MODELING OF CROSS-DISCIPLINE INTERACTION

TECHNICAL FIELD

[0001] This application relates to generative design. More particularly, this application relates to generative design in complex multi-disciplinary environments.

BACKGROUND

[0002] Predictive modeling of cross-discipline interaction problems, such as of fluidstructure, thermo-electric-mechanical is of great significance in numerous engineering applications, such as aircraft design, electrical system design, etc. However, existing approaches are based on solving coupled governing equations (i.e., nonlinear partial differential equations) numerically, which are extremely computationally expensive and require significant domain knowledge. In complex systems such multi-disciplinary interactions result in emergent behavior that can only be captured through explicit modeling, either using physics based PDE equations or designed rules. In such cases, the problem of optimizing the design poses a challenge as there is a need to execute computationally expensive multi-disciplinary solvers. This computational bottleneck creates a great challenge to realizing true multi-disciplinary optimal designs.

SUMMARY

[0003] Embodiments described in this application include a method of optimizing a design in a multi-discipline system by constructing a multi-disciplinary model. The multidisciplinary model is built by discovering a first latent space of a first machine learning network for a first discipline from a plurality of disciplines, then discovering at least a second latent space of at least a second machine learning network for at least a second discipline and aligning the first latent space with the at least second latent space to define a combined latent space representative of the first discipline and the at least second discipline. The multi-disciplinary model contains information that relates to common characteristics and interaction of system features across multiple disciplines. The methods of this disclosure allow the inputting a desired response for one of the first and second discipline to the multi-disciplinary model, which in turn will generate an output representative of a set of design parameters for the first discipline and the second discipline. The desired response for input to the multi-discipline model may be received from a user via a user interface. In an embodiment, a field from a first discipline may be used as input to the multi-disciplinary model, which generates a second field from a discipline other than the first discipline.

[0004] The multi-disciplinary model may be built based on a probabilistic model. According to one embodiment, a Gaussian Process Latent Variable Model may be used. The multi-disciplinary model works faster and is more efficient because it identifies a nonlinear low-dimensional latent variable shared among a plurality of disciplines and training the multi-disciplinary model to only search the identified shared latent variable. This reduces the space that needs to be explored. Other efficiencies are achieved by constructing the multi-disciplinary model and the reduced order model offline, while the inference module performs online in communication with a user interface.

[0005] A system for designing a multi-disciplinary system is also described, a computer processor in communication with a non-transitory computer memory storing instructions that cause the computer processor to receive simulation data from simulations run using fields relating to each of a plurality of disciplines. A latent space for responses for each discipline of the plurality of disciplines is identified and then the latent spaces are aligned into a common latent space for the plurality of disciplines. A multidisciplinary model is built based on the common latent space. The instructions may further allow the computer processor to implement an inference module configured to infer multidisciplinary data from the multi-disciplinary model; and display a visualization of the inferred data to a user. The inference module may receive a set of design parameters from a first discipline of the plurality of disciplines and output a predicted quantity of a second discipline of the plurality of disciplines. The computer processor may further receive a desired response of a first discipline of the plurality of disciplines and output a predicted quantity of a second discipline of the plurality of disciplines. Embodiments may further allow the computer processor to perform an inverse inference using the multidisciplinary model to generate design parameters for a plurality of disciplines based on a desired response for a selected one of the plurality of disciplines. The system may further include a reduced order model module for creating a lower order model of the multidisciplinary model that displays interacting parameters between more than one of the plurality of disciplines. The output of the inference model and reduced order model may be visualized and displayed to a user. The multi-disciplinary model may be stored in a model store in communication with the inference module, the model store storing the multi-disciplinary model. BRIEF DESCRIPTION OF THE DRAWINGS

[0006] The foregoing and other aspects of the present invention are best understood from the following detailed description when read in connection with the accompanying drawings. For the purpose of illustrating the invention, there is shown in the drawings embodiments that are presently preferred, it being understood, however, that the invention is not limited to the specific instrumentalities disclosed. Included in the drawings are the following Figures:

[0007] FIG. 1 is a block diagram for an architecture for optimizing a design for a multidisciplinary system according to aspects of embodiments described in this disclosure.

[0008] FIG. 2 is an illustration of identifying and aligning latent space for multiple disciplines according to embodiments of this disclosure.

[0009] FIG. 3 is a block diagram of the creation and use of a multi-discipline model according to embodiments of this disclosure.

[0010] FIG. 4 is a process flow diagram of a method of optimizing a multi-discipline system according to embodiments of this disclosure.

[0011] FIG. 5 is a block diagram of a computer system that may be used to implement computer-based methods and systems for optimization of multi-disciplinary systems according to embodiments of this disclosure.

DETAILED DESCRIPTION

[0012] Embodiments that will be described in this application introduce a design generation system that addresses the problem of high computational cost of conventional multi-disciplinary optimization paradigms by leveraging data-driven modeling of multi- disciplinary and cross-domain interactions. Methods and design systems embodiments in this description include the following modules:

[0013] A fast online cross-discipline inference module: This module predicts quantities of interest from one discipline, given a desired response or a set of desired design parameters from the other discipline. This module acts as a forward model, predicting output values based on an input.

[0014] A fast online inverse inference module: This module enables the inference of the corresponding design parameters of the cross-discipline simulation, given a desired response from either one of the disciplines. In this case, an inverse model is used to start with a desired output value and predicting the set of inputs that will produce that result.

[0015] An offline model development module: This module leverages a probabilistic model to construct a cross-discipline shared latent space model that enables the traversal from one discipline to another.

[0016] A reduced-order model generation module: This module synthesizes a lower order model relating the cross-domain parameters quantifying the interacting parameters and their relative strengths providing simple insights into the complex behaviors of the different disciplines.

[0017] Most existing approaches involve solving coupled governing equations (i.e., nonlinear partial differential equations) numerically, which are computationally expensive and require significant domain knowledge. Such systems are commercially available (e.g., ANSYS Workbench, Dassault iSight, SIEMENS HEEDS, etc.) and also available in open-source options (e.g., Stanford Unstructured, a.k.a., SU2). Domain expert knowledge is required to map parameters across the different disciplines. For example, there is need to know that the pressure fields of a fluid simulation act as boundary conditions on the structural simulations in a fluid-structure interaction problem, in addition to knowing how these different fields relate to each other (e.g., identifying which boundaries are related to each other).

[0018] There have been attempts to accelerate optimization using machine learning, in particular surrogate modeling. However, surrogate models are traditionally built for a single discipline. In such cases, interactions between different disciplines still have to be manually specified. Further, the ability to infer design parameters is only possible through optimization approaches. Such approaches rely on enforcing observed or desired conditions as optimization constraints, which may be computationally intractable in the case of large field responses.

[0019] Recently, there have been attempts that focus on building surrogate models to model the cross-discipline interaction. However, the proposed methods are either only targeting the end quantities of interest without the ability to infer cross-values, or utilizing deep learning-based dimensional reduction approach, such as variational autoencoders. These approaches are data-hungry in general, which potentially prevent their applications in practical engineering design context, where the available data is relatively scarce.

[0020] Accordingly, there is currently no approach in practice that leverages the modeling of cross-domain interactions to infer quantities that result.

[0021] A proposed system is illustrated in FIG 1 . The system leverages existing cross- disciplinary simulation data 101 to build a single model 105 that enables the inference of design parameters 117, discipline specific simulation responses while ensuring certain other disciplinary or system responses are satisfied 115. The framework consists of a database 101 , a probabilistic model development module 103, a design parameter inference module111 , a response inference module 113, and an interaction discovery module 109. The design system is intended to augment existing optimization and design space exploration frameworks such as SIEMENS HEEDS, Dakota, etc. by leveraging their capabilities for data generation. In the considered system, it is assumed that the data is already generated and stored in the database 101.

[0022] A user interface 119 allows a user to interact with the inference module 109. A user may specify a desired output value or a design parameter in one discipline that act as constraints 115 to the inference module 109. In one aspect, the inference module may perform a forward inference model for inferring a response 113. In this case, the value or design parameter is received as input in one discipline, and the output of the inference is another response value for a different discipline. In another aspect, an inverse model may be implemented to generate a set of cross-discipline design parameters based on provided desired output value. The inferred values are the design parameters 111 for a multitude of disciplines based on a desired output of one of the disciplines.

[0023] An optimizer 121 receives the multi-disciplinary model 105 from the model storage 107. A reduced order model 125 is generated from a reduced order model discovery module, which provides information relating the interactions between disciplines. The reduced order model 125 may be presented to a user via the user interface 119. [0024] The multi-disciplinary model 105 is created by identifying the latent space in each discipline, then aligning the latent spaced into a common latent space for all of the disciplines. The multi-disciplinary model is created offline and stored in a model store 107.

[0025] FIG. 2 provides a conceptual illustration of how the multi-disciplinary modeling process is carried out. The process begins with the assumption of bijective mappings between the different disciplinary responses. The modeling process may be viewed as including a two-step process, the first of which is the discovery of a latent space for each individual discipline and the second being the process of aligning the different latent spaces. The discovery of these individual latent spaces is obtained by assessing embeddings on a lower dimensional space which minimize an error-based loss function for each domain. The alignment across domain latent spaces is also obtained with similar techniques to those of the individual latent space discovery.

[0026] The values in a first domain 201 and a second domain 203 contain latent manifold spaces 211 , 213, respectively where values of a similar type are grouped together. The latent manifold 211 of the first discipline is aligned with the latent manifold 213 of the second discipline to create a combined common or shared latent manifold for all the disciplines or domains under consideration. The multi-disciplinary model may then be instructed to use the common latent space as a search domain when inferring information in the model.

[0027] FIG. 3 illustrates a high-level view of the multi-disciplinary model 105. The model 105 used in the design system is based on a probabilistic modeling 105. For example, a Gaussian Process Latent Variable Model (GPLVM) may be used as the underlying model. Alternately, any probabilistic embedding models such as ones using neural networks can be leveraged. The overall concept is shown in FIG. 3 in the context of the GPLVM. The model’s 105 goal is to find a nonlinear low dimensional latent variable shared among the high dimensional responses from all disciplines found in the joint low dimensional latent space 309 characterized as the nonlinear mappings from the latent variables to responses from all disciplines. This model 309 simultaneously builds these mappings 309. After the model 105 is built, computationally efficient cross-discipline inference and inverse inference may be carried out during an online stage to facilitate the design space exploration involving the cross-discipline behaviors.

[0028] The development of the model is carried on offline and stored in a model repository 107 as shown in FIG. 1. Once trained, this model 105 is accessible to the user through a user interface 119 (either graphical, text-based, or command line) for online inference where the user can provide the desired behavior of one or more responses 115 and infer the other unknown parameters of the design 117.

[0029] The modeling methodology introduced may be summarized in the following steps. First, data collection/generation occurs. Sets of simulation parameters and their corresponding discipline responses (i.e., velocity fields and pressure field for fluid simulation; displacement fields and stress fields for structural simulations; thermal stresses and temperature fields for thermal simulations; electric fields in electrical simulations) that are required to train the model are generated and stored in the data store database 101. Next, model training is carried out. During the training stage, the shared latent variables 220 are found among the simulation parameter, and the discipline responses. Moreover, a nonlinear mapping from the shared latent variable to those disciplinary responses are built 309 Once the model is trained, prediction/inference with the trained model, where given one of the fields from any one of the disciplines (e.g., velocity profile in a certain direction for the fluid), other corresponding fields in the other disciplines may be inferred. The corresponding simulation setting/design parameters may be inferred, given the mapping between the simulation setting and responses are bijective.

[0030] Provided with a desired response from a first discipline 303, the trained model 301 may provide suggested design parameters 305 for the first discipline 211 , but may also or in the alternative, provide suggestions for design parameters 307 relating to a second discipline 213 by virtue of the joint latent space 309.

[0031] The discovery of reduced order representations of parameter interactions is also trained offline. This process involves solving a model fitting problem involving the minimization of a residual. By assuming a certain form of the reduced order model, e.g., linear I quadratic I etc. model, an optimizer discovers the coefficients associated with the reduced order model that enables the easy traversal between the different disciplines. Moreover, an explainable representation that can be presented to the engineer for the observed cross-disciplinary interaction and potentially, emergent behavior is achievable.

[0032] The quick estimation of sensitivities, e.g., changes required in the electrical response when there is a change to the mechanical behavior, in complex systems is easily observable using the reduced order model.

[0033] Referring now to FIG. 4, a process flow for the optimization of design in complex multi-disciplinary system is provided. Data from simulations using a multitude of domains or disciplines is stored for use of the system 401. For each discipline, a latent space for the discipline is identified 403. The individual latent spaces are aligned to identify a common latent space for all disciplines 405.

[0034] Once the multi-disciplinary model is trained, a user may provide inputs to the multi-disciplinary model, which may use the common latent space to infer data values 407. The inferred values may be represented in a visualization that is presented to the user 409. Based on the displayed data inferred by the model, the user may make a design decision using parameters inferred by the multi-disciplinary model 401.

[0035] This invention presents a systematic manner to capture the cross-disciplinary interactions that are present in complex systems. This approach has the following advantages compared to existing approaches, the capability of forward prediction as well as inverse inference of the cross-domain interaction within a single model, reduced requirements on the size of training dataset. This method requires less training data compared to deep learning-based approaches. Within the same distribution of the training dataset, the enclosed embodiments achieve the predictive accuracy consistent with fidelity of the training dataset, with much less training data leveraging the properties of probabilistic models. The online inference speed of the approaches presented is on par with deep learning models and much faster than traditional simulation approaches. Embodiments of this disclosure produce explainable interactions and representations for cross-disciplinary interactions making it easier for engineers to validate their systems and understand complex behaviors.

[0036] FIG. 5 illustrates an exemplary computing environment 500 within which embodiments of the invention may be implemented. Computers and computing environments, such as computer system 510 and computing environment 500, are known to those of skill in the art and thus are described briefly here.

[0037] As shown in FIG. 5, the computer system 510 may include a communication mechanism such as a system bus 521 or other communication mechanism for communicating information within the computer system 510. The computer system 510 further includes one or more processors 520 coupled with the system bus 521 for processing the information.

[0038] The processors 520 may include one or more central processing units (CPUs), graphical processing units (GPUs), or any other processor known in the art. More generally, a processor as used herein is a device for executing machine-readable instructions stored on a computer readable medium, for performing tasks and may comprise any one or combination of, hardware and firmware. A processor may also comprise memory storing machine-readable instructions executable for performing tasks. A processor acts upon information by manipulating, analyzing, modifying, converting, or transmitting information for use by an executable procedure or an information device, and/or by routing the information to an output device. A processor may use or comprise the capabilities of a computer, controller, or microprocessor, for example, and be conditioned using executable instructions to perform special purpose functions not performed by a general-purpose computer. A processor may be coupled (electrically and/or as comprising executable components) with any other processor enabling interaction and/or communication there-between. A user interface processor or generator is a known element comprising electronic circuitry or software or a combination of both for generating display images or portions thereof. A user interface comprises one or more display images enabling user interaction with a processor or other device.

[0039] Continuing with reference to FIG. 5, the computer system 510 also includes a system memory 530 coupled to the system bus 521 for storing information and instructions to be executed by processors 520. The system memory 530 may include computer readable storage media in the form of volatile and/or nonvolatile memory, such as read only memory (ROM) 531 and/or random-access memory (RAM) 532. The RAM 532 may include other dynamic storage device(s) (e.g., dynamic RAM, static RAM, and synchronous DRAM). The ROM 531 may include other static storage device(s) (e.g., programmable ROM, erasable PROM, and electrically erasable PROM). In addition, the system memory 530 may be used for storing temporary variables or other intermediate information during the execution of instructions by the processors 520. A basic input/output system 533 (BIOS) containing the basic routines that help to transfer information between elements within computer system 510, such as during start-up, may be stored in the ROM 531 . RAM 532 may contain data and/or program modules that are immediately accessible to and/or presently being operated on by the processors 520. System memory 530 may additionally include, for example, operating system 534, application programs 535, other program modules 536 and program data 537.

[0040] The computer system 510 also includes a disk controller 540 coupled to the system bus 521 to control one or more storage devices for storing information and instructions, such as a magnetic hard disk 541 and a removable media drive 542 (e.g., floppy disk drive, compact disc drive, tape drive, and/or solid-state drive). Storage devices may be added to the computer system 510 using an appropriate device interface (e.g., a small computer system interface (SCSI), integrated device electronics (IDE), Universal Serial Bus (USB), or FireWire).

[0041] The computer system 510 may also include a display controller 565 coupled to the system bus 521 to control a display or monitor 566, such as a cathode ray tube (CRT) or liquid crystal display (LCD), for displaying information to a computer user. The computer system includes an input interface 560 and one or more input devices, such as a keyboard 562 and a pointing device 561 , for interacting with a computer user and providing information to the processors 520. The pointing device 561 , for example, may be a mouse, a light pen, a trackball, or a pointing stick for communicating direction information and command selections to the processors 520 and for controlling cursor movement on the display 566. The display 566 may provide a touch screen interface which allows input to supplement or replace the communication of direction information and command selections by the pointing device 561. In some embodiments, an augmented reality device 567 that is wearable by a user, may provide input/output functionality allowing a user to interact with both a physical and virtual world. The augmented reality device 567 is in communication with the display controller 565 and the user input interface 560 allowing a user to interact with virtual items generated in the augmented reality device 567 by the display controller 565. The user may also provide gestures that are detected by the augmented reality device 567 and transmitted to the user input interface 560 as input signals.

[0042] The computer system 510 may perform a portion or all of the processing steps of embodiments of the invention in response to the processors 520 executing one or more sequences of one or more instructions contained in a memory, such as the system memory 530. Such instructions may be read into the system memory 530 from another computer readable medium, such as a magnetic hard disk 541 or a removable media drive 542. The magnetic hard disk 541 may contain one or more datastores and data files used by embodiments of the present invention. Datastore contents and data files may be encrypted to improve security. The processors 520 may also be employed in a multiprocessing arrangement to execute the one or more sequences of instructions contained in system memory 530. In alternative embodiments, hard-wired circuitry may be used in place of or in combination with software instructions. Thus, embodiments are not limited to any specific combination of hardware circuitry and software.

[0043] As stated above, the computer system 510 may include at least one computer readable medium or memory for holding instructions programmed according to embodiments of the invention and for containing data structures, tables, records, or other data described herein. The term “computer readable medium” as used herein refers to any medium that participates in providing instructions to the processors 520 for execution. A computer readable medium may take many forms including, but not limited to, non- transitory, non-volatile media, volatile media, and transmission media. Non-limiting examples of non-volatile media include optical disks, solid state drives, magnetic disks, and magneto-optical disks, such as magnetic hard disk 541 or removable media drive 542. Non-limiting examples of volatile media include dynamic memory, such as system memory 530. Non-limiting examples of transmission media include coaxial cables, copper wire, and fiber optics, including the wires that make up the system bus 521 . Transmission media may also take the form of acoustic or light waves, such as those generated during radio wave and infrared data communications. [0044] The computing environment 500 may further include the computer system 510 operating in a networked environment using logical connections to one or more remote computers, such as remote computing device 580. Remote computing device 580 may be a personal computer (laptop or desktop), a mobile device, a server, a router, a network PC, a peer device, or other common network node, and typically includes many or all of the elements described above relative to computer system 510. When used in a networking environment, computer system 510 may include modem 572 for establishing communications over a network 571 , such as the Internet. Modem 572 may be connected to system bus 521 via user network interface 570, or via another appropriate mechanism.

[0045] Network 571 may be any network or system generally known in the art, including the Internet, an intranet, a local area network (LAN), a wide area network (WAN), a metropolitan area network (MAN), a direct connection or series of connections, a cellular telephone network, or any other network or medium capable of facilitating communication between computer system 510 and other computers (e.g., remote computing device 580). The network 571 may be wired, wireless or a combination thereof. Wired connections may be implemented using Ethernet, Universal Serial Bus (USB), RJ- 6, or any other wired connection generally known in the art. Wireless connections may be implemented using Wi-Fi, WiMAX, and Bluetooth, infrared, cellular networks, satellite or any other wireless connection methodology generally known in the art. Additionally, several networks may work alone or in communication with each other to facilitate communication in the network 571.

[0046] [0047] An executable application, as used herein, comprises code or machine- readable instructions for conditioning the processor to implement predetermined functions, such as those of an operating system, a context data acquisition system or other information processing system, for example, in response to user command or input. An executable procedure is a segment of code or machine-readable instruction, subroutine, or other distinct section of code or portion of an executable application for performing one or more particular processes. These processes may include receiving input data and/or parameters, performing operations on received input data and/or performing functions in response to received input parameters, and providing resulting output data and/or parameters.

[0048] A graphical user interface (GUI), as used herein, comprises one or more display images, generated by a display processor and enabling user interaction with a processor or other device and associated data acquisition and processing functions. The GUI also includes an executable procedure or executable application. The executable procedure or executable application conditions the display processor to generate signals representing the GUI display images. These signals are supplied to a display device which displays the image for viewing by the user. The processor, under control of an executable procedure or executable application, manipulates the GUI display images in response to signals received from the input devices. In this way, the user may interact with the display image using the input devices, enabling user interaction with the processor or other device.

[0049] The functions and process steps herein may be performed automatically or wholly or partially in response to user command. An activity (including a step) performed automatically is performed in response to one or more executable instructions or device operation without user direct initiation of the activity.

[0050] The system and processes of the figures are not exclusive. Other systems, processes and menus may be derived in accordance with the principles of the invention to accomplish the same objectives. Although this invention has been described with reference to particular embodiments, it is to be understood that the embodiments and variations shown and described herein are for illustration purposes only. Modifications to the current design may be implemented by those skilled in the art, without departing from the scope of the invention. As described herein, the various systems, subsystems, agents, managers, and processes can be implemented using hardware components, software components, and/or combinations thereof.