EP-4736054-A1 - PREDICTING FEASIBLE DESIGNS FOR A PHYSICAL SYSTEM

EP4736054A1EP 4736054 A1EP4736054 A1EP 4736054A1EP-4736054-A1

Abstract

Predicting a feasible region of a design space for a physical system includes, for one or more iterations, determining a set of design points. The determining includes, for outputs of the physical system, sampling respective functions from respective probabilistic models, wherein the respective functions predict values of the outputs at design points, and selecting a design point based on an objective function that penalises a distance from a boundary of the feasible region as predicted by values of the respective functions. The selecting of at least some design points is performed in parallel. At each iteration, data is obtained comprising empirical values of the output(s) at the determined design points, and using the obtained data to determine updated values of trainable parameters of the model. The method includes, after the one or more iterations, predicting the feasible region using the data obtained during the one or more iterations.

Inventors

STOJIC, Hrvoje
COWLEY, WILLIAM
VULLO, Alessandro
PICHENY, Victor

Assignees

Secondmind Limited

Dates

Publication Date: 20260506
Application Date: 20240626

Claims (1)

CLAIMS 1. A computer-implemented method of predicting a feasible region of a design space for a physical system, the method comprising: for one or more iterations: determining a set of design points within the design space, wherein determining a given design point in the set comprises: for one or more outputs of the physical system, sampling respective functions from respective probabilistic models each having a set of trainable parameters, wherein the respective functions predict values of the one or more outputs at design points within the design space; and selecting the given design point based on an objective function that penalises a distance from a boundary of the feasible region as predicted by values of the respective functions, wherein the selecting of at least some of the design points in the set is carried out in parallel; obtaining data comprising values of the one or more outputs of the physical system at each design point of the determined set of design points; and determining, using the obtained data, updated values of the set of trainable parameters; and after the one or more iterations, predicting the feasible region of the design space using the data obtained during the one or more iterations. 2. The computer-implemented method of claim 1, wherein the predicting of the feasible region of the design space uses the respective probabilistic models for the one or more outputs of the physical system. 3. The computer-implemented method of claim 1 or 2, wherein: the boundary of the feasible region depends on a variable threshold value of one of the outputs of the physical system; and selecting the given design point comprises sampling the variable threshold value from a distribution of threshold values to predict the distance from the boundary of the feasible region. 4. The computer-implemented method of any preceding claim, wherein obtaining the data comprises executing simulations of the physical system at the determined set of design points. 5. The computer-implemented method of any preceding claim, wherein the obtaining of the data is carried out in parallel for at least some of the design points in the set. 6. The computer-implemented method of any preceding claim, wherein for a given iteration, determining each design point in the set comprises optimising a respective objective function within a respective trust region of the design space, the respective trust regions differing between at least some design points in the set. 7. The computer-implemented method of claim 6, wherein for the given iteration, determining each design point in the set uses a respective group of one or more probabilistic models, the respective groups corresponding to the respective trust regions of the design space. 8. The computer-implemented method of any preceding claim, wherein the probabilistic model comprises at least one of a Gaussian process regression model, a sparse Gaussian process, a deep Gaussian process, a Bayesian neural network, and a deep ensemble. 9. The computer-implemented method of any preceding claim, further comprising: obtaining, using the respective probabilistic models for the one or more outputs of the physical system, a plurality of design points predicted to lie within the feasible region of the design space; and bounding the plurality of design points using a set of geometric shapes of equal dimensionality to the design space, thereby to determine a representation of the feasible region of the design space. 10. The computer-implemented method of any of claims 1 to 8, further comprising: obtaining, based on the data obtained during the one or more iterations, a plurality of design points predicted or measured to lie within the feasible region of the design space; and bounding the plurality of design points using a set of geometric shapes of equal dimensionality to the design space, thereby to determine a representation of the feasible region of the design space. 11. The computer-implemented method of any preceding claim, wherein: the one or more outputs of the physical system is a plurality of outputs; and the objective function selectively penalises distances between the respective functions and the respective threshold values of the plurality of outputs. 12. The computer-implemented method of claim 11, wherein the selective penalising is selective in dependence on the distances between the respective functions and the respective threshold values of the plurality of outputs. 13. The computer-implemented method of any preceding claim, wherein the physical system comprises at least part of a vehicle. 14. The computer-implemented method of claim 13, wherein the at least part of the vehicle comprises one or more of a hybrid powertrain system, a vehicle architecture, an electric motor, a battery system, a thermal management system, a regenerative braking system, a tyre, and an aerodynamic component. 15. The computer-implemented method of any preceding claim, wherein the respective functions sampled for any given design point in the set are independent from the function or functions used to determine any other given design point in the set. 16. The computer-implemented method of any preceding claim, wherein the selecting of at least some of the design points in the set is carried out in parallel across a plurality of processor cores or processor nodes. 17. A computer-implemented method of determining a representation of a feasible region of a design space for a physical system, the method comprising: obtaining a plurality of design points predicted or measured to lie within the feasible region of the design space; and bounding the plurality of design points using a set of geometric shapes of equal dimensionality to the design space, thereby to determine the representation of the feasible region of the design space. 18. The computer-implemented method of claim 9, 10 or 17, wherein the plurality of design points is an intermediate set of design points, and bounding the plurality of design points using the set of geometric shapes comprises: bounding the intermediate set with an intermediate geometric shape of equal dimensionality to the design space; and iteratively, for the or each intermediate set: applying a clustering algorithm in dependence on the intermediate geometric shape to split the intermediate set into a plurality of intermediate sets; bounding each of the plurality of intermediate sets with a respective intermediate geometric shape; and in the event that a volume of the design space occupied by the respective intermediate geometric shapes after the splitting is no less than a volume of the design space occupied by the intermediate geometric shape before the splitting, adding the intermediate geometric shape before the splitting to the set of geometric shapes. 19. The computer-implemented method of claim 17 or 18, wherein obtaining the plurality of design points predicted or measured to lie within the feasible region of the design space comprises: obtaining respective models for one or more outputs of the physical system; and evaluating the respective models for the one or more the outputs at a plurality of design points in the design space to predict the plurality of design points lying within the feasible region of the design space. 20. The computer-implemented method of any one of claims 9, 10, or 17 to 19, further comprising determining an uninterrupted at least part of the feasible region of the design space by identifying a connected at least subset of the set of geometric shapes. 21. The computer-implemented method of claim 20, further comprising determining, for the uninterrupted at least part of the feasible region of the design space, at least one of a hypervolume, an exterior axis-aligned bounding box, and a largest interior axis-aligned bounding box. 22. The computer-implemented method of claim 20, comprising outputting, via a user interface, information indicative of said at least one of a hypervolume, an exterior axis-aligned bounding box, and a largest interior axis-aligned bounding box. 23. The computer-implemented method of any one of claims 9, 10 or 17 to 22, wherein the set of geometric shapes comprises at least one of a set of hyper-ellipsoids and a set of hyper-rectangles. 24. A method comprising: predicting a feasible region of a design space for a physical system using the computer-implemented method of any of claims 1 to 16; and manufacturing a prototype of the physical system with values of the design parameters falling within the predicted feasible region of the design space. 25. A method comprising: determining a representation of a feasible region of a design space for a physical system using the computer-implemented method of any of claims 9, 10, and 17 to 23; and manufacturing a prototype of the physical system with values of the design parameters falling within the feasible region of the design space as indicated by the determined representation of the feasible region. 26. A data processing system comprising means for carrying out the method of any of claims 1 to 23. 27. A computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method of any of claims 1 to 23.

Description

PREDICTING FEASIBLE DESIGNS FOR A PHYSICAL SYSTEM Technical Field The present disclosure relates to predicting feasible regions of a design space for a physical system. The disclosure has particular, but not exclusive, relevance to predicting feasible regions of a design space for a vehicle. Background Design of a complex system such as a vehicle typically begins with a definition of top-level requirements and constraints, then proceeds to progressively more detailed definitions of lower-level subsystems and components. Following this design phase, integration and testing start at the bottom-level components, progressively building back up to the top-level system. This is referred to as the “V model” of a system development lifecycle. During the design phase, feedback from downstream (lower-level) stages is iteratively provided to upstream (higher-level) stages until a set of designs of subsystems and components is determined. If a low-level subsystem or component is unable to meet requirements as imposed by a higher level component, system or subsystem, then the higher-level design may need to be modified. This may, in turn, change the requirements on other lower-level subsystems or components as they compensate for the modification. This can result in costly reworks and delays in development. Set-based design is a design paradigm in which, rather than fixing on a single design early on in the design process, design decisions are delayed until a late stage in the design process when more information is available. At a given stage of the process, a feasible set of designs is predicted, for example using simulation tools, providing flexibility to deal with uncertainties or adjustments in lower-level components or subsystems if and when they arise. In this way, reworks may be avoided, and development time reduced. A problem with this approach is that, for complex physical systems, the simulation tools used to predict the feasibility of designs at each stage are often very computationally expensive and time-consuming to run. Furthermore, a large number of simulation runs may be required to uncover the feasible set of designs, particularly if the dimensionality of the design space is large. Due to these challenges, companies can be prevented from reaping the benefits of less reworking and delays in later stages of the system development lifecycle. Summary According to an aspect of the present disclosure, there is provided a computer- implemented method of predicting a feasible region of a design space for a physical system. The method includes, for one or more iterations, determining a set of design points within the design space. Determining a given design point in the set includes, for one or more outputs of the physical system, sampling respective functions from respective probabilistic models each having a set of trainable parameters, wherein the respective functions predict values of the one or more outputs at design points within the design space, and selecting the given design point based on an objective function that penalises a distance from a boundary of the feasible region as predicted by values of the respective functions. The selecting of at least some of the design points in the set is performed in parallel. At each iteration, the method includes obtaining data comprising values of the one or more outputs of the physical system at each design point of the determined set of design points, and using the obtained data to determine updated values of the set of trainable parameters. The method includes, after the one or more iterations, predicting the feasible region of the design space using the data obtained during the one or more iterations. The one or more outputs of the physical system may be subject to respective constraints, and the feasible region may be a region of the design space in which the respective constraints for the one or more outputs of the physical system are all satisfied. By sampling the respective functions from the respective probabilistic models and independently selecting the design points based on predictions provided by the respective functions, determining the set of design points can be parallelised across potentially many nodes or processor cores. At each iteration, an arbitrarily large number of design points can be determined in a highly efficient manner with a processing cost that scales only linearly with the number of points. The determined design points are predicted by the probabilistic model(s) to lie close to the boundary of the feasible region, so that the method automatically progresses from exploring a large proportion of the design space at early iterations to concentrating on the most informative parts of the design space (i.e. near the ground truth boundary of the feasible region) at later iterations. As a result, the feasible region of the design space may be uncovered using relatively few rounds of empirical and/or simulated data collection. Predicti