Multi-instantiation Simulation for Large-scale Environments

Abstract

The present invention particularly relates to a computer-implemented method for simulating together a plurality of physical simulation instances included in a global physical simulation. The method includes creating a database of local simulation instances. The creating (S0) includes providing a set of local simulations. The creating further includes, for each local simulation in the set of local simulations, calculating a corresponding reduced model of the local simulation. The creating further includes, for each local simulation in the set of local simulations, storing the corresponding local simulation instance in the database. The corresponding local simulation instance includes the corresponding calculated reduced model. The method further includes selecting at least two local simulation instances in the database of local simulation instances. The method further includes calculating the global physical simulation. The calculating of the global physical simulation includes reusing each corresponding calculated reduced model included in each of the at least two selected local simulation instances.

Description

Technical Field

[0001] The present invention relates to the fields of engineering and physical simulation. Background Art

[0002] Nowadays, the development of renewable and sustainable technologies is highly regarded. To name just a few examples, there are renewable energies for coping with environmental regulations, the development of clean smart cities, and concepts for transportation.

[0003] In order to make the development of sustainable solutions feasible for the development of renewable and sustainable technologies, it is generally believed that numerical simulation tools must be used. In fact, the need to consider large-scale uncertain conditions (wind speed, building distribution, weather conditions during aircraft travel, etc.) and the interaction effects between different factors of a given scenario (different buildings, different wind turbines of an aircraft, different parts of an aircraft, etc.) make it infeasible to use experiments in the design stage.

[0004] Meanwhile, an established method for evaluating a design is to use numerical methods via dedicated software. However, setting up numerical simulations in the early design stage is very time-consuming, especially when the environment (the environment is also called a scenario, where a scenario is the 3D space in which the simulation is performed) to which the new design will be submitted changes repeatedly. This is mainly due to the fact that for each environmental change, the scenario must be adjusted accordingly, that is, it is necessary to re-mesh, re-apply boundary conditions and recalculate the entire result (see "Physics in Design: Real-time Numerical Simulation Integrated into the CAD Environment" by Marijn P. Zwier, Wessel W. Wits. Procedia CIRP, Volume 60, 2017, Pages 98 - 103, ISSN 2212 - 8271, https: / / doi.org / 10.1016 / j.procir.2017.01.054). Similarly, in the case of a large domain (i.e., a large scenario environment), the costs associated with simulation means (simulation time, data storage, etc.) increase exponentially (see "Computational Fluid Dynamics: Principles and Applications" by J. Blazek. ISBN: 978 - 0 - 08 - 044506 - 9. Elservier Science, 2005, 2nd Edition).

[0005] For large-scale simulations (e.g., fluid flow simulations, structural mechanics simulations, plasma dynamics simulations), or for any field of simulation that uses multi-instantiated physical simulations or requires the use of physical models simulated in a virtual world (e.g., video games or animated movies), it is necessary to run simulation tools for the entire domain. When faced with scenarios that require computing several simulations included in a large-scale simulation together, only solutions that run the entire set of all simulations are known. Such solutions are not suitable for instantiations of large-scale simulations that require a large number of changes to the scene layout.

[0006] In this context, there is still a need for improved methods for simulating multiple physical simulation instances included in a physical simulation together. Summary of the Invention

[0007] Accordingly, a computer-implemented method is provided for simulating multiple physical simulation instances included in a global physical simulation together. The method includes creating a database of local simulation instances. Creating (S0) includes providing a set of local simulations. The set of local simulations includes at least two local simulations. A local simulation is a physical simulation that is part of the global physical simulation and can be computed individually and independently of the multi-physical simulation. Each local simulation in the set of local simulations has been computed. Creating also includes, for each local simulation in the set of local simulations, computing a corresponding reduced model of the local simulation. Creating also includes, for each local simulation in the set of local simulations, storing the corresponding local simulation instance in the database. The corresponding local simulation instance includes the corresponding computed reduced model. The method also includes selecting at least two local simulation instances from the database of local simulation instances. The method also includes computing the global physical simulation. Computing the global physical simulation includes reusing each corresponding computed reduced model included in each of the at least two selected local simulation instances.

[0008] This constitutes an improved method for simulating multiple physical simulation instances included in a physical simulation together.

[0009] The method may include one or more of the following:

[0010] - The global physical simulation is associated with a global domain, and each local simulation is associated with a corresponding local domain, and the method further includes:

[0011] ● Before computing each corresponding reduced model of each local simulation:

[0012] ■ Selecting a corresponding region of interest of the local simulation, the corresponding region of interest being a non-empty subdomain of the corresponding local domain;

[0013] ● At the calculation of each corresponding reduced model for each local simulation:

[0014] ■ Each corresponding reduced model is calculated at the boundary of the corresponding region of interest;

[0015] ● At the calculation of the global physical simulation:

[0016] ■ Place the corresponding regions of interest of each local simulation of at least two selected simulation instances in the global domain; and

[0017] ■ Only the remaining part of the global domain is calculated, where the remaining part is the part of the global domain occupied by the non - regions of interest, and the global domain includes the regions occupied by each corresponding region of interest of each local simulation of at least two selected local simulation instances respectively;

[0018] - The method further includes, at the placement of the corresponding regions of interest of each local simulation of at least two selected local simulation instances, joining the boundaries of the corresponding regions of interest with the boundaries of the regions occupied by the corresponding regions of interest in the global domain;

[0019] - The method further includes, for each local simulation in the set of local simulations, after the calculation of the corresponding reduced model:

[0020] ● Define probes, which are points in the corresponding local domain of the local simulation, adjacent to the corresponding regions of interest, and each probe includes the simulation data of the local simulation, where the stored local simulation instances including the corresponding calculated reduced models also include the probes and the corresponding regions of interest;

[0021] - During the calculation of the global physical simulation, at least two of the at least two selected local simulation instances interact, and this interaction causes the probes of at least one of the at least two local simulation instances to be enriched, and due to the enriched probes, the corresponding calculated reduced model included in the local simulation instance whose probes are enriched is corrected;

[0022] - The method further includes, for each local simulation instance whose probes are enriched:

[0023] ● Before the correction of the corresponding calculated reduced model, calculate the difference between the set of all enriched probes and the set of corresponding probes before they were enriched;

[0024] ● Determine whether the difference exceeds a predetermined threshold; and

[0025] ● If it is determined that the difference exceeds the predetermined threshold, then correct the corresponding calculated reduced model;

[0026] - The method further includes:

[0027] ● At the creation of the database of local simulation instances, a machine learning algorithm is learned on the local simulation instances stored in the database, and the machine learning algorithm provides a corresponding relationship between the probes stored in the local simulation instances and the corresponding calculated reduced models stored in the local simulation instances for each local simulation instance in the database; and

[0028] ● For each local simulation instance whose probes are enriched, correcting the corresponding calculated reduced model included in the local simulation instance includes applying the machine learning algorithm, and the correction is performed based on the corresponding relationship;

[0029] - At each correction of the corresponding reduced model due to the enrichment of the probes, the simulation instance is stored in the database, and the simulation instance includes the corrected reduced model and the enriched probes;

[0030] - The method further includes after the calculation of the global physical simulation:

[0031] ● Adding a new local simulation instance to the database of local simulation instances, and the addition of the new local simulation instance includes:

[0032] ■ Providing a new local simulation that has been calculated and is associated with a corresponding local domain;

[0033] ■ Selecting a corresponding region of interest of the new local simulation, and the corresponding region of interest is a non - empty sub - domain of the corresponding local domain;

[0034] ■ Calculating a corresponding reduced model of the new local simulation at the boundary of the corresponding region of interest;

[0035] ■ Defining probes, where the probes are points of the corresponding local domain that are adjacent to the corresponding region of interest, and each probe includes simulation data of the new local simulation; and

[0036] ■ Storing the new local simulation instance in the database, and the new local simulation instance includes the corresponding reduced model of the new local simulation, the probes of the new local simulation, and the corresponding region of interest of the new local simulation,

[0037] The addition results in the new simulation instance being one of the local simulation instances in the database of local simulation instances, and the method further includes:

[0038] ● After the addition of the new local simulation instance, re - learning the machine learning algorithm on the database of simulation instances;

[0039] ● Re - selecting at least two local simulation instances in the database of local simulation instances, and the at least two re - selected local simulation instances include the new local simulation instance; and

[0040] ● Recalculate the global physical simulation by using at least two reselected local simulation examples;

[0041] - The method further includes modifying the global physical simulation after re - learning and before recalculating;

[0042] - Adding and recalculating are iterated;

[0043] - Each corresponding local domain of each local simulation includes a corresponding physical object, and the local simulation simulates the corresponding physical behavior associated with the corresponding physical object; and the global physical simulation simulates the physical behavior of the set of all corresponding physical objects; and / or

[0044] - All local simulations are perturbations of a given local simulation, and the given local simulation is part of the set of local simulations.

[0045] A computer program is also provided, which includes instructions for performing the method.

[0046] A computer - readable storage medium having a computer program recorded thereon is also provided.

[0047] A computer is also provided, which includes a processor coupled to a memory and a display, and the computer program is recorded on the memory. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Examples of the present invention will now be described by way of non - limiting examples and with reference to the accompanying drawings, wherein:

[0049] - Figure 1 A flowchart showing an example of the method is shown;

[0050] - Figure 2 A flowchart showing an example of creating a database of local simulation examples according to the method is shown;

[0051] - Figure 3 A flowchart showing an example of calculating the global physical simulation according to the method is shown;

[0052] - Figure 4 A flowchart showing an example of reusing each corresponding calculated reduced model according to the method is shown;

[0053] - Figure 5 An example of a computer of the present invention is shown;

[0054] - Figure 6 An example of simulating a plurality of physical simulation examples together according to the prior - art method is shown;

[0055] -Figure 7 Shows an example of simulating multiple physical simulation instances together according to the method;

[0056] - Figures 8-9 Shows two screenshots that show examples of selecting corresponding regions of interest;

[0057] - Figure 10 Shows a screenshot illustrating an example of defining a probe;

[0058] - Figure 11 Shows a screenshot illustrating an example of placing a corresponding region of interest;

[0059] - Figure 12 Shows a screenshot illustrating an example of placing a corresponding region of interest;

[0060] - Figure 13 Shows a diagram of an example of calculating a reduced model;

[0061] - Figure 14 Shows an example of a base element; and

[0062] - Figure 15 Shows an implementation of a junction. Detailed Description

[0063] Referring Figure 1 to the flowchart of [[ID=]], a computer-implemented method is provided for simulating multiple physical simulation instances included in a global physical simulation together. The method includes creating a database of S0 local simulation instances. Creating S0 includes providing a set of S10 local simulations. The set of local simulations includes at least two local simulations. A local simulation is a physical simulation that is part of the global physical simulation and can be calculated separately and independently of the global physical simulation. Each local simulation in the set of local simulations has been calculated. Creating S0 also includes, for each local simulation in the set of local simulations, calculating a corresponding reduced model of the S30 local simulation. Creating S0 also includes, for each local simulation in the set of local simulations, storing the corresponding S50 local simulation instance in the database, the corresponding local simulation instance including the corresponding calculated reduced model. The method also includes selecting S1 at least two local simulation instances from the database of local simulation instances. The method also includes calculating S2 the global physical simulation. Calculating S2 of the global physical simulation includes reusing S220 each corresponding calculated reduced model included in each of the at least two local simulation instances selected.

[0064] This method improves the co-simulation of multiple physical simulation instances included in a global physical simulation. First, the local part of the global physical simulation (i.e., the local simulation where the calculated reduced model is reused) has already been calculated. Thus, when calculating the global physical simulation, this method does not recalculate the already calculated local part. In other words, this method allows the calculation of a physical simulation while co-simulating the local part of the physical simulation, which is relatively fast and conserves computer resources. Second, when calculating the global physical simulation, only the reduced models of the already calculated local parts of the global physical simulation are reused. The reduced models of the simulation require fewer storage and computing resources than the simulation itself, but still capture the physical properties of the simulation. Thus, each reused reduced model is substantially equivalent to the simulation result of the corresponding local simulation. This means that this method not only calculates the physical simulation including the local part in a faster and more economical way, but also guarantees a certain physical accuracy at the same time. In addition, in the example, the time scale of each local simulation is different from the time scale of the global physical simulation. These multi-scale problems may make the calculation of the global physical simulation complex and / or expensive in terms of time and / or computing resources because different physical models may evolve on different time scales, all of which need to be considered. By not recalculating the local simulation, the calculation S2 of the global physical simulation according to the present invention can consider only the time scale of the global physical simulation without considering the time scale of the local simulation, thus reducing or even avoiding these multi-scale problems.

[0065] In all of this specification, including the above and the following, at least one means one or more, and at least two means two or more.

[0066] This method is computer-implemented. This means that the steps (or substantially all steps) of this method are performed by at least one computer or any similar system. Thus, the steps of this method may be performed by a computer either fully automatically or semi-automatically. In the example, at least some of the steps of this method may be triggered by user-computer interaction. The required level of user-computer interaction may depend on the foreseen level of automation and be balanced with the need to fulfill the user's wishes. In the example, this level may be user-defined and / or pre-defined.

[0067] A typical example of the computer-implemented manner of the method is to use a system (e.g., a computer system) suitable for this purpose to perform the method. The system may include a processor coupled to a memory and a graphical user interface (GUI), with a computer program recorded on the memory, the computer program including instructions for performing the method. The memory may also store a database. The memory is any hardware suitable for such storage and may include several physically different parts (e.g., one part for the program and possibly one part for the database).

[0068] Figure 5 An example of the system is shown, where the system is a client computer system such as a user's workstation.

[0069] The example client computer includes a central processing unit (CPU) 1010 connected to an internal communication bus 1000, and a random access memory (RAM) 1070 also connected to the bus. The client computer is further provided with a graphics processing unit (GPU) 1110, and the graphics processing unit (GPU) 1110 is associated with a video random access memory 1100 connected to the bus. In the art, the video RAM 1100 is also referred to as a frame buffer. A mass storage device controller 1020 manages access to a mass storage device such as a hard disk drive 1030. Mass storage devices suitable for tangibly embodying computer program instructions and data include all forms of non-volatile memory, for example including semiconductor memory devices such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM disks 1040. Any of the foregoing may be supplemented by, or incorporated in, a specially designed ASIC (application specific integrated circuit). A network adapter 1050 manages access to a network 1060. The client computer may also include a haptic device 1090, for example, a cursor control device, a keyboard, etc. In the client computer, the cursor control device is used to allow a user to selectively position a cursor at any desired location on a display 1080. Additionally, the cursor control device allows the user to select various commands and input control signals. The cursor control device includes a plurality of signal generating devices for inputting control signals to the system. Typically, the cursor control device may be a mouse, and the buttons of the mouse are used to generate signals. Alternatively or additionally, the client computer system may include a touchpad and / or a touchscreen.

[0070] A computer program may include instructions executable by a computer, the instructions including units for causing the above system to execute the method. The program may be recorded on any data storage medium including the memory of the system. For example, the program may be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations thereof. The program may be implemented as an apparatus (e.g., a product tangibly embodied in a machine-readable storage device) for execution by a programmable processor. Method steps may be performed by the programmable processor executing the instruction program to perform the functions of the method by operating on input data and generating output. Thus, the processor may be programmable and coupled to receive data and instructions from a data storage system, at least one input device, and at least one output device, and to send data and instructions to them. The application program may be implemented in a high-level procedural programming language or an object-oriented programming language, or in assembly language or machine language if desired. In any case, the language may be a compiled language or an interpreted language. The program may be a full installation program or an update program. Applying the program to the system in any case results in instructions for executing the method.

[0071] The system may be any combination of a CAD system, a CAE system, a CAM system, a PDM system, and / or a PLM system. In these different systems, modeling objects are defined by corresponding data. A modeling object is any object defined by data, for example, stored in a database. By extension, the expression "modeling object" designates the data itself. Depending on the type of system, modeling objects may be defined by different kinds of data. Thus, they may be referred to as CAD objects, PLM objects, PDM objects, CAE objects, CAM objects, CAD data, PLM data, PDM data, CAM data, CAE data. However, these systems are not mutually exclusive, since modeling objects may be defined by data corresponding to any combination of these systems. The system may thus very well be both a CAD and a PLM system, as will be apparent from the definition of such a system provided below.

[0072] A CAD system additionally denotes any system that is at least suitable for designing a modeled object based on a graphical representation of the modeled object, for example, CATIA. In this case, the data defining the modeled object includes data that permits the representation of the modeled object. For example, a CAD system may use edges or lines (and in some cases surfaces or faces) to provide a representation of a CAD modeled object. Lines, edges, or faces can be represented in various ways such as non-uniform rational B-splines (NURBS). In particular, a CAD file contains specifications according to which a geometric structure can be generated, which in turn permits the generation of a representation. The specifications of the modeled object can be stored in a single CAD file or multiple CAD files. The typical size of a file representing a modeled object in a CAD system is in the range of one megabyte per part. And a modeled object typically can be an assembly composed of thousands of parts.

[0073] A PLM system additionally denotes any system that is suitable for managing modeled objects representing a physically manufactured product (or a product to be manufactured). Thus, in a PLM system, the modeled object is defined by data suitable for manufacturing a physical object. These data can typically be dimensional values and / or tolerance values. In order to correctly manufacture an object, it is actually preferable to have such values.

[0074] A CAM solution additionally denotes any solution, software, or hardware that is suitable for managing the manufacturing data of a product. Manufacturing data generally includes data related to the product to be manufactured, the manufacturing process, and the required resources. A CAM solution is used to plan and optimize the entire manufacturing process of a product. For example, a CAM solution can provide a CAM user with information about feasibility, the duration of the manufacturing process, or the quantity of resources (e.g., a specific robot) that can be used for a particular step of the manufacturing process; and thus permits making decisions regarding management or the required investment. CAM is a subsequent process after the CAD process and a potential CAE process. Such a CAM solution is provided by Dassault Systèmes under the trademark provided.

[0075] A CAE solution additionally denotes any solution, software, or hardware that is suitable for analyzing the physical behavior of a modeled object. A well-known and widely used CAE technique is the finite element method (FEM), which typically involves dividing a modeled object into elements capable of calculating and simulating the physical behavior through equations. Such a CAE solution is provided by Dassault Systèmes under the trademark Provided. Another developing CAE technology involves modeling and analyzing a complex system composed of multiple components from different physical domains without CAD geometry data. CAE solutions allow simulations and thus optimize, improve, and validate the product to be manufactured. Such CAE solutions are provided by Dassault Systèmes under the trademark Provided.

[0076] PDM stands for Product Data Management. A PDM solution refers to any solution, software, or hardware suitable for managing all types of data related to a specific product. PDM solutions can be used by all participants involved in the product lifecycle: mainly engineers, but also project managers, finance personnel, salespeople, and buyers. PDM solutions are generally based on a product-oriented database. PDM solutions allow participants to share consistent data about their products and thus prevent participants from using divergent data. Such PDM solutions are provided by Dassault Systèmes under the trademark Provided.

[0077] This method is used to simulate multiple physical simulation instances included in a global physical simulation together.

[0078] A physical simulation is any simulation from one or more physical domains, such as electronics, electricity, mechanics, mechatronics, fluid mechanics, gravitational mechanics, statistical mechanics, wave physics, statistical physics, particle systems, hydraulic systems, quantum physics, geophysics, astrophysics, chemistry, aerospace, geomagnetism, electromagnetism, plasma physics, or computational fluid dynamics (CFD). A physical simulation can also be a multi-physical simulation, i.e., a simulation involving multiple physical domains. It can be a simulation of at least one behavior over time of any physical or multi-physical system from one or more physical domains including the list of examples above.

[0079] "Global" means that the physical simulation includes at least one local part, hereinafter called a local simulation, which is a physical simulation that is part of the global physical simulation but can be calculated separately and independently of the global physical simulation. It can be understood that the global simulation can be a multi-physical simulation, where each local part is a physical simulation from a corresponding physical domain. It can be understood that any local simulation can also be a multi-physical simulation. It should be understood that the calculation of the global simulation involves the calculation of the local simulation and further calculations. The further calculations depend on the calculation of the local simulation, and the calculation of the local simulation is not sufficient to perform the calculation of the global calculation.

[0080] A physical or multi - physical system is any real - world system or physical entity whose behavior (e.g., over time) can be simulated via at least one physical model from at least one physical domain (such as one of the examples of the physical domains above). The real - world system or physical entity can be a real - world object, an electronic product, an electrical product, a mechanical product, a chemical product, a mechatronic product, a particle system, or an electromagnetic product. The physical model can be an electronic model, an electrical model, a mechanical model, a statistical model, a particle model, a hydraulic model, a quantum model, a geological model, an astronomical model, a chemical model, an electromagnetic model, or a fluid model. The physical model can be a system of equations of one or more equations, e.g., one or more differential equations and / or partial differential equations and / or algebraic equations. A multi - physical system typically has subsystems, where the subsystems themselves are physical or multi - physical systems and the subsystems are fully connected via physical relationships or logical relationships given, for example, by physical laws. Thus, a multi - physical system is used to represent a real - world system or any physical entity that includes subsystems, where these subsystems are linked together by physical or logical relationships (e.g., mechanical relationships (e.g., connections corresponding to the transfer of force or motion), electrical relationships (e.g., corresponding to electrical connections in, for example, an electrical circuit), hydraulic relationships (e.g., corresponding to conductors for transmitting flux), logical relationships (e.g., corresponding to information flow), fluid relationships (e.g., corresponding to fluid flow), chemical relationships, and / or electromagnetic relationships). The system is called "multi - physical" because the physical or logical relationships of a multi - physical system can belong to multiple physical domains (although this is not necessary).

[0081] A physical or multi - physical system can correspond to an industrial product to be manufactured in the real world after its virtual design, such as (for example, mechanical) parts or assemblies of parts, or more generally, any rigid - body assembly (such as a moving mechanism), a rigid - body mechanism. CAD and / or CAE software solutions allow the design of products in various and unrestricted industrial fields, including: aerospace, architecture, construction, consumer goods, high - tech equipment, industrial equipment, transportation, marine and / or offshore or shipping. Thus, a physical or multi - physical system can represent such an industrial product: the industrial product can be part (or all) of a land vehicle (including, for example, automotive and light - truck equipment, racing cars, motorcycles, trucks and motor vehicle equipment, trucks and buses, trains), part (or all) of an aircraft (including, for example, airframe equipment, aerospace equipment, propulsion equipment, defense products, aviation equipment, space equipment), part (or all) of a naval vehicle (including, for example, naval equipment, commercial ships, offshore equipment, yachts and workboats, ship equipment), mechanical parts (including, for example, industrial manufacturing machinery, heavy mobile machinery or equipment, installation equipment, industrial equipment products, manufactured metal products, tire - manufacturing products), mechatronic or electronic parts (including, for example, consumer electronics, safety and / or control and / or instrumentation products, computing and communication equipment, semiconductors, medical equipment and devices), consumer goods (including, for example, furniture, home and garden products, leisure products, fashion products, products of hard - goods retailers, products of soft - goods retailers), packaging (including, for example, food and beverage and tobacco, beauty and personal care, household - product packaging). Global physical simulation can be a simulation of the behavior of at least one industrial product to be manufactured in the real world, for which the industrial product has been designed. The simulation can simulate at least one behavior (e.g., evolution over time) of the at least one industrial product after the design of the at least one industrial product. After this method, after simulating at least one industrial product by this method, the at least one industrial product can be manufactured in the real world.

[0082] Simulating a physical or multi - physical system modeled by at least one physical model generally includes: calculating an approximation of the physical behavior of the system over time (e.g., evolution over time) by computing at least one physical model, and / or storing the results and / or displaying the results. Before computing at least one physical model, at least one grid (or mesh) and / or at least one time step and / or at least one simulation parameter can be provided. This provision can be performed according to a user action. The computing generally (but not always) includes discretizing one or more equations of at least one physical model according to at least one grid and / or at least one time step. The discretization can be performed by using any known numerical method.

[0083] Global or local simulation includes a simulation state (which may be referred to as "state" for simplicity hereinafter). The state is a representation of the physical state of a physical system at a given time, and the behavior of the physical system over time is simulated by this simulation. For example, the physical state can be any physical quantity at a given time. A physical quantity (also known as a quantity of physics) is a physical property of a phenomenon, object, or substance that can be quantified by measurement. Physical quantities can be, but are not limited to: length, mass, time, current, temperature, amount of substance, luminous intensity, absorptance, absorbed dose rate, acceleration, angular acceleration, angular momentum, angular rate (or angular velocity), area, areal density, capacitance, catalytic activity, catalytic activity concentration, chemical potential, crack, current density, equivalent dose, dynamic viscosity, charge, charge density, electric displacement, electric field strength, electrical conductivity, electrical conductance, electric potential, resistance, resistivity, energy, energy density, entropy, force, frequency, fuel efficiency, half-life, heat, heat capacity, heat flux density, illuminance, impedance, impulse, inductance, irradiance, intensity, jerk, snap (or jounce), kinematic viscosity, linear density, luminous flux (or optical power), Mach number (or Mach), magnetic field strength, magnetic flux, magnetic flux density, magnetization, mass fraction, (mass) density (or volumetric density), mean lifetime, molar concentration, molar energy, molar entropy, molar heat capacity, moment of inertia, momentum, magnetic permeability, permittivity, plane angle, power, pressure, pop, (radioactive) activity, (radioactive) dose, radiance, radiant intensity, reaction rate, refractive index, magnetic resistance, solid angle, velocity, specific energy, specific heat capacity, specific volume, spin, strain, stress, surface tension, temperature gradient, thermal conductivity, torque, speed, volume, volume flow rate, wavelength, wavenumber, wave vector, weight, work, Young's modulus. The state can also be a vector of physical quantities. The simulation typically includes an initial time and a final time, and includes at least one time step between the initial time and the final time. Each time step has a state, including the initial time and the final time.

[0084] Computing the simulation represents computing all simulation results, and the simulation results are data containing information representing the state. Thus, computing the simulation represents essentially computing all information representing all states at all times. The simulation of the present invention can be computed by using any known numerical method and / or any existing computer program capable of deriving and / or displaying simulation results at different time steps.

[0085] The method includes creating a database of S0 local simulation instances.

[0086] Creating S0 includes providing a set of S10 local simulations.

[0087] Each local simulation in the set of local simulations has been computed. In an example, providing S10 includes loading and / or accessing (e.g., in a database) the set of local simulations that have been computed. Thus, providing S10 represents making the data of the set of local simulations available to a system for performing the method, e.g., the data is loaded into a memory (e.g., volatile memory) of the system or can be retrieved by the system from a memory (e.g., non-volatile memory). In an example, each local simulation in the set can be computed and the result of the computation stored in a database before providing S10. In all cases, at providing S10, all local simulations in the set have been computed, which means that all simulation results of all local simulations are available, e.g., for running and / or displaying the local simulations and / or computing their corresponding reduced models. The set of local simulations includes at least one local simulation.

[0088] Each local simulation is a physical simulation that is part of a global physical simulation and can be computed separately and independently of the global physical simulation. As already said, a local simulation is not sufficient to perform the computation of the global computation.

[0089] A local simulation is part of a global physical simulation when computing the global physical simulation requires using results obtained during the computation of the local simulation and / or data derived from such results. A local simulation can be computed separately and independently of the global physical simulation when computing the local simulation does not require using any results obtained during the computation of the global physical simulation and / or any data derived from such results. In other words, each local simulation represents an independent sub-simulation (or local part) of the global physical simulation. In an example, a local simulation is part of a global physical simulation when it is modeled by at least one physical model that is also used to model the global physical simulation. In these examples, "computed separately and independently" means that the at least one physical model can be solved and / or discretized and / or approximated and / or computed without solving and / or discretizing and / or approximating other physical models involved in the modeling of the global physical simulation. In other words, the at least one physical model is self-consistent and / or self-sufficient for running and / or computing the local simulation. In these examples, there can be at least one other physical model that is involved in the modeling of the global physical simulation and takes as input and / or parameter the result of solving and / or discretizing and / or approximating the at least one physical model and / or data derived from such result.

[0090] To illustrate the definitions of local simulation and global simulation, non-limiting examples are now given. The simulation of a wind farm including wind turbines is taken as an example. The global physical simulation is the overall behavior of the wind farm under a given wind condition. Each local simulation individually simulates the behavior of one wind turbine under a given wind condition. The simulation for calculating the overall behavior of the wind farm requires the simulation of the behavior of each wind turbine in the field. However, the simulation for calculating a behavior of one wind turbine can be done without simulating the entire wind farm.

[0091] The creation S0 of a database of local simulation examples includes, for each local simulation in the set of local simulations, calculating (S30) the corresponding reduced model of the local simulation.

[0092] The computed reduced model of the simulation is a model computed from the simulation using reduced order modeling techniques. Reduced order modeling (ROM) is a technique for reducing the dimension and computational complexity of a mathematical model. The ROM (hereinafter referred to as the reduced model) is constructed from a high-fidelity simulation (e.g., the computed full simulation) and can subsequently be used to generate simulations for lower-level computations. An example of a ROM method is Galerkin projection (e.g., see Rowley, Clarence W., Tim Colonius, and Richard M. Murray, “Model reduction for compressible flows using POD and Galerkin projection.” Physica D: Nonlinear Phenomena 189.1-2 (2004): 115-129, and Barone, Matthew F. et al., “Reduced order modeling of fluid / structure interaction.” Sandia National Laboratories Report, SAND No 7189 (2009): 44-72), which is particularly common in fluid dynamics. The Galerkin projection method uses proper orthogonal decomposition (POD) to reduce the dimension of the flow simulation and then finds the dynamics in that reduced space.There are other methods on this basis, for example, reduced basis methods and balanced truncation (see, e.g., Veroy, K and A. T. Patera, "Certified real-time solution of the parametrized steady incompressible Navier–Stokes equations: rigorous reduced-basis a posteriori error bounds." International Journal for Numerical Methods in Fluids 47.8-9 (2005): 773-788, and Rowley, Clarence W, "Model reduction for fluids, using balanced proper orthogonal decomposition." Modeling And Computations In Dynamical Systems: In Commemoration of the 100th Anniversary of the Birth of John von Neumann. 2006. 301-317). Generally speaking, ROM uses techniques such as POD or singular value decomposition (SVD) to calculate a basis representing the main components of the simulation based on the states of the computed full simulation. SVD provides a way to decompose a matrix into singular vectors and singular values. SVD allows the discovery of some of the same type of information as eigen decomposition and can represent, for example, the main components of a mechanical system. "Model reduction" is also mentioned in the Encyclopedia of Computational Mechanics by Francisco Chinesta, Antonio Huerta, Gianluigi Rozza, and Karen Willcox (edited by Erwin Stein, René de Borst, and Thomas J. R. Hughes, 2004). The calculation of the reduced model according to this method uses any technique of ROM, such as the techniques described in the above references. The reduced model of the simulation of the present invention can also be called a surrogate model of the simulation.

[0093] Each respective computed reduced model of each computed local simulation includes a basis having elements. The elements of these bases may hereinafter be referred to as basis elements. The basis elements are components of a factorization computed from all local simulation data. The basis elements may also be referred to as state modes. In an example, the basis elements are energy modes of the physical system being simulated by the local simulation. At any time, each state of the local simulation can be generated by a linear combination of a finite number of state modes. The linear combination approximates the state and may be referred to as a reduced state.

[0094] The basis can be written as B = (e 1 ; e 2 ; … e n ), where e i is a basis element. Any state state(t) at time t can be approximated by its reduced state PState(t), which is a linear combination of these basis elements, as follows:

[0095] PState(t) = w 1 (t) * e 1 + w 2 (t) * e 2 + … + w n (t) * e n (Equation (1))

[0096] Here, w i are the weights for the contribution of each basis element to compute the reduced state PState(t). The basis B remains constant over time, and only the weights can evolve over time. Updating the weights in a timely manner advances the simulation results in time. Computing the reduced model of the simulation includes computing all elements of the basis B and all weights at all times t that are time steps included between the initial time and the final time of the simulation. Thus, once the reduced model is computed, by using Equation (1), any reduced state PState(t) representing any state state(t) of the simulation computed at any time step t is available.

[0097] Figure 13 is a diagram showing an example of the computation of the reduced model. This computation takes as input the states 1400 of the full simulation computed at all time steps of the full simulation. This computation includes a computation 1402 of the basis, which is based on all the states 1400 of the computed full simulation. In Figure 13 's example, the computed basis is the basis of the computed snapshots 1404 of the full simulation. In other words, the basis elements are the computed snapshots of the full simulation in this example. Figure 14 Three screenshots of snapshots 1408, 1410, and 1412 are shown in

[0098] Creating S0 also includes storing, in a database, a respective local simulation instance corresponding to each local simulation in a set of local simulations. The respective local simulation instance includes a respective computed reduced model.

[0099] The local simulation instances of the local simulations form data representing the local simulations. The local simulation instance includes a respective computed reduced model of the local simulation. The local simulation instance may also include data relative to the local simulation, e.g., the state of the local simulation (and / or data derived from the state) and / or the simulation result of the local simulation (and / or data derived from the simulation result). In general, the expression "instance of a simulation" refers to a specific occurrence of a simulation such that the system performing the method has an example of the simulation. The database of local simulation instances may also be a library of local simulation instances.

[0100] A non - limiting example showing the definition of a local simulation instance is as follows: The local simulation is a simulation of a wind turbine under a given wind condition. The local simulation instance forms data representing the simulation of the wind turbine since it includes a computed reduced model of the computed simulation of the wind turbine under the given wind condition and may include data of the computed simulation relative to the wind turbine under the given wind condition.

[0101] The method also includes selecting S1 at least two local simulation instances in the database of local simulation instances.

[0102] The selection S1 of at least two local simulation instances in the database of local simulation instances may be performed according to a user action. Typically, the user accesses the database of local simulation instances and selects S1 local simulation instances. It should be understood that a local simulation instance may be selected S1 at least twice (i.e., two or more times), in which case the at least two local simulation instances include at least two exemplars of the same local simulation instance.

[0103] The method also includes computing S2 a global physical simulation. The computing S2 of the global physical simulation includes reusing S220 each respective computed reduced model included in each of the at least two local simulation instances selected.

[0104] Reusing the computed reduced models of local simulations during the computation S2 of the global physical simulation includes using, in the computation, one or more reduced states of the computed reduced models of local simulations and / or data derived from one or more reduced states of the computed reduced models of local simulations. In an example, the simulation state of at least one local simulation among at least two selected local simulation instances and / or data derived from these simulation states can generally form, for example, the (multiple) inputs and / or (multiple) parameters and / or (multiple) boundary conditions of one or more physical models intervening at different time steps in the modeling of the global physical simulation. In these examples, reusing each corresponding computed reduced model of S220 represents that, when forming the (multiple) inputs and / or (multiple) parameters of the one or more physical models, the reduced state of at least one local simulation and / or data derived from these reduced states replace the simulation state and / or data derived from these simulation states.

[0105] It should be understood that although each local simulation in the set of local simulations is part of the global physical simulation, the computation S2 of the global physical simulation does not necessarily include reusing all the corresponding computed reduced models of all local simulations. In other words, during the computation S2 of the global physical simulation, the independent local parts of the global physical simulation can still be computed without replacing the local parts with the corresponding reduced models of the corresponding local simulations. However, at least two independent local parts (corresponding to at least two selected local simulation instances) are replaced by two corresponding reduced models.

[0106] In an example, the global physical simulation is associated with a global domain, and each local simulation is associated with a corresponding local domain. In these examples, the method further includes selecting S20 a corresponding region of interest of the local simulation before computing S30 each corresponding reduced model of each local simulation. The corresponding region of interest is a non-empty subdomain of the corresponding local domain. In these examples, at the computation S30 of each corresponding reduced model of each local simulation, each corresponding reduced model is computed at the boundary of the corresponding region of interest. In these examples, the method further includes, at the computation S2 of the global physical simulation, placing S210 the corresponding region of interest of each local simulation among the at least two selected simulation instances in the global domain. Only the remaining part of the global domain is computed. The remaining part is the part of the global domain occupied by the non-region of interest. The global domain includes the regions respectively occupied by the corresponding regions of interest of each local simulation among the at least two selected local simulation instances.

[0107] The simulation domain is typically meshed or discretized. For certain physical simulations (e.g., large-scale physical simulations), meshing the simulation domain can be tricky and multi-scale problems may be encountered and addressed. Multi-scale problems typically refer to situations where local portions of the simulation domain need to be meshed at a different scale (e.g., with a different spatial discretization) compared to other portions of the simulation domain. Typically, a global physical simulation may require a specific meshing of the global domain, and each local simulation in a collection of local simulations may require (e.g., respectively require) a different meshing of each corresponding local domain. Then the global physical simulation and / or the adapted physical modeling must be computed based on these different meshes. Thus, the computation S2 of the global physical simulation may be more expensive in terms of time and / or computational resources. The present invention overcomes these difficulties because not every part of the global domain occupied by the corresponding regions of interest is computed. The corresponding reduced models computed at the boundaries of these regions of interest are reused, and thus, only the meshing of the remaining parts of the global domain is involved in the computation of the global physical simulation. Thus, the present invention avoids or significantly reduces multi-scale problems.

[0108] In the present invention, a domain (respectively a sub-domain) is a domain (respectively a sub-domain) in its mathematical sense. The boundary of a domain (respectively a sub-domain) should also be understood in its mathematical sense. The domain of the present invention can be a two-dimensional or three-dimensional domain. The local domain and the global domain are simulation domains. A simulation domain is a domain that models a physical region of the real world in which (a) physical phenomenon(s) related to the simulation occur(s). Referring to a simulation as being associated with a domain means that the domain is the simulation domain of that simulation. In an example, each corresponding local domain and global domain are meshed respectively. For example, at the initial stage of the method, meshing can be performed according to user actions. In an example, each corresponding local domain corresponds to (e.g., is equal to, equivalent to) a corresponding sub-domain of the global domain. In these examples, each corresponding local domain can model the same physical region of the real world, which is different from the corresponding sub-region of the real world physical region modeled by the corresponding sub-domain of the global domain.

[0109] Now a non-limiting example illustrating the definitions of the global domain and the local domain is discussed. This example relates to the example of simulating a wind farm including wind turbines discussed previously. The global domain is a three-dimensional volume that models the wind farm under wind conditions. Each local domain is a three-dimensional volume that contains (e.g., all of) a part of a wind turbine and models the wind turbine and the air around the wind turbine.

[0110] The selection S20 of the corresponding region of interest (also referred to as the region of interest) for the local simulation can be performed automatically. In this case, the selection S20 can be performed to meet one or more of the following criteria:

[0111] – "Change in scalar value on the corresponding local domain": In this case, since all simulation results and the calculated state of the local simulation are known, the method can calculate and / or identify the change in one or more scalar values associated with the local simulation on the corresponding local domain based on these results and states. For example, changes in energy and / or energy exchange. Then, the method can automatically select the region of interest based on these changes. For example, by selecting a smaller box as the region of interest, in which all changes (or a predetermined large portion of the changes) are greater than a predetermined threshold and / or less than a predetermined maximum value. The change in one or more scalar values can be calculated according to the state mode. For example, according to the energy mode when calculating the change in energy or energy exchange. Such a criterion selects the corresponding region of interest as part of the corresponding local domain where a substantial portion of a given physical phenomenon (e.g., energy exchange) occurs. The predetermined threshold and / or the predetermined maximum value can be selected according to user actions (e.g., at the initial stage of the method).

[0112] – "Smaller box around the solid": In this case, the local simulation simulates a physical phenomenon involving a solid such as a physical object or product. The corresponding local domain typically contains a representation of the solid (e.g., geometry), and then the method automatically selects a smaller box S20 that contains the solid.

[0113] Typically, the selection S20 of the corresponding region of interest for the local simulation can also be performed to meet any reasonable combination of the above criteria. The method can, for example, select the corresponding region of interest such that the region of interest contains both the solid included in the local domain and a significant change in the scalar (e.g., a physical quantity such as energy) around the solid. Additionally, the method can automatically prevent the selected corresponding region of interest from being empty and / or too large (e.g., larger than the corresponding local domain and / or larger than the global domain).

[0114] In an example, the selection S20 of the corresponding region of interest for the local simulation can be performed according to user actions. In these examples, the user can be automatically prohibited from selecting an empty and / or too large subdomain. In an example, each local simulation can be displayed to the user on the GUI, and the user interacts with the GUI (e.g., using a touch or haptic device) to select each region of interest on each displayed local simulation to perform the selection S20.

[0115] Now refer to Figure 8 and Figure 9 Describe an example of the selection S20 of the corresponding region of interest according to user actions. The user loads S10 the local simulation 82. The local simulation 82 and its corresponding local domain 84 are displayed in the window 80 of the GUI. AlthoughFigure 9 and Figure 10 are screenshots, but it should be understood that they may be videos such as the progress of a partial simulation over time displayed within window 80. By using a haptic device or touch, the user forms a corresponding region of interest 86 that he / she wishes to select within the corresponding local domain 84. The polyline 90 represents the boundary of the corresponding region of interest 86. The user can form the corresponding region of interest 86 by forming the boundary of the corresponding region of interest 86 (here the polyline 90).

[0116] In the example, for each corresponding reduced model of each local simulation at the boundary of the corresponding region of interest, S30 is calculated. Calculating S30 the corresponding reduced model at the boundary of the corresponding region of interest includes calculating the reduced state of the corresponding local simulation on or substantially on the boundary of the corresponding region of interest. For example, all reduced states of the corresponding local simulation can be calculated, but only those on or substantially on the boundary of the corresponding region of interest can be retained. In this case, the reduced states inside the corresponding region of interest will not be retained. The reduced states calculated at the boundary of the corresponding region of interest of the region occupying the global domain are sufficient to calculate S2 the global physical simulation at the junction between the region occupied by the corresponding region of interest and the rest of the global domain. This allows the rest to be simulated and / or calculated without having to recalculate the occupied region. In the example, in order to model and / or simulate and / or approximate and / or calculate the communication and / or junction and / or exchange between the occupied region of the global domain and the rest, it is actually sufficient to use the reduced states calculated at the boundary of the occupied region in the calculation.

[0117] Placing S210 the corresponding region of interest in the global domain includes replacing the region of the global domain with the corresponding region of interest. The placement S210 can be performed according to a user action. In the example, for example, the corresponding region of interest is displayed on the GUI, and the user moves (or shifts) the corresponding region of interest into the global domain that is also displayed nearby. The movement of the corresponding region of interest can be performed by interacting with the GUI (e.g., using touch or a haptic device). For example, as is known in the art, the user performs a drag-and-drop operation. After moving the corresponding region of interest into the global domain, the method can automatically replace the region of the global domain on which the corresponding region of interest has been moved with the corresponding region of interest. If several corresponding regions of interest are placed during the placement S210 of the corresponding region of interest, the method can automatically prevent any overlap of the regions of interest. In the example, the user inputs, for example, by using a keyboard, where the corresponding region of interest is to be placed in the global domain.

[0118] Now refer to Figure 11Discuss an example of placing corresponding regions of interest for S210. In this example, for instance, window 110 is displayed to the user on the GUI. The frame 112 within window 110 includes three previously selected corresponding regions of interest 114 for three partial simulations. One of the corresponding regions of interest can be Figure 9 the corresponding region of interest 96. Although Figure 11 is a screenshot, it should be understood that it may be a video of each corresponding region of interest of each partial simulation, such as the progress over time, displayed within window 110. The user moves each corresponding region of interest he wishes to place into the global domain 118 of the global physical simulation 116, which is displayed within window 110, and thereby places the corresponding region of interest at the position he / she desires. One corresponding region of interest can be moved multiple times. The remaining part, i.e., the part of the global domain 118 occupied by non-corresponding regions of interest, is the only part calculated at calculation S2 of the global physical simulation within the global domain 118.

[0119] "Only calculate the remaining part of the global domain" means only calculate the simulation state and / or results of the global physical simulation within the remaining part.

[0120] Refer to Figure 6 and Figure 7 , and now discuss the comparison between the following two examples: An example of simulating multiple physical simulation instances together according to the prior art method shown in Figure 6 and an example of simulating multiple physical simulation instances together according to the method of the present invention shown in Figure 7 . In both examples, it is necessary to simulate three wind turbines operating in a wind farm under a given wind condition.

[0121] In Figure 6 the prior art example, it is necessary to fully run simulation 60, which includes three simulations 62, 64, and 66 for a given wind turbine. Each simulation 62, 64, and 66 for a given wind turbine is fully calculated. When at least one of the simulations 62, 64, and 66 for a given wind turbine is moved into the domain 68 of simulation 60, simulation 60 must be fully calculated again, which includes fully calculating each simulation 62, 64, and 66 for a given wind turbine again.

[0122] In Figure 7 the example of the method, during the creation S0 of the database of local simulation instances, the user loads a local simulation 70 of a wind turbine under a given wind condition. The local simulation is associated with a corresponding local domain 700. The method selects S20 the corresponding region of interest 702 of the local simulation 70. Here, for example, according to what is described above Figure 8 andFigure 9 An example is given where, based on a user action, a selection S20 of a corresponding region of interest is performed. At the boundary 704 of the corresponding region of interest 702, a corresponding reduced model of the local simulation 70 is calculated S30, and this corresponding reduced model is included in a local simulation instance corresponding to the local simulation 70, which local simulation instance is stored in a database of local simulation instances. At a selection S1 of at least two local simulation instances, the local simulation instance corresponding to the local simulation 70 is selected three times by the user. The user places S210 three exemplars 74, 76, and 78 of the corresponding region of interest of the local simulation 70 in the global domain 72 of a global physical simulation (i.e., a simulation of a wind farm including three wind turbines operating in a wind condition). At a calculation S2 of the global physical simulation, only the remaining part of the global domain 72 is calculated, i.e., the part occupied by the non-region of interest. Advantageously, it is not necessary to re-run the very expensive simulation of the wind turbine region.

[0123] In the example, the method includes, at the corresponding region of interest of each local simulation of at least two selected local simulation instances placed S210, joining the boundary of the corresponding region of interest with the boundary of the region of the global domain occupied by the corresponding region of interest.

[0124] The joining includes a modification or a series of modifications to at least one algorithm and / or numerical method involved in the calculation of the global physical simulation. The joining thereby incorporates the corresponding region of interest and the corresponding reduced model calculated at the boundary of the corresponding region of interest into at least one algorithm and / or numerical method, which allows the calculation of the global physical simulation by reusing the corresponding reduced model(s). The modification or series of modifications can be performed automatically, for example, when the user drags the corresponding region of interest in the global domain. The modification or series of modifications can also be performed based on a user action (e.g., by interaction with a keyboard and / or a haptic device).

[0125] Now refer to Figure 15 Discuss how the joining is implemented.

[0126] Figure 15 The global domain Ω of the global simulation and the local domain Ωm of one of at least one local simulation are shown. In this implementation, the global domain Ω and the local domain Ωm are discretized separately (e.g., differently). Figure 15 The corresponding region of interest 1500 of the local domain Ωm shown by the white area is shown. In this implementation, the local domain Ωm includes a recovery region 1502, which is the region of the local domain Ωm not occupied by the region of interest 1500.

[0127] In this implementation, the joining is based on the discretization of Ω and the corresponding points of the region of interest 1500. The corresponding points are points located at or substantially at the boundary of the region of interest 1500. The corresponding points are shown as Figure 15 the bullet points in. For clarity, this is only an example, but the corresponding points are not necessarily bullet points. In this implementation, the reduced state of the local simulation is calculated at or substantially at the corresponding points and at or substantially at the recovery region 1502. Then, the joining includes verifying the consistency between the reduced state calculated at or substantially at the corresponding points and the reduced state calculated at or substantially at the recovery region 1502. Verifying the consistency may include determining whether the physical quantities (e.g., energy or displacement) of the reduced state calculated at or substantially at the corresponding points are homogeneous with the physical quantities of the reduced state calculated at or substantially at the recovery region 1502. When it is determined that the physical quantities are homogeneous, as previously discussed, then the joining may incorporate the region of interest 1500 and the calculated reduced model calculated at the corresponding points in at least one algorithm and / or numerical method.

[0128] Alternative implementations do not use the recovery region 1502. In these alternative implementations, the joining does not include verifying the consistency. In these alternative implementations, as previously discussed, the joining may directly incorporate the region of interest 1500 and the calculated reduced model calculated at the corresponding points in at least one algorithm and / or numerical method.

[0129] In the example, the method further includes, after the calculation S30 of the corresponding reduced model, defining S40 probes for each local simulation in the set of local simulations. The probes are points of the corresponding local domains of the local simulations that are adjacent to the corresponding regions of interest. Each probe includes the simulation data of the local simulation. In these examples, the stored local simulation instances including the corresponding calculated reduced models also include the probes and the corresponding regions of interest.

[0130] Defining S40 probes and storing them improves the accuracy of the calculation S2 of the global physical simulation because the local simulation data is stored and can be used for the calculation S2 in addition to the corresponding calculated reduced models.

[0131] The simulation data included in the probes refers to any data derived from the simulation results and / or simulation states of the local simulations corresponding to the probes. In addition to being coupled to the calculated reduced model itself, the probes (e.g., all probes) can also be coupled to the corresponding calculated reduced models to be used in the calculations at the reuse step S220. The simulation data can also include simulation results and / or simulation states. In an example, the probes are evenly distributed (or substantially evenly distributed) on the boundaries of each region of interest. This allows the same level of simulation data to be accessed at any location around the corresponding region of interest.

[0132] The definition S40 of the probes can be performed semi-automatically. For example, when selecting S20 the corresponding region of interest, in this case, the method can automatically create an even distribution of probes along the boundary of the corresponding region of interest. In these examples, the user can then select and / or export and / or retrieve the simulation data and record it on the probes. Alternatively, the user can select the positions of the probes and then select and / or export and / or retrieve the simulation data and record it on the probes. In any case, the definition S40 of the probes includes the creation of the probes and the selection and / or export and / or retrieval of the simulation data, as well as the recording of the simulation data on the created probes.

[0133] In an example, the probes and the corresponding regions of interest are stored at the storage step S50. In an example, the number of probes per region of interest is greater than a predetermined threshold selected, for example, based on user actions at the initial stage of the method. This ensures that certain accuracy requirements are met. In fact, the more probes there are, the more simulation data to be accessed and used in the calculation S2 of each global simulation, and the higher the accuracy of the calculation S2.

[0134] Reference Figure 8 、 Figure 9 and Figure 10 Now, an example of defining the probes S40 is described. In this example, the provision S10 of the local simulation 82 and the selection S20 of the corresponding region of interest 86 have been performed according to the examples described previously Figure 8 and Figure 9 . After the selection S20 of the corresponding region of interest 86, the user defines S40 the probes substantially on the boundary 90 of the corresponding region of interest 86. For explanatory purposes only, the probes are represented by squares adjacent to the boundary 90 in Figure 10 . The definition S40 of the probes can be performed, for example, by picking the positioning of the probes (i.e., points on the boundary 90 (or substantially on the boundary 90)) according to the user's interaction with the GUI, and a square representing the probes is automatically created substantially at the picked position. Then, the simulation data to be included in the probes can be selected and / or retrieved and recorded in the probes.

[0135] Now refer to Figure 12 An example of placing S210 is described in the case where probes have been defined for each local simulation instance. Specifically, Figure 12 An example of the region of interest corresponding to the placement S210 is shown, but the difference is that according to the reference Figure 11 、 Figure 8 、 Figure 9 and Figure 10 In the above-described example, S40 probes have been defined on all corresponding regions of interest 114. In Figure 12 , the probes are shown on the corresponding regions of interest that have been moved to the global domain 118.

[0136] In the example, during the calculation S2 of the global physical simulation, at least two local simulation instances among at least two selected local simulation instances interact. The interaction causes the probes of at least one of the at least two local simulation instances to be enriched S221. Due to the enriched S221 probes, as shown in Figure 4 , the corresponding calculated reduced model included in the local simulation instance whose probes are enriched is corrected S225.

[0137] Therefore, the method takes into account the interactions between the local parts of the global physical simulation. These interactions can actually correspond to real physical interactions (e.g., modeling them). Therefore, the method allows the global physical simulation to be simulated while simulating the real-world interactions that may occur in the real world. Therefore, from a physical perspective, the resulting global physical simulation of the simulation is more accurate.

[0138] When the reuse S220 of a corresponding calculated reduced model of one of the two simulation instances requires the correction of the corresponding calculated reduced model of the other of the two simulation instances to perform the reuse S220 of the corresponding calculated reduced model of the other of the two simulation instances and / or vice versa, the two simulation instances interact. In the example, the word "requires" should be understood as "theoretically requires", which means that theoretically the correction of the corresponding calculated reduced model of the other of the two simulation instances is required. However, the method can determine that the interaction is weak enough that the method does not actually perform the theoretical correction. This will be described in detail later.

[0139] Interaction between two local simulation examples (e.g., a first local simulation example and a second local simulation example) causes probes in at least one of the two local simulation examples (e.g., the first local simulation example) to be enriched. Enriching a probe means enriching one or more probes. Enriching the probes of the first local simulation example may include adding simulation data to the probes, e.g., simulation data retrieved and / or derived from the simulation data of at least one probe of the second local simulation example. Alternatively or additionally, enriching a probe may include removing simulation data that has already been included in the probe. Alternatively or additionally, enriching a probe may include modifying simulation data that has already been included in the probe. It can be understood that, in appropriate cases, the probes of the second local simulation example or the probes of both local simulation examples can be enriched similarly.

[0140] In an example, the probes of a local simulation example are related to the corresponding computed reduced model of the local simulation example, and based on this relationship, enriching one or more of the probes will (e.g., automatically) trigger a correction of the corresponding computed reduced model. In an example, correcting the corresponding reduced model S225 means modifying its reduced state (or a part of its reduced state), e.g., by modifying basis elements (or a part thereof) and / or weights (or a part thereof), or by modifying the number of state patterns that contribute to the reduced state (or the part of the reduced state).

[0141] Returning to the example described above Figure 12 The probes of each local simulation example are shown on the region of interest. In an example, the purpose of this display is to assist the user in placing the corresponding region of interest. In fact, how to capture the interaction between local simulation examples can depend on the number of probes and their positions on each corresponding region of interest. By showing the probes, the user can thus perform the placement S210 of the corresponding region of interest to capture the amount of interaction that he truly wishes to simulate.

[0142] In an example, the method further includes, for each local simulation example whose probes are enriched, calculating S222 the difference between the set of all enriched probes and the set of corresponding probes before they were enriched, before the correction S225 of the corresponding computed reduced model. In these examples, the method further includes determining S223 whether the difference exceeds a predetermined threshold. In these examples, the method further includes correcting S225 the corresponding computed reduced model if it is determined that the difference exceeds the predetermined threshold. Figure 4 Illustrates Figure 4 such an example.

[0143] By adapting the correction S225 of the corresponding computed reduced model to determine that the difference exceeds a predetermined threshold, the method only considers significant interactions. In an example, this means that the method only considers interactions corresponding to real-world physical interactions (e.g., simulating, modeling them) and / or discards interactions that may be due to or correspond to numerical artifacts.

[0144] The difference may mean there is a gap, contradiction, or error. The difference can lie in one or more numerical values that express how the enriched probe is different from the corresponding (i.e., the same) probe before its enrichment (e.g., how the simulation data of the enriched probe is different from the simulation data of the probe when it was not enriched). The determination S223 that the difference exceeds a predetermined threshold can be automatically performed by the method. In an example, the predetermined threshold can be selected based on a user action (e.g., at the initial stage of the method).

[0145] If it is determined that the difference exceeds the threshold, the method performs the correction S225 of the computed reduced model. In an example, the correction S225 of the computed reduced model can trigger a new enrichment S221 of the probe, for example, in combination with other computations in the computation S2 of the global physical simulation. That is, the enrichment S221 and the correction S225 can be iterated S226 during the execution of the computation S2 of the global physical simulation. However, if the difference does not exceed the threshold, the computed reduced model will not be corrected (i.e., the computed reduced model remains unchanged). In an example, due to other computations in the computation S2 of the global simulation, the method can still anticipate a new enrichment S221 of the probe. That is, the enrichment S221 and the determination S223 can be iterated S226 during the execution of the computation S2 of the global simulation. In other words, during the computation S2 of each global simulation instance, the method can perform the iteration S226 of: enrichment S221 and determination S223 and / or enrichment S221 and correction S225.

[0146] In an example (e.g., Figure 2 the example shown), the method further includes learning S60 a machine learning algorithm at the creation S0 of a database of local simulation instances. The machine learning algorithm is learned on the local simulation instances stored in the database. For each local simulation instance in the database, the machine learning provides a corresponding relationship between the probe stored in the local simulation instance and the corresponding computed reduced model stored in the local simulation instance. In these examples, for each local simulation instance, the correction S225 includes applying S224 the machine learning algorithm to the corresponding computed reduced model in the local simulation instance. The correction S225 is performed based on the corresponding relationship.

[0147] The machine learning algorithm is used as a tool to correct the corresponding calculated reduced model of S225. The machine learning algorithm is learned at S0 for the creation of the database and, where appropriate, is used at S225 for correction. Thus, interactions are considered without the need to recalculate any local simulations, but using the information learned on the calculated local simulations.

[0148] The machine learning algorithm can be learned by any known machine learning technique. Learning the machine learning algorithm on the local simulation instances stored in the database means that the database forms the learning set or training set of the machine learning algorithm. Thus, the learning set or training set of the machine learning algorithm includes all reduced models, probes, and regions of interest of all local simulations. The machine learning algorithm can also be referred to as a correction model.

[0149] For each local simulation instance, the corresponding relationship includes one or more mathematical formulas and / or one or more algorithms that provide the correspondence between the corresponding calculated reduced model of the local simulation instance and the probe. In an example, the set of all corresponding relationships forms the decision forest of the machine learning algorithm.

[0150] For each local simulation instance whose probe is enriched, correcting the corresponding calculated reduced model of the S225 local simulation instance includes applying the S224 machine learning algorithm only when it has been determined at S223 that the difference exceeds a predetermined threshold. In an example, the machine learning algorithm takes as input the pattern and / or weight (e.g., all of it) and / or data derived from the pattern and / or weight (e.g., reduced state, e.g., all reduced states) and the probe of the local simulation instance (e.g., all probes, e.g., only the enriched probes). In an example, these inputs are pushed into the set of all corresponding relationships, and the machine learning algorithm outputs a correction to the corresponding calculated reduced model. The correction can consist of a new corresponding calculated reduced model that includes: new weights and / or new state patterns and / or the weights and / or state patterns of the uncorrected corresponding calculated reduced model.

[0151] In an example, at each correction S225 of the corresponding reduced model due to enrichment of the probe S221, the simulation instance is stored in the database, which includes the corrected reduced model and the enriched probe.

[0152] Thus, the database is enriched with new local simulation instances that come from the calculation S2 of the global physical simulation.

[0153] Return to reference Figure 1, in an example, the method includes, after computing S2 the global physical simulation, adding S3 a new local simulation instance to a database of local simulation instances. Adding S3 the new local simulation instance includes providing a new local simulation. The new local simulation has been computed and is associated with a corresponding local domain. Adding S3 the new local simulation instance includes selecting a corresponding region of interest of the new local simulation. The corresponding region of interest is a non-empty sub-domain of the corresponding local domain. Adding S3 the new local simulation instance includes computing S3 a corresponding reduced model of the new local simulation at the boundary of the corresponding region of interest. Adding S3 the new local simulation instance includes defining probes. The probes are points of the corresponding local domain that are adjacent to the corresponding region of interest. Each probe includes simulation data of the new local simulation. Adding S3 the new local simulation instance includes storing the new local simulation instance in the database. The stored new local simulation instance includes the corresponding reduced model of the new local simulation, the probes of the new local simulation, and the corresponding region of interest of the new local simulation. Adding S3 the new local simulation instance causes the new local simulation instance to be one of the local simulation instances in the database of local simulation instances. The method further includes re-learning S4 a machine learning algorithm on the database of simulation instances after adding S3 the new local simulation instance. The method further includes re-selecting S5 at least two local simulation instances in the database of local simulation instances. The re-selected at least two local simulation instances include the new local simulation instance. The method further includes re-computing S7 the global physical simulation using the re-selected at least two local simulation instances.

[0154] Thus, the method enables the database of local simulation instances to be enriched with new local simulation instances and a machine learning algorithm to be re-learned on the enriched database. When re-computing the global physical simulation, the new local simulation instances that he / she has selected to add to the database of the global physical simulation can then be included and an improved machine learning algorithm can be used to perform the computation.

[0155] The provision of the new local simulation can be performed as a provision S10 of each local simulation in a set of local simulations. The selection of the corresponding region of interest of the new local simulation can be performed as a selection S20 of each corresponding region of interest of each local simulation in a set of local simulations. The computation of the corresponding reduced model of the new local simulation can be performed as a computation S30 of each corresponding reduced model of each local simulation in a set of local simulations. The definition of the probes of the new local simulation can be performed as a definition S40 of the probes of each local simulation in a set of local simulations.

[0156] Re - learning the S4 machine - learning algorithm on a database of local simulation instances consists of re - executing the learning of the machine - learning algorithm S60, but this time on a database of local simulation instances that includes new local simulation instances, rather than on the database of previously created local simulation instances.

[0157] Re - selecting S5 at least two local simulation instances consists of re - executing the selection of at least two local simulation instances S1, but this time the selection is performed among the local simulation instances of a database of local simulation instances that includes new local simulation instances, rather than in the database of previously created local simulation instances.

[0158] Re - calculating S7 the global physical simulation using the re - selected at least two local simulation instances consists of re - executing the calculation of the global simulation instance S2, only for the corresponding calculated reduced models of the local simulation instances of the at least two re - selected local simulation instances that are reused S220.

[0159] In an example, the method further includes modifying S6 the global physical simulation after re - learning S4 and before re - calculating S7.

[0160] Thus, the user can calculate at least two different versions of the global physical simulation.

[0161] Modifying the global physical simulation can include changing one or more physical parameters and / or changing one or more boundary conditions and / or changing the meshing of the global domain and / or changing the time scale of the global physical simulation and / or changing the arrangement of the corresponding regions of interest of the regions occupying the global domain.

[0162] Reference Figure 7 , which describes an example of simulating three wind turbines 74, 76, and 78 operating together in a wind farm under a given wind condition according to the method, modifying the global physical simulation can, for example, consist of changing the positions of the wind turbines 74, 76, and 78 in the global domain 72 and / or changing the wind condition (e.g., by modifying one or more parameters and / or one or more boundary conditions of the global physical simulation).

[0163] In an example, the addition S3 and the re - calculation S7 are iterated S8, as Figure 1 shown in

[0164] In an example, each local domain of each local simulation includes a corresponding physical object. The local simulation simulates the corresponding physical behavior associated with the corresponding physical object. In these examples, the global physical simulation simulates the physical behavior of the set of all corresponding physical objects.

[0165] In the context of the present invention, a physical object is a product or an assembly of products or a real-world physical entity. A physical behavior associated with an object can be the behavior of the object itself, or the behavior of the object in its surrounding environment (e.g., the real-world environment), or the behavior of the object interacting with the environment. A physical behavior associated with a number of objects is, for example, a physical behavior performed by the plurality of objects together in the same environment (e.g., the real-world environment). It can include interactions between the objects and / or between the objects and the environment.

[0166] A table listing non-limiting examples of global physical simulations, physical objects, and physical behaviors is provided below. The method can anticipate simulating one or more of the examples of global physical simulations given in the table below.

[0167]

[0168]

[0169] Table 1: Examples of Global Physical Simulations

[0170] In the example, the interaction between two local simulation instances can model and / or simulate real-world physical interactions from the following list of non-limiting examples:

[0171] - (Multiple) perturbations to the wind around a wind turbine caused by another nearby operating wind turbine;

[0172] - (Multiple) perturbations to the air around an aircraft engine caused by another nearby operating aircraft engine;

[0173] - (Multiple) perturbations to the heat around an aircraft engine caused by another nearby operating aircraft engine;

[0174] - (Multiple) perturbations to the magnetic field around a torus in a thermal nuclear power station caused by a nearby torus;

[0175] - (Multiple) perturbations to the radio coverage of an antenna caused by other nearby antennas;

[0176] - (Multiple) perturbations caused by a structural connection between mechanical parts.

[0177] Any example of a global physical simulation cited in Table 1 can be characterized by one or more reasonable examples of the interactions listed in the above table. The method can also anticipate reasonable combinations of the perturbations in the above table.

[0178] In the examples, all local simulations in the set of local simulations are perturbations of a given local simulation. In these examples, the given local simulation is also part of the set of local simulations.

[0179] A first simulation is a perturbation of a second simulation if the first simulation has been defined (e.g., set or programmed) by changing one or more of the following characteristics of the second simulation: boundary conditions, initial conditions, spatial discretization, the value of at least one physical parameter, time scale.

[0180] In all examples, the method may also include displaying all computed global physical simulations (e.g., simultaneously or iteratively) on a display such as a GUI after each computation of a global physical simulation.

Claims

1. A computer-implemented method for simulating together multiple physical simulation instances included in a global physical simulation, the method comprising: - creating (S0) a database of local simulation instances, the creating (S0) comprising: ● providing (S10) a set of local simulations, wherein: ■ the set of local simulations includes at least two local simulations; ■ a local simulation is such a physical simulation that it is part of the global physical simulation and can be computed individually and independently of the global physical simulation, wherein the global physical simulation is associated with a global domain, and each local simulation is associated with a corresponding local domain, the corresponding local domain including a corresponding physical object; and ■ each local simulation in the set of local simulations has been computed; ● for each local simulation in the set of local simulations, computing (S30) a corresponding reduced model of the local simulation; and ● for each local simulation in the set of local simulations, storing (S50) a corresponding local simulation instance in the database, the corresponding local simulation instance including the corresponding computed reduced model; - selecting (S1) at least two local simulation instances from the database of local simulation instances; and - computing (S2) the global physical simulation, the computing (S2) of the global physical simulation including reusing (S220) each corresponding computed reduced model included in each of the at least two selected local simulation instances, wherein the method further comprises: - before the computing (S30) of each corresponding reduced model of each local simulation: selecting (S20) a corresponding region of interest of the local simulation, the corresponding region of interest being a non-empty subdomain of the corresponding local domain; - at the computing (S30) of each corresponding reduced model of each local simulation: each corresponding reduced model is computed at the boundary of the corresponding region of interest; - at the computing (S2) of the global physical simulation: placing (S210) the corresponding region of interest of each local simulation of the at least two selected simulation instances in the global domain; and only the remaining part of the global domain is computed, the remaining part being the part of the global domain occupied by non-interest regions, the global domain including regions occupied by the corresponding regions of interest of each local simulation of the at least two selected local simulation instances, wherein the method further comprises, for each local simulation in the set of local simulations, after the computing (S30) of the corresponding reduced model: - defining (S40) a probe, the probe being a point of the corresponding local domain of the local simulation, the point being adjacent to the corresponding region of interest, each probe including simulation data of the local simulation; wherein the stored local simulation instance including the corresponding computed reduced model further includes the probe and the corresponding region of interest, wherein: - During the computation (S2) of the global physical simulation, at least two of the at least two selected local simulation instances interact, and the interaction causes the probes of at least one of the at least two local simulation instances to be enriched (S221); and - Due to the enriched (S221) probes, the corresponding computed reduced model included in the local simulation instance in which the probes are enriched is corrected (S225), where: - The global physical simulation is a simulation of the operation of a wind farm under a given wind condition, the wind farm includes wind turbines, and the global domain is a three-dimensional volume that models the wind farm under the given wind condition; - Each local simulation is a simulation of the operation of a corresponding one of the wind turbines in the wind farm under the given wind condition. A local simulation instance corresponding to the local simulation forms data representing the simulation of the operation of the corresponding one of the wind turbines in the wind farm under the given wind condition and includes a computed reduced model of the simulation of the operation of the corresponding one of the wind turbines in the wind farm under the given wind condition. The local domain associated with the local simulation is a three-dimensional volume included in the global domain, which contains the corresponding one of the wind turbines and models the corresponding one of the wind turbines and the air around the corresponding one of the wind turbines; and - The interaction between at least two local simulation instances simulates the disturbance of the wind around the wind turbine caused by another nearby operating wind turbine.

2. The method according to claim 1, further comprising, at the placement (S210) of the corresponding region of interest of each of the at least two selected local simulation instances, joining the boundary of the corresponding region of interest with the boundary of the region occupied by the corresponding region of interest in the global domain.

3. The method according to claim 1, further comprising, for each local simulation instance in which the probes are enriched: - Before the correction (S225) of the corresponding computed reduced model, computing (S222) the difference between the set of all enriched probes and the set of corresponding probes before they were enriched; - Determining (S223) whether the difference exceeds a predetermined threshold; and - If it is determined that the difference exceeds the predetermined threshold, correcting (S225) the corresponding computed reduced model.

4. The method according to claim 3, wherein, the method further comprises: - At the creation (S0) of the database of local simulation instances, learning (S60) a machine learning algorithm on the local simulation instances stored in the database, the machine learning algorithm providing, for each local simulation instance in the database, the corresponding relationship between the probes stored in the local simulation instance and the corresponding computed reduced model stored in the local simulation instance; and - For each local simulation instance in which the probes are enriched, the calibration (S225) includes applying (S224) the machine learning algorithm to the corresponding calculated reduced model in the local simulation instance, and the calibration (S225) is performed based on the corresponding relationship.

5. The method according to claim 1, wherein, At each calibration (S225) of the corresponding reduced model due to the enrichment (S221) of the probes, the simulation instance is stored in the database, and the simulation instance includes the calibrated reduced model and the enriched probes.

6. The method according to claim 4, further comprising, after the calculation (S2) of the global physical simulation: - Adding (S3) a new local simulation instance to the database of local simulation instances, the addition (S3) of the new local simulation instance comprises: ● Providing a new local simulation that has been calculated and is associated with a corresponding local domain; ● Selecting a corresponding region of interest of the new local simulation, the corresponding region of interest being a non-empty sub-domain of the corresponding local domain; ● Calculating a corresponding reduced model of the new local simulation at the boundary of the corresponding region of interest; ● Defining probes, where the probes are points of the corresponding local domain that are adjacent to the corresponding region of interest, and each probe includes simulation data of the new local simulation; and ● Storing the new local simulation instance in the database, the new local simulation instance including the corresponding reduced model of the new local simulation, the probes of the new local simulation, and the corresponding region of interest of the new local simulation; The addition (S3) causes the new simulation instance to be one of the local simulation instances in the database of local simulation instances, The method further comprises: - After the addition (S3) of the new local simulation instance, relearning (S4) the machine learning algorithm on the database of simulation instances; - Re-selecting (S5) at least two local simulation instances in the database of local simulation instances, the at least two re-selected local simulation instances including the new local simulation instance; and - Recalculating (S7) the global physical simulation using the at least two re-selected local simulation instances.

7. The method according to claim 6, further comprising modifying (S6) the global physical simulation after the relearning (S4) and before the recalculating (S7).

8. The method according to claim 6, wherein, The addition (S3) and the recalculating (S7) are iterated (S8).

9. The method according to claim 1, wherein: - The local simulation simulates the corresponding physical behavior associated with the corresponding physical object; - The global physical simulation simulates the physical behavior of the set of all corresponding physical objects.

10. The method according to claim 1, wherein, All local simulations are perturbations of a given local simulation, and the given local simulation is part of a set of local simulations.

11. A computer program product comprising instructions for performing the method according to any one of claims 1 to 10.

12. A system comprising a processor coupled to a memory and a display, the memory having recorded thereon instructions for performing the method according to any one of claims 1 to 10.

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