composition are mapped back to the input space at240such that a material composition with an optimized material property or combination of different material properties is predicted at250.

The preceding description is merely illustrative in nature and is in no way intended to limit the disclosure, its application, or uses. Work of the presently named inventors, to the extent it may be described in the background section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present technology.

The headings (such as “Background” and “Summary”) and sub-headings used herein are intended only for general organization of topics within the present disclosure and are not intended to limit the disclosure of the technology or any aspect thereof. The recitation of multiple variations or forms having stated features is not intended to exclude other variations or forms having additional features, or other variations or forms incorporating different combinations of the stated features.

As used herein the term “about” when related to numerical values herein refers to known commercial and/or experimental measurement variations or tolerances for the referenced quantity. In some variations, such known commercial and/or experimental measurement tolerances are +/−10% of the measured value, while in other variations such known commercial and/or experimental measurement tolerances are +/−5% of the measured value, while in still other variations such known commercial and/or experimental measurement tolerances are +/−2.5% of the measured value. And in at least one variation, such known commercial and/or experimental measurement tolerances are +/−1% of the measured value.

As used herein, the terms “comprise” and “include” and their variants are intended to be non-limiting, such that recitation of items in succession or a list is not to the exclusion of other like items that may also be useful in the devices and methods of this technology. Similarly, the terms “can” and “may” and their variants are intended to be non-limiting, such that recitation that a form or variation can or may comprise certain elements or features does not exclude other forms or variations of the present technology that do not contain those elements or features.

The broad teachings of the present disclosure can be implemented in a variety of forms. Therefore, while this disclosure includes particular examples, the true scope of the disclosure should not be so limited since other modifications will become apparent to the skilled practitioner upon a study of the specification and the following claims. Reference herein to one variation, or various variations means that a particular feature, structure, or characteristic described in connection with a form or variation, or particular system is included in at least one variation or form. The appearances of the phrase “in one variation” (or variations thereof) are not necessarily referring to the same variation or form. It should be also understood that the various method steps discussed herein do not have to be carried out in the same order as depicted, and not each method step is required in each variation or form.

The foregoing description of the forms and variations has been provided for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure. Individual elements or features of a particular form or variation are generally not limited to that particular form or variation, but, where applicable, are interchangeable and can be used in a selected form or variation, even if not specifically shown or described. The same may also be varied in many ways. Such variations should not be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure.