Computer-implemented method for obtaining real-time maps of physical quantities characterizing complex and uncertain systems from insufficient and indirect measurements
The hyperphysics framework addresses the challenge of unreliable indirect measurements by combining simulations with real-time data to create accurate, non-invasive maps of complex systems, enhancing medical treatment monitoring and network analysis.
Patent Information
- Application Number
- JP2025517688
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2022-10-03
- Filing Date
- 2023-10-02
- Publication Date
- 2025-11-13
AI Technical Summary
Existing methods for obtaining real-time maps of physical quantities in complex and uncertain systems from indirect and insufficient measurements are unreliable and invasive, leading to inaccurate temperature monitoring in medical treatments and electronic devices, and incomplete data in network diffusion processes.
A computer-implemented method using a hyperphysics framework that combines multiphysics simulations of mutated system replicas with indirect measurements to create a reliable, real-time map of physical quantities, leveraging a library of simulations to interpolate accurate data.
Provides accurate, real-time, and reliable maps of physical quantities in complex systems using non-invasive techniques, overcoming uncertainties in medical treatments, electronic devices, and network diffusion processes.
Smart Images
Figure 2025537042000001_ABST
Abstract
Description
[Technical Field]
[0001] The present invention relates to a computer-implemented method for obtaining real-time maps of physical quantities characterizing complex and uncertain systems from insufficient and indirect measurements. [Background technology]
[0002] Attempting to reliably reconstruct the physical properties of a system from scant and indirect observations of the system itself represents an extremely important and open problem in many fields of research, e.g., medical imaging, epidemiology, astronomy, and geophysics.
[0003] Various approaches can be found in the literature, where this problem is addressed through inversion methods based on Bayesian inference and neural networks (see Patent Application No. WO2015016990A1; G. Wang, J.C. Ye, and B. De Man, "Deep learning for tomographic image reconstruction", Nat. Mach. Intell., vol. 2, pp. 737-48, 2020).
[0004] In particular, a first area of investigation is temperature monitoring in microwave cancer hyperthermia.
[0005] Microwave hyperthermia is a type of cancer treatment in which tumor cells are selectively exposed to supraphysiological temperatures (42°C-44°C) using appropriate antenna systems to adversely affect cancer growth (HH Kampinga, "Cell biological effects of hyperthermia alone or combined with radiation or drugs: a short introduction to newcomers in the field", Int. J. Hyperthermia, vol. 22, no. 3, pp. 191-6, 2006).
[0006] Hyperthermia in combination with radiotherapy and / or chemotherapy has proven beneficial in the treatment outcomes of a wide variety of tumors (NR Datta et al., "Local hyperthermia combined with radiotherapy and- / or chemotherapy: Recent advances and promises for the future", Cancer Treat. Rev., vol. 41, no. 9, pp. 742-53, 2015).
[0007] In cancer hyperthermia, temperature control is a major technical challenge, especially for deep-seated tumors. In this context, treatment planning is the basis for optimally configuring the applicator's antenna feeding to maximize the temperature rise in the tumor and minimize the risk of overheating in the surrounding healthy tissue. This is performed using appropriate numerical solvers, where both a patient phantom (derived from CT and MRI scans) and the antenna applicator are modeled, and antenna feeding optimization is implemented to target the specific absorption rate (SAR) (or directly the temperature) at the tumor target (MM Paulides et al., "Simulation techniques in hyperthermia treatment planning", Int. J. Hyperthermia, vol. 29, no. 4, pp. 346-57, 2013).
[0008] One of the greatest limitations of simulation-based planning is the uncertainty in characterizing the dielectric and (especially) thermal parameters of different tissues, which must be assigned to a segmented phantom before solving Maxwell's and bioheat equations. This uncertainty can lead to unreliable temperature predictions in the region of interest (ROI), making it necessary to obtain direct measurements during treatment. Intraluminal temperature measurements, i.e., catheters placed within body cavities, often prove ineffective due to the high degree of uncertainty introduced by distance from the tumor site and physiological functions (e.g., breathing, swallowing, and, in the case of tumors in the head and neck region, variable tissue contact within the oral cavity). Therefore, in current clinical practice, invasive interstitial catheters are required to obtain any reliable temperature measurements (MM Paulides, GM Verduijn, and N. Van Holthe, "Status quo and directions in deep head and neck hyperthermia," Radiat. Oncol., vol. 11, no. 21, 2016). In addition to causing considerable discomfort to the patient, these local measurements provide very limited spatial information.
[0009] Although different techniques for non-invasive temperature measurement during hyperthermia have been investigated since the very beginning, there is still no method that is sufficiently reliable to be suitable for widespread use in the clinic.
[0010] Research into the use of microwave radiometry as a non-invasive method of measuring temperature dates back to 1974-75 (AH Barret, and PC Myers, "Microwave thermography: a method of detecting subsurface thermal patterns", Bibl. Radiol., vol. 6, pp. 45-56, 1975). This technique requires the definition of a mathematical (inverse) problem to extract temperature information of the subcutaneous tissue from measurements of emitted blackbody radiation. The extremely weak signal levels, sparsity and noise contamination of the data make this technique extremely difficult and makes it impossible to provide a deep temperature estimate. Furthermore, simultaneous use with hyperthermia poses additional technical problems due to the presence of the radiant applicator (S. Jacobsen and P.R. Stauffer, "Multifrequency Radiometric Determination of Temperature Profiles in a Lossy Homogeneous Phantom Using a Dual-Mode Antenna With Integral Water Bolus," IEEE Trans. Microw. Theory Techn., vol. 50, no. 7, 2002).
[0011] Another method for gathering indirect, noninvasive information about temperature during thermal therapy is radio frequency (RF) tomography (microwave or impedance tomography) (M. Haynes, J. Stang, and M. Moghaddam, “Real-time microwave imaging of differential temperature for thermal therapy monitoring,” IEEE Trans. Biomed. Eng., vol. 61, no. 6, 2014; M. Bevacqua et al., “A Method for Effective Permittivity and Conductivity Mapping of Biological Scenarios via Segmented Contrast Source Inversion,” Prog. Electromagn. Res., vol. 164, 2019), which derives temperature information from changes in the dielectric properties of body tissues.
[0012] All these techniques for non-invasive temperature control are still under development, and the use of these methods in clinical practice remains a distant goal. Therefore, currently, temperature measurement data from radiometry and RF tomography are considered to be insufficient, indirect, and highly uncertain sources of information.
[0013] Probes for estimating deep body temperature from the skin surface using heat flux measurements have also been implemented (Patent Application No. WO2011126543A1; K.-I. Kitamura et al., "Development of a new method for the non-invasive measurement of deep body temperature without a heater", Med. Eng. Phys., vol. 32, 2010) and may be considered as another means of providing indirect non-invasive temperature information during heat therapy.
[0014] Recently, research has been directed to the possibility of controlling the temperature in patients during hyperthermia treatment using magnetic resonance (MR) thermometry (G.C. van Rhoon, and P. Wust, "Introduction: non-invasive thermometry for thermotherapy", Int. J. Hyperthermia, vol. 21, no. 6, pp. 489-95, 2005). Although promising, temperature monitoring using MR can be affected by inhomogeneities in the magnetic flux density and melting artifacts. Furthermore, this technique requires performing the treatment inside an MR scanner with a suitable MR-compatible antenna setup, limiting the possibility of performing this type of temperature monitoring to specially organized clinical centers.
[0015] A second area of investigation is temperature monitoring in electronic devices.
[0016] One of the challenges in the design of electronic devices is the proper handling of thermal loads. This issue affects both the design of the integrated circuit (IC) and the spatial arrangement inside the housing. The main difficulty relates to measuring the temperature at critical points during runtime.
[0017] For ICs, we want to estimate chip-level thermal profiles from runtime temperature sensor readings and face the problem of having only a few sensors that are not even located at the points of interest. One solution is to assume that power density is probabilistic with known mean and variance, and then estimate the posterior mean and variance of the temperature across the chip from temperature readings at a few fixed locations on the chip (Y. Zhang et al., "Chip Level Thermal Profile Estimation Using On-chip Temperature Sensors," 2008 IEEE Int. Conf. on Computer Design, 2008). To use this approach, an efficient method for deriving thermal profiles from power density profiles is required (Y. Zhan and S.S. Sapatnekar, "High-Efficiency Green Function-Based Thermal Simulation Algorithms," IEEE Trans. On CAD of Int. Circ. and Syst., vol. 26, no. 9, 2007).
[0018] A black-box model based on a neural network trained to correlate several execution counter readings (executed instructions, CPU cycles (frequency), number of branches executed, etc.) to the temperature profile on the chip is described in M. Rapp, O. Elfatairy, M. Wolf, J. Henkel and H. Amrouch, "Towards NN-based Online Estimation of the Full-Chip Temperature and the Rate of Temperature Change", 2020 ACM / IEEE 2nd Workshop on Machine Learning for CAD (MLCAD), 2020.
[0019] Regarding the entire housing, since many devices are intended to be used in direct physical contact with the user, it is of interest for safety reasons to know the temperature of the entire housing of the device. A common approach is based on processing available data and using regression analysis. To compensate for the fact that sensors are rarely placed in the most favorable locations to record temperatures and that the location of the hottest point may change at runtime (e.g., when a DVD reader is inserted or a PCI card is added) (see US8762097B2), the use of virtual sensors has been proposed. These are mathematical models built before the device is sold to the general public that correlate various input sources, such as system power sensors, physical temperature sensors, and / or system configuration information (e.g., cooling system status, e.g., fan speed per fan, etc.), to the temperature measured at the location of interest under different operating conditions. A similar concept is described in US10488873B2, where the temperature at a hot spot on the surface of an electronic device is correlated to the temperature of an internal part, and the readings are then used to estimate the temperature on the surface and to implement a control procedure to reduce it if it exceeds a threshold.
[0020] Faced with the problem that the available data do not meet common assumptions about the validity of regression analysis (e.g., the data are correlated with time, but regression analysis assumes they are not), the response can be divided into a steady state (not correlated with time) and a transient, the latter of which can be estimated using a filtering algorithm based on considering three frequencies in the response (see US9546914B2).
[0021] In any case, none of the above approaches are able to satisfactorily measure the thermal load of an electronic device at critical points during runtime.
[0022] The third area of research is monitoring the spread of malicious agents in a network of agents.
[0023] Starting with the work of Bernoulli and Snow in the 18th and 19th centuries, respectively, [Table 1] ,Scientists now have many mathematical tools to model and analyze ,diffusion processes in ensembles of interacting agents (H. Hethcote, "The mathematics of ,infectious diseases", SIAM Rev., vol. 42, no. 2, 2000).
[0024] These tools identify sources of infection (D. Shah and T. Zaman, "Detecting sources of computer viruses in networks: theory and experiment," ACM SIGMETRICS Perf. Eval. Review, vol. 3, no. 1, 2010; D. Shah and T. Zaman, "Rumors in a Network: Who's the Culprit?," IEEE Trans. on Inf. Th., vol. 57, no. 8, 2011; C. H. Comin and L. da Fontoura Costa, "Identifying the starting point of a spreading process in complex networks," Phys. Rev. E, vol. 84, 2011; N. Antulov-Fantulin et al., "Statistical Inference Framework for Source Detection of Contagion Processes on Arbitrary Network Structures," 2014 IEEE Eighth International Conference on Self-Adaptive and Self-Organizing Systems Workshops, 2014; F. Altarelli et al. "Bayesian inference of epidemics on networks via belief propagation", Phys. Rev. Lett., vol. 112, no. 11, 2014), analyzing the cost / benefit tradeoffs of different strategies to suppress the spread (A. Baker et al., "Epidemic mitigation by statistical inference from contact tracing data", PNAS, vol. 118, no. 32, 2021), and devising optimal immunization strategies (F.Altarelli et al. "Containing Epidemic Outbreaks by Message-Passing Techniques", Phys. Rev. X vol. 4, no. 2, 2014) have been applied to try to answer different questions.
[0025] At the core of these tools are simpler ones (R. Ross, "An application of the theory of probabilities to the study of a priori pathometry.—Part I", Proc. R. Soc. Lond. A, vol. 92, no. 638, 1916; R. Ross and H. Hudson "An application of the theory of probabilities to the study of a priori pathometry.—Part II", Proc. R. Soc. Lond. A, vol. 93, no. 650, 1917; R. Ross and H. Hudson, "An application of the theory of probabilities to the study of a priori pathometry.—Part III", Proc. R. Soc. Lond. A, vol. 93, no. 65, 1917; W. O. Kermack and A. G. McKendrick, "A contribution to the mathematical theory of epidemics", Proc. R. Soc. Lond. A, vol. 115, no. 772, 1927; D. Kendall, "Deterministic and stochastic epidemics in closed populations", in J. Neymann (ed.) Contributions to Biology and Problems of Health, vol. 4., University of California Press, Berkeley, 2020) to more complex ones (R. Hinch. et al., "OpenABM-Covid19 - An agent-based model for non-pharmaceutical interventions against COVID-19 including contact tracing", PLOS Comp.Until now, models of diffusion processes and descriptions of networks of interactions exist (Nature Phys., vol. 17, no. 7, 2021). Both aspects are severely affected by data uncertainty and incompleteness (MEJ Newman, "Network structure from rich but noisy data", Nature Phys., vol. 14, 2018). Summary of the Invention
[0026] It is therefore an object of the present invention to provide a computer-implemented method for obtaining real-time maps of physical quantities characterizing complex and uncertain systems from insufficient and indirect measurements, which real-time maps are complete, accurate, physically sound and highly reliable.
[0027] It is a further object of the present invention to provide a computer-implemented method for obtaining a real-time map of a physical quantity characterizing a complex and uncertain system from insufficient and indirect measurements, which real-time map can be obtained from any complex and uncertain system.
[0028] It is a further object of the present invention to provide a computer-implemented method for obtaining real-time maps of physical quantities characterizing complex and uncertain systems from scarce and indirect measurements, wherein the real-time maps can be obtained using non-invasive techniques.
[0029] The proposed invention relates to the implementation of a technique for determining an accurate map of a physical quantity in real time using measurement data that may be scarce and indirectly correlated to the quantity of interest.
[0030] By insufficient set of measurement data is intended a set of measurement data that is not by itself capable of characterizing the phenomenon.
[0031] The physical quantity of interest may characterize a complex phenomenon whose knowledge is affected by uncertainty.
[0032] The proposed technique provides a high-confidence representation of the phenomenon by matching the few available indirect measurements with a library of different models of the system under investigation.
[0033] To populate such a library, multiphysics simulations of an imperfect copy of the system may be used, where the copy has intentional variations added to account for all uncertainties that affect the modeling.
[0034] The representation obtained at the end of the matching process is called the hyperphysics framework.
[0035] The presented method can find applications in all fields of engineering, physics, or social sciences where real-time monitoring of physical quantities describing complex systems is required and where only a few indirect measurements are available.
[0036] The underlying objective of the method presented here is to provide accurate and reliable assessments of physical quantities for complex and uncertain systems that cannot be measured directly due to safety reasons, infeasibility, or budgetary issues. The source of the quantity of interest is difficult to reach, while some of its effects may be visible.
[0037] On the one hand, if direct measurements are not available, and on the other hand, numerical simulation of the system cannot by itself provide reliable results due to the inevitable uncertainties that characterize some of the model parameters and also some of the model equations.
[0038] More specifically, the first stage of the proposed method consists in creating a large set of simulations of deliberately mutated replicas of the system, called the augmented model, in which different parameters are varied to describe the various states the system can exist in. When properly processed, this expanded set of simulations constitutes a priori information sources that can be collapsed towards a reliable representation of the system via a set of indirect, if imprecise, measurements. In other words, all real-time data acquisition can be incorporated into the augmented model's simulation framework, and the actual performance of the system can be conveniently reconstructed at any point in time using "model-based interpolation."
[0039] In the following, the proposed method will first be described as a general technique that can be applied to any uncertain system using indirect and insufficient measurements of the physical quantities involved.
[0040] The description then focuses on the specific example of temperature monitoring in microwave cancer hyperthermia. In this context, the uncertain system is the human body under treatment, the augmented model consists of a library of patient-specific simulations of intentionally mutated replicas of the patient, and the physical quantity of interest is the temperature throughout the region of interest. By applying the proposed method, the inherent information contained in the augmented model is sufficient to provide a reliable temperature map of the patient using only real-time data acquired with non-invasive thermography techniques.
[0041] Finally, two other applications of the inventive method presented here relate to temperature monitoring in electronic devices and monitoring the spread of communicating agents in networks (agents may be people or computers, malicious agents may be pathogens or malicious software).
[0042] In one embodiment of the present invention, there is provided a computer-implemented method for obtaining a real-time map h(x) of the distribution in D-dimensional space of a physical quantity f(x) that describes a real phenomenon (1) that characterizes a complex and uncertain system, wherein the physical quantity f(x) is not accessible to direct measurements, the method comprising:
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[0043] In a further embodiment of the invention, the simulation comprises a numerical multiphysics simulation or a simplified model.
[0044] In a further embodiment of the invention, the particular set of values s n is the set of sampled parameters s1, s2, ..., s p , p=1,...,P, and each sampled parameter s p are the ranges of each
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[0045] In a further embodiment of the invention, the set of sampled parameters is
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[0046] In a further embodiment of the present invention, the set of sampled parameters is
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[0047] In a further embodiment of the invention, the random points are
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[0048] In a further embodiment of the invention, the system of L equations with N unknowns is solved using the least squares method.
[0049] In a further embodiment of the present invention, L <Nである。
[0050] In a further embodiment of the invention, N / L is in the range of 5-50.
[0051] In a further embodiment of the invention, the complex and uncertain system is a region of interest of a human body to be treated by a concentrated deposition of power radiated by an antenna applicator; the physical quantity f(x) is a temperature T(x) of the treated region of interest of the human body; the mathematical model is obtained by using data of magnetic resonance imaging or computed tomography of the treated region of interest of the human body; the set of parameters s includes values of dielectric and thermal parameters characterizing different tissues of the region of interest; and the insufficient set of L indirect measurements.
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[0052] In a further embodiment of the invention, the complex and uncertain system is an electronic operating device, in particular a composite device such as an integrated circuit or a laptop; the physical quantity f(x) is the temperature T(x) of the operating device, in particular its outer surface or one of its internal parts; the mathematical model is obtained by data derived from a plot or a frequency response of the operating device; the set of parameters s comprises a random combination of one or more of electrical, magnetic, chemical, thermal, hydrodynamic and mechanical parameters characterizing the operating device; and the insufficient set of L indirect measurements.
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[0053] In a further embodiment of the invention, the complex and uncertain system is a network of communicating agents including a plurality of nodes; The physical quantity f(x) is the spreading process of a pathogen or malicious software on the network; the mathematical model is obtained from information about the relationships between pairs of the plurality of nodes and / or from information about the spatial proximity of the plurality of nodes; the set of parameters s includes spreading parameters and reference values of the network topology; and the insufficient set of L indirect measurements is obtained using tests performed at the node level or on multiple nodes. [Brief explanation of the drawings]
[0054] The invention will be described in detail hereinafter by way of non-limiting embodiments with reference to the accompanying figures. [Figure 1] FIG. 1 is a schematic representation of the proposed method conceived to achieve a reliable assessment of general complex phenomena for which no direct measurements are available. [Figure 2a] FIG. 1 shows two respective examples of possible sampling in the space of configuration parameters when three parameters are considered, with each point in the grid corresponding to a member of the extended model. [Figure 2b] FIG. 1 shows two respective examples of possible sampling in the space of configuration parameters when three parameters are considered, with each point in the grid corresponding to a member of the extended model. [Figure 3] FIG. 2 reports a schematic representation of how the method described in FIG. 1 is applied to the real-time construction of a reliable temperature map of a patient in microwave cancer hyperthermia treatment. [Figure 4] FIG. 2 reports a schematic representation of how the method described in FIG. 1 can be applied to real-time temperature monitoring in electronic devices. [Figure 5] FIG. 2 reports a schematic representation of how the method described in FIG. 1 is applied to monitoring the growth in a network of communicating agents. DETAILED DESCRIPTION OF THE INVENTION
[0055] Referring to Figure 1, the function
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[0056] A physical quantity describing a true phenomenon 1, which is assumed to be inaccessible to direct measurement, is denoted as f(x) (step 1a).
[0057] The first step 2 of the procedure consists in describing a case-specific numerical model of the system for simulating the spatial distribution of the physical quantity of interest f(x): the approximated physical quantity obtained through this case-specific numerical model is
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[0058] Next, a library of approximations of the function f(x) that describes the true phenomenon 1
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[0059] distribution
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[0060] Once the extended model 3 is prepared, an important further step of the proposed method consists in searching for an approximation of the physical quantity f(x) related to the real phenomenon 1 in the following equation:
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[0061] operator
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[0062] In one embodiment, the number of L equations is less than the number N of unknowns.
[0063] In a further embodiment, the ratio between the number of unknowns N and the number of equations L is in the range of 5-50.
[0064] The underlying goal of the proposed method is to address the insufficient set of indirect measurements.
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[0065] The pre-computed mathematical model of the phenomenon (extended model 3) and the heterogeneous physically acquired data (indirect measurements 4) are treated in a uniform manner as information sources and processed simultaneously to obtain a hyperphysics framework 5 of the system, which provides a reliable and real-time reconstruction, or map, h(x), of the physical quantities related to the true phenomenon 1 in the entire domain of interest (step 5a).
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[0066] The diversified nature of the extended model 3, which takes into account the multiple different configurations in which the system can exist, allows adjustments based on less rigorous and less precise measurements to direct the reconstruction towards a realistic distribution h(x) of the physical quantity f(x) that describes the true phenomenon 1.
[0067] As mentioned above, the extended model 3 has configuration parameters s1, s2, ..., s whose actual values are unknown. p Different combinations ofn The system consists of a library of simulations obtained by modeling the system for
[0068] Each parameter s p is the range
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[0069] In the example shown in FIG. 2a, the set of sampled parameter values 6 is a discrete set
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[0070] Referring to FIG. 2b, another example of a possible set 7 of sampled parameter values includes only random points 6d distributed in the space defined in equation (3).
[0071] The random points 6d may be uniformly distributed in the space defined in equation (3).
[0072] The two examples reported in Figures 2a and 2b are clearly non-exhaustive and several alternative samplings can be considered.
[0073] A first practical application of the above method relates to the problem of temperature monitoring in microwave hyperthermia treatment, as shown diagrammatically in Figure 3. In this case, the complex and uncertain system is the human body under thermal stress, and the phenomenon to be described is the temperature rise in the treated area due to the concentrated deposition of a portion of the power radiated by the antenna applicator.
[0074] Referring to FIG. 3, as is customary in thermotherapy pre-treatment planning, a patient 8 in the treatment position undergoes an MRI (Magnetic Resonance Imaging) or CT (Computed Tomography) scan 9.
[0075] The MRI (or CT) data is then processed in an appropriate tool to perform a segmentation of specific tissues in the patient's region of interest (ROI) 8a, and a patient-specific 3D model 10 is generated.
[0076] The segmented patient anatomy is then imported into a numerical solver 11, where baseline values of the dielectric and thermal parameters s base (i.e., values reported in the literature) were assigned to different tissues and the temperature maps of patient 8
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[0077] Due to the high degree of uncertainty characterizing these parameters, especially the thermal parameters, the temperature map
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[0078] The application of the proposed method in this framework is a set of simulations of deliberately mutated replicas of the region of interest.
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[0079] By leveraging the information inherent in this set of simulations, the actual temperature distribution in the patient can be conveniently reconstructed at any time using “model-based interpolation” via a set of indirect measurements 13.
[0080] This insufficient and inaccurate set of measurements
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[0081] The resulting hyperphysics framework 14 matches a pre-computed simulated ensemble of states (augmented model 12) with an indirect set of measurements 13a to generate an accurate full temperature map T of the patient. h (x)14a is provided.
[0082] This map 14a can be continuously updated over time to provide real-time monitoring of the patient's temperature throughout treatment.
[0083] A second practical application of the above method relates to the problem of temperature monitoring in electronic devices, as shown diagrammatically in Figure 4. In this case, the complex and uncertain system is an electronic operating device (e.g., a composite device such as an integrated circuit or a laptop), and the phenomenon to be described is the temperature in the device, both on its outer surface and in some of its internal parts.
[0084] Referring to FIG. 4, as is customary in system design, data 15 is available that can be derived from a representation and other information (e.g., frequency response) of an electronic operating device with its processing units and their interconnections.
[0085] These data 15 are imported in a numerical solver 16, where the design reference values s of the dielectric and thermal parameters are calculated. base (i.e., values reported in literature and data sheets) are assigned to different components 17 of an electronic operating device to generate a temperature map of the device.
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[0086] Due to the high degree of uncertainty in characterizing these parameters (which affects the size and shape of different components and their dielectric and thermal parameters, as well as the ambient conditions), the temperature map
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[0087] The application of the proposed method in this framework is a set of simulations of deliberately mutated replicas of the device.
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[0088] By leveraging the information contained in this set of simulations, the actual temperature distribution in the device can be conveniently reconstructed using "model-based interpolation" via a set of indirect measurements 19. This incomplete and inaccurate set of measurements
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[0089] The resulting hyperphysics framework 20 matches a pre-computed simulated ensemble of states (augmented model 18) with an indirect set of measurements 19a to produce an accurate full temperature map T of the device. h (x) 20a is provided. This map 20a can be continuously updated over time to provide real-time monitoring of the temperature of the electronic operating device during its entire run time.
[0090] A third practical application of the above method concerns the problem of monitoring the spread of a network of communicating agents. The agents may be, for example, people (or a community of people) or computers. They may be the quantity of a pathogen, e.g., a coronavirus, or malicious software, spreading across the network. Figure 5 illustrates schematically the application of the proposed method to this case of interest. The complex and uncertain system is a network of interacting agents, and the phenomenon to be described is the spread among the nodes of the network.
[0091] Referring to FIG. 5, data on k=1, . . . , K nodes and links between pairs thereof may be available from relationship and proximity data 22 for agents.
[0092] These data are imported into a numerical solver 23, where the design reference value of the expansion parameter s base (i.e., values reported in the literature) are assigned to different parts of the network 24 to facilitate the expansion process on the network.
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[0093] Due to the high degree of uncertainty that characterizes the model (this uncertainty affects both the expansion parameters and also the topology of the network), the process
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[0094] The application of the proposed method in this framework is a set of simulations of deliberately mutated replicas of the network.
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[0095] By leveraging the information contained in this set of simulations, the actual temperature distribution in the device can be conveniently reconstructed using "model-based interpolation" via a set of indirect measurements 26. This incomplete and inaccurate set of measurements
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[0096] The resulting hyperphysics framework 27 matches a pre-computed simulated ensemble of states (augmented model 25) with an indirect set of measurements 26a, providing an accurate full-evaluation map h(t,k) 27a of the expansion across the network. This map 27a can be continuously updated over time, providing real-time monitoring of the spread across the network.
[0097] Thus, the advantages of the present invention are apparent from the description provided above.
[0098] A computer-implemented method for obtaining real-time maps of physical quantities characterizing complex and uncertain systems from insufficient and indirect measurements advantageously provides real-time, complete, accurate, physically sound, and reliable maps of the quantities of interest.
[0099] Moreover, the computer-implemented method according to the present invention can be advantageously applied to any uncertain system.
[0100] Furthermore, in the computer-implemented method according to the present invention, the indirect measurement data can be obtained using non-invasive techniques, which is particularly advantageous when the method is applied in medical treatments related to the human body.
[0101] While this description has addressed some of the possible variations, it will be apparent to those skilled in the art that other embodiments may be implemented, and some elements may be replaced by other technically equivalent elements. Accordingly, the present invention is not limited to the illustrative examples set forth herein, but may be subject to numerous modifications, improvements, or substitutions of equivalent parts and elements without departing from the basic inventive concept as set forth in the following claims. (Other possible items) (Item 1) 1. A computer-implemented method for obtaining a real-time map h(x) of the distribution in a D-dimensional space of a physical quantity f(x) describing a real phenomenon (1) characterizing a complex and uncertain system, the physical quantity f(x) being inaccessible to direct measurements, the computer-implemented method comprising: The spatial distribution of the physical quantity f(x) using a set of parameters (s)
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Claims
1. 1. A computer-implemented method for obtaining a real-time map h(x) of the distribution in a D-dimensional space of a physical quantity f(x) describing a real phenomenon (1) characterizing a complex and uncertain system, the physical quantity f(x) being inaccessible to direct measurements, the computer-implemented method comprising: The spatial distribution of the physical quantity f(x) using a set of parameters (s) [Number 84] describing the complex and uncertain system with a mathematical model for simulating the A particular set of values ｎ a library of approximations of the physical quantity f(x) by performing a plurality of simulations through the assignment of [Number 85] constructing the formula [Number 86] calculating the real-time map h(x) representing a real-time approximation of the physical quantity f(x) at ｎ , n=1,...,N is the magnitude of the difference |ν ｌ is an expansion factor determined by solving a system of L equations with N unknowns to minimize |, where l=1,...,L, and the difference is [Number 87] where x ｌ is a D-dimensional point, [Number 88] is the physical quantity f(x) in the measurement process [Number 89] The effect of x on ｌ is the value measured at [Number 90] is the measurement process for the lth measurement involved [Number 91] is a mathematical model of [Number 92] is the mathematical model applied to the function g [Number 93] Point x ｌ , l=1,...,L, A computer-implemented method comprising:
2. The computer-implemented method of claim 1 , wherein the simulation comprises a numerical multiphysics simulation or a simplified model.
3. The particular set of values s ｎ is the set of sampled parameters s １ , s ２ ,...,s ｐ , p=1,...,P, and each sampled parameter s ｐ are the ranges of each [Number 94] fluctuates within [Number 95] and [Number 96] is a fixed limit, and the particular set of values s ｎ Below: [Number 97] The space given by the Cartesian product of each of the ranges is [Number 98] The computer-implemented method of claim 1 , wherein the method is selected from the group consisting of:
4. The set of sampled parameters is [Number 99] The computer-implemented method of claim 3 , comprising random points distributed in
5. The set of sampled parameters is [Number 100] The computer-implemented method of claim 4 , further comprising a boundary point given by the Cartesian product of
6. The random points are [Number 101] The computer-implemented method of claim 4 , wherein the eigenvalues are uniformly distributed in .
7. The computer-implemented method of claim 1 , wherein the system of L equations with N unknowns is solved using a least squares method.
8. The computer-implemented method of claim 1 , wherein L<N.
9. 2. The computer-implemented method of claim 1, wherein N / L is in the range of 5 to 50.
10. said complex and uncertain system being a region of interest in the human body that is treated by a concentrated deposition of power radiated by an antenna applicator; said physical quantity f(x) being the temperature T(x) of said treated region of interest; the mathematical model is obtained by using magnetic resonance imaging or computed tomography data of the region of interest to be treated of the human body; the set of parameters s includes values of dielectric and thermal parameters characterizing different tissues of the region of interest; The insufficient set of L indirect measurements [Number 102] is obtained by non-invasive indirect methods, in particular radiometry and microwave tomography, or as a result of temperature measurements obtained through a non-invasive intraluminal catheter placed away from the region of interest, or by a minimally invasive catheter at or near the region of interest.
11. said complex and uncertain system is an electronic operating device, in particular a composite device such as an integrated circuit or a laptop; said physical quantity f(x) is the temperature T(x) of said electronic operating device, in particular its outer surface or one of its internal parts; the mathematical model is obtained by data derived from a drawing or frequency response of the electronic operating device; the set of parameters s includes a random combination of one or more of electrical, magnetic, chemical, thermal, hydrodynamic, and mechanical parameters that characterize the electronic operating device; The insufficient set of L indirect measurements [Number 103] is obtained using a thermal sensor placed in an area of the electronic operating device that is easily accessible, or from other indirect measurements.
12. the complex and uncertain system is a network of communicating agents including a plurality of nodes; The physical quantity f(x) is the process of spreading a pathogen or malicious software on the network; the mathematical model is obtained from information about relationships between pairs of the plurality of nodes and / or from information about spatial proximity of the plurality of nodes; The set of parameters s includes an expansion parameter and a reference value of the network topology; The computer-implemented method of any one of claims 1 to 9, wherein the deficient set of L indirect measurements is obtained using tests performed at a node level or on multiple nodes.