A programmable metasurface-based computational space construction and in-situ training method thereof

Abstract

This invention discloses a computational space construction and in-situ training method based on a programmable metasurface. By deploying multiple independently controllable metasurface units in physical space, an electromagnetic computational space with strong multipath coupling characteristics is constructed. This method applies positive and negative physical perturbations to the computational space and performs forward physical measurements respectively. Based on the differential feedback of the measurement results, the metasurface parameters are updated, achieving in-situ training and adaptive control without precise physical modeling. The method does not rely on analytical gradients or digital twin models and can achieve rapid convergence and functional reconstruction of the computational space in complex, dynamic, and strongly scattering environments. This computational space can be used for applications such as electromagnetic wave focusing, target recognition, spatial positioning, and intelligent wireless environment construction, and has advantages such as simple system structure, strong adaptability, and high engineering feasibility.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic wave manipulation and intelligent metasurface technology, and in particular to a computational space construction method based on a programmable metasurface and its in-situ training method, which can be applied to fields such as electromagnetic wave focusing, target recognition, spatial positioning, and intelligent wireless environment construction. Background Technology

[0002] Against the backdrop of the ever-increasing demand for hardware computing power in ubiquitous intelligence, physical neural networks, as an emerging computing paradigm, have received widespread attention in recent years. Unlike traditional digital computing, computation and learning in this paradigm are not accomplished by explicit digital operations, but rather originate directly from the dynamic behavior of the physical system itself. Physical neural networks utilize intrinsic physical mechanisms such as wave propagation, interference, multipath coupling, and nonlinear material responses (Pontula, S., Vaidya, S., Roques-Carmes, C. et al. 2025. Non-reciprocal frequency conversion in a non-hermitian multimode nonlinear system. Nat. Commun. 16, 7544) to construct physical implementations of artificial neural networks in various physical media such as optics, electromagnetics, acoustics, and mechanics (Wang, Z., Qian, C., Lin, P. et al. 2024. 3D intelligent cloaked vehicle equipped with thousand-level reconfigurable full-polarization metasurfaces. Adv. Mater. 36, 2400797). By leveraging the natural evolution of information within physical processes, physical neural networks achieve highly parallel computing at the system level, possessing ultra-high-speed processing capabilities and extremely high energy efficiency (McMahon, PL 2023. The physics of optical computing. Nat. Rev. Phys. 5, 717–734), fundamentally breaking through the performance limitations of traditional digital processing architectures that require discrete modeling and numerical simulation of continuous physical processes.

[0003] In recent years, physical neural networks have demonstrated significant system diversity and functional flexibility, including diffractive optical neural networks (Lin, X. et al. 2018. All-optical machine learning using diffractive deep neural networks. Science 361, 1004–1008), neuromorphic metasurfaces (Qian, C., Wang, Z., Qian, H. et al. 2022. Dynamic recognition and mirage using neuro-metamaterials. Nat. Commun. 13, 2694), and applications in real-time imaging (Meng, W., Fröch, JE, Cheng, K. et al. 2025. Ultranarrow-linewidth wavelength-vortex metasurfaceholography. Sci. Adv. 11, eadt9159) and wavefront modulation (Lu, H., Zhao, J., Zheng, B. et al. 2023. Eye accommodation-inspired neuro-metasurface focusing. Nat. Commun. 14, Remarkable results have been achieved in tasks such as 3301) and adaptive perception (Qian, C., Jia, Y., Wang, Z. et al. 2024. Autonomousaeroamphibious invisibility cloak with stochastic-evolution learning. Adv. Photon. 6, 016001). Physical neural networks provide a highly promising development path for building high-speed, low-energy artificial intelligence systems that are deeply integrated with the real physical world.

[0004] Despite significant progress, the practical deployment of large-scale, trainable physical neural networks still faces fundamental challenges, with a core issue being the difficulty in building accurate and differentiable system models in real-world physical environments. Unlike digital neural networks, where neuron activation, weights, and gradients can be explicitly characterized, the computational behavior of physical neural networks stems from complex wave-mediated interactions. In complex environments, a stable one-to-one correspondence between physically tunable parameters and computational functionality often does not exist. This inherent isomorphism breaking makes constructing differentiable models or digital twins that can realistically describe system behavior extremely difficult (Wright, LG et al. 2022. Deep physical neural networks trained with backpropagation. Nature 601, 549–555). Therefore, most existing physical neural networks still rely on digital backpropagation, external optimization loops, or pre-characterized system responses, thus limiting their autonomous learning capabilities in real-world environments (Momeni, A., Rahmani, B., Malléjac, M. et al. 2023. Backpropagation-free training of deep physical neural networks. Science 382, ​​1297–1303). Meanwhile, factors such as physical nonlinearity, environmental perturbations, multipath scattering, and hardware errors introduce systematic deviations between model predictions and actual outputs, leading to a significant discrepancy between numerical gradients and true physical gradients. These problems collectively constrain the further development of current physical neural networks in terms of scale, robustness, and environmental adaptability, highlighting the urgent need for a new paradigm that enables in-situ model-free learning based on direct physical measurements. Summary of the Invention

[0005] The purpose of this invention is to provide a computational space construction method based on a programmable metasurface and its in-situ training method, so as to solve the problems of existing technologies that rely on accurate physical models and are difficult to achieve in-situ training and adaptive control in complex environments.

[0006] The objective of this invention is achieved through the following technical solution: a computational space construction and in-situ training method based on programmable metasurfaces. This method constructs a computational space with multipath coupling characteristics by deploying multiple independently controllable programmable metasurfaces in the physical space. Based on physical measurement feedback from positive and negative perturbations, the surface parameters are differentially updated, thereby completing in-situ training of the computational space without establishing an analytical physical model. The method includes the following steps: (1) Construction of computational space: Multiple independently controllable programmable metasurfaces are deployed in the target physical space. Each programmable metasurface is composed of multiple units with discrete electromagnetic response states. Each programmable metasurface forms multipath coupling through the propagation of electromagnetic waves in space, thereby constructing a computational space with overall electromagnetic response characteristics. (2) Physical response acquisition: An input electromagnetic excitation is applied to the computation space, and the physical response of the computation space under the current metasurface parameter configuration is acquired through at least one detector. An evaluation quantity for characterizing the degree of completion of the computation task is constructed based on the physical response. (3) Forward perturbation measurement: Based on the current metasurface parameter configuration, a first set of physical perturbations is applied to the metasurface parameters, and forward physical measurement is performed under the perturbation parameter configuration to obtain the first physical response; (4) Negative perturbation measurement: Based on the current metasurface parameter configuration, a second set of physical perturbations opposite to the first set of physical perturbations are applied to the metasurface parameters, and forward physical measurement is performed under the parameter configuration after perturbation to obtain the second physical response; (5) Parameter update: Based on the difference between the evaluation values ​​corresponding to the first physical response and the second physical response, the update value of the metasurface parameters is generated, and the metasurface parameters are updated. (6) Iterative training: Repeat steps (3) to (5) until the evaluation quantity meets the preset conditions and the computational space for completing in-situ training is obtained.

[0007] Furthermore, the electromagnetic response state of the programmable metasurface unit is a discrete phase state, and each unit realizes multiple reflection or transmission phases through multiple controlled electronic devices under preset state combinations. The discrete phase states constitute a finite set of realizable states.

[0008] Furthermore, the metasurface parameters are represented in discrete integer or discrete encoding form. During parameter updates, projection or quantization operations are performed on the updated metasurface parameters to map them back to the finite set of realizable states.

[0009] Furthermore, the positive disturbance measurement and negative disturbance measurement include: Based on the current metasurface parameter configuration, a set of perturbation vectors is generated, which are used to characterize the synchronous change mode of multiple metasurface unit parameters; The disturbance vector is mapped to the corresponding metasurface control command and applied to the programmable metasurface; Under the control command, forward physical measurements are performed on the computational space to obtain the corresponding physical response; The perturbation vectors corresponding to the positive and negative perturbations have opposite directions or complementary relationships in the parameter space.

[0010] Furthermore, the perturbation vector is a multidimensional perturbation vector, whose components are generated in a random, pseudo-random or preset sequence manner, and is used to act on multiple metasurface units or multiple programmable metasurfaces simultaneously.

[0011] Furthermore, the parameter update includes: Based on the physical responses obtained from the positive and negative disturbance measurements, the corresponding evaluation quantities are calculated respectively. The evaluation quantities corresponding to the positive and negative perturbations are differentially calculated to obtain directional information reflecting the influence of metasurface parameter changes on the evaluation quantities; Based on the directional information and combined with a preset update step size, the current metasurface parameters are adjusted, and an updated metasurface parameter configuration is generated.

[0012] Furthermore, the physical response is acquired by multiple spatially distributed detectors, each corresponding to a different spatial location, a different functional output channel, or a different computational task dimension.

[0013] Furthermore, the construction of the evaluation metric includes: The physical responses of the detectors at multiple spatial locations were acquired respectively; The multiple physical responses are normalized, weighted, or logically combined to generate a multidimensional response vector. Based on the matching relationship between the multidimensional response vector and the preset target, an evaluation quantity is constructed to guide the updating of metasurface parameters; the evaluation quantity is in scalar or vector form and is used to characterize the degree of matching between the physical response and the preset target.

[0014] Furthermore, by changing the arrangement of detectors, the construction of evaluation quantities, or training objectives, different computational or control tasks can be configured and implemented in the same physical computing space.

[0015] Furthermore, the computational space is trained to perform at least one of the following functions: electromagnetic wave energy focusing, target or pattern recognition, spatial location positioning, wireless channel modulation, environmental perception, or electromagnetic environment adaptive optimization.

[0016] The technical solution of this invention can be summarized as follows: 1. A computational space construction method based on programmable metasurfaces is proposed. By deploying multiple independently adjustable programmable metasurfaces in the target physical space and coordinating the discrete electromagnetic response states of each metasurface unit, electromagnetic waves can form multipath propagation and strong coupling relationships in space, thereby constructing the physical space into a computational space with overall adjustable electromagnetic response characteristics, providing a basic carrier for subsequent physical calculations and training; 2. A computational space in-situ training method based on physical perturbation and measurement feedback is proposed. By applying positive and negative perturbations to the metasurface parameters in the computational space and performing forward physical measurements respectively, adaptive updates of the metasurface parameters are achieved based on the difference information between the evaluation quantities corresponding to the two measurement results. This allows in-situ training of the computational space to be completed without the need to establish an analytical physical model or digital twin model. 3. A physical response evaluation and control mechanism for multi-output tasks is proposed. By deploying detectors corresponding to multiple spatial locations or functional channels in the computational space, multidimensional physical responses are acquired, and an evaluation quantity is constructed based on the physical responses to guide the updating of metasurface parameters. This enables the same computational space to achieve multiple functions such as electromagnetic wave focusing, target recognition, spatial positioning, or adaptive optimization of the electromagnetic environment through different training objectives and evaluation methods.

[0017] The beneficial effects of this invention are that, by constructing a physical computation space based on a programmable metasurface and introducing a physical measurement feedback training mechanism based on positive and negative perturbations, this invention can achieve in-situ training and adaptive control of the computation space without establishing an analytical electromagnetic model or digital twin model. This effectively reduces the system's dependence on accurate modeling and offline simulation, significantly simplifying the system design and optimization process. This invention directly utilizes real physical measurement results to guide metasurface parameter updates, avoiding the complex electromagnetic modeling and parameter sensitivity analytical calculation processes of traditional methods. It can still work stably in complex, multipath, strong scattering, or dynamically changing electromagnetic environments, greatly improving training efficiency and environmental adaptability. This invention is the first to propose an in-situ training method that uses the physical space itself as a trainable computational carrier, allowing the computation and learning process to occur directly in a real electromagnetic system, realizing a shift from "model-based design optimization" to "physical feedback-based adaptive learning." Furthermore, by introducing a mechanism to construct evaluation quantities from the physical responses of multiple detectors, the same computational space can achieve multiple functions such as electromagnetic wave energy focusing, target or pattern recognition, spatial location positioning, wireless channel control, and adaptive optimization of the electromagnetic environment through different training objectives and evaluation methods, demonstrating good generalization ability and scalability. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the overall computational space structure based on a programmable metasurface as described in this invention; as follows: Figure 1 As shown, multiple programmable metasurfaces are distributed at different locations in the target physical space, forming a computational space through the multipath propagation and mutual coupling of electromagnetic waves in the space; detectors are set in the space to acquire physical responses, and the computational space can achieve functions such as identification, localization, and electromagnetic energy focusing through different training targets; Figure 2 This is a schematic diagram illustrating the principle of the in-situ training method in computational space described in this invention. Figure 3 This is a schematic diagram of the structure and experiment of the computational space described in this invention in the target recognition task; Figure 3 (a) shows a schematic diagram of a computational space structure consisting of multiple programmable metasurfaces, and the relative positional relationship between the detector and the target being identified within the space; Figure 3 (b) shows a schematic diagram of the structure of a programmable metasurface unit; Figure 3 (c) shows the phase response characteristics of the programmable metasurface unit under different control states, which is used to illustrate the ability of the metasurface to control electromagnetic waves; Figure 3 (d) Figure 3 (e) shows a schematic diagram of the received power distribution corresponding to different identification tags; Figure 3 (f) Figure 3 (h) shows the curve of recognition accuracy changing with training rounds during the recognition task training process; Figure 3 (g) Figure 3 (i) shows the confusion matrix results after the recognition task was completed, which reflects the recognition accuracy of different categories; Figure 4 This is a schematic diagram and training result diagram of the electromagnetic focusing experimental system of the computational space under different physical scenarios described in this invention; Figure 4 (a) shows a schematic diagram of the overall arrangement of multiple programmable metasurfaces, detectors, and scene targets in the experimental environment; Figure 4 (b) shows a schematic diagram of the spatial structure in another experimental scenario to illustrate the applicability of the method of the present invention under different environmental conditions; Figure 4 (c) shows a schematic diagram of the parameter configuration of the programmable metasurface under different scenario conditions; Figure 4 (d) shows the changes in the detector's received signal and the training convergence trend during the training process in Scenario 1; Figure 4 (e) shows the changes in the detector's received signal and the training convergence trend during the training process in scenario 2. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] See Figure 1This invention proposes a computational space construction and in-situ training method based on a programmable metasurface, comprising the following steps: (1) Construction of a computational space based on programmable metasurfaces: Multiple independently controllable programmable metasurfaces are deployed in the target physical space to control the propagation characteristics of electromagnetic waves within the space. Each programmable metasurface consists of an array of several subwavelength-scale units, each unit having multiple discrete electromagnetic response states. State switching is achieved through controlled electronic devices, thereby discretely controlling the reflection or transmission phase of the incident electromagnetic wave. By distributing multiple programmable metasurfaces at different locations in the space, the electromagnetic wave undergoes multiple reflections, scattering, and couplings during propagation, thus forming a multipath propagation structure within the physical space. The joint configuration of the states of multiple metasurface units determines the overall electromagnetic response characteristics of the entire space, thereby giving the physical space a computational attribute that can be controlled as a whole, thus constituting a physical computational space.

[0021] (2) Computational space parameter representation and initialization: To facilitate training and control, the discrete electromagnetic response state of each programmable metasurface unit is mapped one-to-one with discrete parameters, so that the state of the entire computational space is represented as a parameter vector composed of multiple discrete parameters. The range of values ​​for this parameter vector constitutes the realizable set of the parameters. Before training begins, the metasurface parameters can be initialized according to empirical rules, random methods, or preset strategies, and corresponding control commands can be applied to each programmable metasurface to put the computational space into its initial working state.

[0022] (3) Physical Response Acquisition and Evaluation Quantity Construction: An input electromagnetic excitation is applied within the computational space, for example, by radiating electromagnetic waves into space through a transmitting antenna. Detectors are deployed at at least one preset location within the computational space to collect the physical response under the current metasurface parameter configuration. The physical response may include, but is not limited to, electromagnetic field strength, power distribution, transmission coefficient, reflection coefficient, or combinations thereof. Based on the physical response data collected by the detectors, an evaluation quantity is constructed to characterize the degree of completion of the computational task. The specific form of the evaluation metric can be set according to different application requirements, such as for energy focusing, signal enhancement, classification, or positioning accuracy assessment.

[0023] (4) Forward measurement based on physical perturbation: see Figure 2 To achieve in-situ training in the computational space, physical perturbations are applied to the parameters based on the current metasurface parameter configuration, and forward physical measurements are performed. Specifically, a set of perturbation vectors is first generated to characterize the way the metasurface parameters change. The disturbance vector is then mapped to the corresponding metasurface control command. This control command is applied to each programmable metasurface, causing its parameter configuration to change synchronously. Perform a forward physics measurement under this perturbation configuration to obtain the first physics response. Based on the same initial parameter configuration, a second set of perturbation vectors is generated that is opposite in direction to or complementary to the aforementioned perturbation vectors. and apply corresponding control commands. Perform a second forward physics measurement to obtain the second physics response. Using the above method, the measurement results of the influence of parameter changes on the physical response can be obtained without analyzing the electromagnetic relationships within the computational space.

[0024] It should be noted that the perturbation vector is a multidimensional perturbation vector, whose components are generated in a random, pseudo-random or preset sequence manner, and are used to act on multiple metasurface units or multiple programmable metasurfaces simultaneously.

[0025] (5) Parameter update based on differential feedback: Evaluation quantities are calculated based on two physical measurement results corresponding to positive and negative disturbances, respectively. The disturbance vectors corresponding to the positive and negative disturbances have opposite directions or complementary relationships in the parameter space. The physical disturbance is achieved by changing the actual control state of the programmable metasurface unit, rather than simply simulating it in the numerical domain. By performing differential operations on the two evaluation quantities, directional update information reflecting the changing trend of the metasurface parameters is obtained. Based on this update information and combined with the preset update step size Adjust the current metasurface parameters to generate a new parameter configuration. Since metasurface parameters are typically discrete, after parameter updates, projection, quantization, or mapping operations are performed on the updated results to bring them back into the preset set of realizable parameters, thereby ensuring the effectiveness and stability of subsequent physical implementations.

[0026] (6) In-situ iterative training process: The above-mentioned perturbation measurement and parameter update process is taken as one training iteration. By continuously repeating the physical perturbation, forward measurement, differential feedback and parameter update process, the overall electromagnetic response of the computational space gradually converges to the preset target. When the number of training iterations reaches the preset upper limit... Stop the training process and configure the current metasurface parameters. This represents the working state of the computational space after training is complete.

[0027] (7) Multi-detector and multi-task application configuration: Multiple detectors are deployed at different spatial locations in the computation space, each corresponding to a different output channel or task dimension. The physical responses corresponding to the detectors at multiple spatial locations are acquired; the multiple physical responses are normalized, weighted, or logically combined to generate a multi-dimensional response vector; based on the matching relationship between the multi-dimensional response vector and the preset target, an evaluation quantity is constructed to guide the updating of metasurface parameters. The evaluation quantity is in scalar or vector form and is used to characterize the degree of matching between the physical response and the preset target.

[0028] By changing the detector deployment, evaluation quantity construction method, or training target, the same physical computing space can be configured to perform different tasks, including but not limited to electromagnetic wave energy focusing, target or pattern recognition, spatial location positioning, wireless channel modulation, or electromagnetic environment adaptive optimization.

[0029] It should be noted that the in-situ training process is completed without the need to establish an analytical electromagnetic model, backpropagation model or digital twin model of the computational space, and the update of the metasurface parameters depends only on physical measurement feedback.

[0030] Implementation Example 1: Object Recognition Experiment Based on Computational Space To verify the feasibility and effectiveness of the computational space based on programmable metasurfaces described in this invention for object recognition tasks, numerical simulation experiments on object recognition based on computational space were conducted. This embodiment uses a full-wave electromagnetic simulation method to verify the object recognition process within the constructed computational space model. For example... Figure 3 As shown in (a), the computational space is composed of multiple independently controllable programmable metasurfaces. In this embodiment, four programmable metasurfaces are exemplarily set, positioned at different locations in free space, surrounding each other to form the computational space. Each programmable metasurface consists of multiple unit arrays. In this embodiment, each metasurface is composed of several rows and columns of units, used to control the incident electromagnetic waves. Figure 3 As shown in (b), each metasurface unit integrates controllable devices, enabling the unit to switch between multiple discrete electromagnetic response states. By driving these controllable devices in different ways, each unit can achieve multiple programmable phase response states. Figure 3 As shown in (c), in this embodiment, different discrete phase response states are exemplarily mapped to a set of discrete parameters to characterize the control state of the metasurface unit.

[0031] Set up the object to be identified within the computing space, such as Figure 3As shown in (a), the object to be identified is represented in the form of a two-dimensional pattern to simulate different categories of identification targets. The identification targets include multiple different categories; in this embodiment, several number-type patterns and letter-type patterns are selected as identification objects. Each identification object is represented in a binary manner and corresponds to a different identification label. During the simulation, a plane electromagnetic wave is radiated into the computational space through a transmitting device. The incident electromagnetic wave undergoes multiple scattering and coupling with the object to be identified and the programmable metasurface in the computational space, forming a complex electromagnetic field distribution. Multiple detection devices are set in the computational space to collect electromagnetic response signals at different spatial locations. The electromagnetic response signals output by the detection devices constitute multi-dimensional physical feedback information for object identification. During the training phase, an evaluation quantity characterizing the correctness of object identification is constructed based on the electromagnetic response signals collected by the detection devices, and the parameters of each programmable metasurface are initialized and iteratively updated according to the in-situ training method described in this invention. By applying physical perturbations to the metasurface parameters and performing forward physical measurements, the computational space gradually forms electromagnetic response features that can distinguish different identification targets. During the identification phase, the category label of the corresponding target is determined by comparing the distribution of electromagnetic energy received by different detection devices. For example... Figure 3 (d) and Figure 3 As shown in (e), the electromagnetic energy corresponding to different categories of targets exhibits significant differences at different detection devices, and the location with the highest energy aligns with the target category label, indicating that the computational space can correctly complete the object recognition task. Figure 3 (f) and Figure 3 As shown in (h), during the training process, the object recognition accuracy gradually increases with the number of training iterations and tends to stabilize after a relatively small number of training rounds, indicating that the computational space can quickly form effective recognition capabilities through in-situ training. Furthermore, as... Figure 3 (g) and Figure 3 As shown in (i), after training, the computational space can provide recognition results consistent with the real labels for different categories of recognition targets, demonstrating high recognition accuracy. The numerical simulation results above verify that the computational space based on a programmable metasurface described in this invention can effectively recognize different object categories through in-situ training, relying solely on the propagation and coupling characteristics of electromagnetic waves in physical space, achieving the fusion of physical computation and intelligent recognition functions without the need to establish an accurate physical model.

[0032] Implementation Example 2: Electromagnetic Wave Energy Focusing Experiment Based on Computational Space To verify the versatility and effectiveness of the computational space described in this invention in complex electromagnetic environments, an electromagnetic wave energy focusing experiment based on the computational space was conducted. This embodiment was completed in a microwave anechoic chamber to simulate a controllable electromagnetic propagation environment with practical engineering significance. The experimental system includes multiple independently adjustable programmable metasurfaces, a transmitting antenna, a detection device, and a measurement and control unit. Multiple programmable metasurfaces are distributed at different locations in the target physical space, forming a computational space; the transmitting antenna radiates electromagnetic waves into the computational space, and the detection device is positioned at a predetermined target focusing location to collect the electromagnetic response signal at that location.

[0033] like Figure 4 (a) and Figure 4 As shown in (b), two representative experimental scenarios were constructed. Scenario 1 places two cylindrical dielectric scatterers within the computational space to simulate a multipath scattering environment with finite obstacles. Scenario 2 arranges various objects within the computational space, including sofas, bookshelves, and dining tables, to simulate an indoor environment with complex structures and strong multipath coupling characteristics. Both scenarios introduce significant electromagnetic scattering and coupling effects, verifying the adaptability of the method of this invention in complex environments. During the experiment, electromagnetic waves are radiated into the computational space via a transmitting antenna. These electromagnetic waves are transversely polarized waves with their electric field direction polarized along a predetermined axis. The detection device, in probe form, is arranged perpendicular to the spatial reference plane and connected to a single measuring instrument to acquire the electromagnetic response signal at the target focusing position. The output signal of the detection device is acquired in real time by the measuring unit to construct an evaluation quantity characterizing the electromagnetic energy intensity at the target location. During the training phase, the parameters of each programmable metasurface are initialized according to the in-situ training method described in this invention. While maintaining the physical structure, physical perturbations are applied to the metasurface parameters, and forward physical measurements are performed. Based on the electromagnetic response signals collected by the detection device, evaluation quantities are calculated, and the metasurface parameters are iteratively updated, thereby gradually guiding the overall electromagnetic response of the computational space to converge towards the target focusing state.

[0034] like Figure 4 (d) and Figure 4 As shown in (e), with the progress of training iterations, the received signal strength at the target focusing position shows a continuous upward trend, while the corresponding training update amplitude gradually decreases, indicating that the electromagnetic response in the computational space gradually stabilizes and converges. In scenario one, the received signal strength at the target position gradually increases from the initial state to a stable state; in scenario two, a significant increase in the received signal strength is also observed, indicating that the method of this invention can still effectively achieve electromagnetic energy focusing under complex multipath scattering and strong coupling conditions. Figure 4As shown in (c), the parameter configurations of each programmable metasurface after training are illustrated in two experimental scenarios. It can be seen that different scenarios correspond to different metasurface parameter distributions, reflecting the adaptive control state of the computational space in response to specific electromagnetic environments. The experimental results verify that the computational space based on programmable metasurfaces described in this invention can achieve adaptive control of electromagnetic wave energy distribution relying solely on measurable physical feedback information, without the need to establish an accurate electromagnetic model. It also exhibits good stability and focusing effect in complex environments such as strong scattering and multipath coupling.

Claims

1. A computational space construction and in-situ training method based on a programmable metasurface, characterized in that, Includes the following steps: (1) Construction of computational space: Multiple independently controllable programmable metasurfaces are deployed in the target physical space. Each programmable metasurface is composed of multiple units with discrete electromagnetic response states. Each programmable metasurface forms multipath coupling through the propagation of electromagnetic waves in space, thereby constructing a computational space with overall electromagnetic response characteristics. (2) Physical response acquisition: An input electromagnetic excitation is applied to the computation space, and the physical response of the computation space under the current metasurface parameter configuration is acquired through at least one detector. An evaluation quantity for characterizing the degree of completion of the computation task is constructed based on the physical response. (3) Forward perturbation measurement: Based on the current metasurface parameter configuration, a first set of physical perturbations is applied to the metasurface parameters, and forward physical measurement is performed under the perturbation parameter configuration to obtain the first physical response; (4) Negative perturbation measurement: Based on the current metasurface parameter configuration, a second set of physical perturbations opposite to the first set of physical perturbations are applied to the metasurface parameters, and forward physical measurement is performed under the parameter configuration after perturbation to obtain the second physical response; (5) Parameter update: Based on the difference between the evaluation values ​​corresponding to the first physical response and the second physical response, the update value of the metasurface parameters is generated, and the metasurface parameters are updated. (6) Iterative training: Repeat steps (3) to (5) until the evaluation quantity meets the preset conditions and the computational space for completing in-situ training is obtained.

2. The computational space construction and in-situ training method based on a programmable metasurface according to claim 1, characterized in that, The electromagnetic response state of the programmable metasurface unit is a discrete phase state, and each unit realizes multiple reflection or transmission phases under a preset state combination through multiple controlled electronic devices. The discrete phase states constitute a finite set of realizable states.

3. The computational space construction and in-situ training method based on a programmable metasurface according to claim 2, characterized in that, The metasurface parameters are represented in discrete integer or discrete encoding form. During parameter updates, projection or quantization operations are performed on the updated metasurface parameters to map them back to the finite set of realizable states.

4. The computational space construction and in-situ training method based on a programmable metasurface according to claim 1, characterized in that, The positive disturbance measurement and negative disturbance measurement include: Based on the current metasurface parameter configuration, a set of perturbation vectors is generated, which are used to characterize the synchronous change mode of multiple metasurface unit parameters; The disturbance vector is mapped to the corresponding metasurface control command and applied to the programmable metasurface; Under the control command, forward physical measurements are performed on the computational space to obtain the corresponding physical response; The perturbation vectors corresponding to the positive and negative perturbations have opposite directions or complementary relationships in the parameter space.

5. The computational space construction and in-situ training method based on a programmable metasurface according to claim 4, characterized in that, The perturbation vector is a multidimensional perturbation vector, whose components are generated in a random, pseudo-random or preset sequence manner, and are used to act on multiple metasurface units or multiple programmable metasurfaces simultaneously.

6. The computational space construction and in-situ training method based on a programmable metasurface according to claim 1, characterized in that, The parameter update includes: Based on the physical responses obtained from the positive and negative disturbance measurements, the corresponding evaluation quantities are calculated respectively. The evaluation quantities corresponding to the positive and negative perturbations are differentially calculated to obtain directional information reflecting the influence of metasurface parameter changes on the evaluation quantities; Based on the directional information and combined with a preset update step size, the current metasurface parameters are adjusted, and an updated metasurface parameter configuration is generated.

7. The computational space construction and in-situ training method based on a programmable metasurface according to claim 1, characterized in that, The physical response is acquired by multiple spatially distributed detectors, each corresponding to a different spatial location, a different functional output channel, or a different computational task dimension.

8. The computational space construction and in-situ training method based on a programmable metasurface according to claim 7, characterized in that, The construction of the evaluation metric includes: The physical responses of the detectors at multiple spatial locations were acquired respectively; The multiple physical responses are normalized, weighted, or logically combined to generate a multidimensional response vector. Based on the matching relationship between the multidimensional response vector and the preset target, an evaluation quantity is constructed to guide the updating of metasurface parameters; the evaluation quantity is in scalar or vector form and is used to characterize the degree of matching between the physical response and the preset target.

9. The computational space construction and in-situ training method based on a programmable metasurface according to claim 1, characterized in that, By changing the arrangement of detectors, the construction of evaluation quantities, or training objectives, different computational or control tasks can be configured and implemented in the same physical computation space.

10. The computational space construction and in-situ training method based on a programmable metasurface according to claim 1, characterized in that, The computational space is trained to perform at least one of the following functions: electromagnetic wave energy focusing, target or pattern recognition, spatial location positioning, wireless channel control, environmental perception, or electromagnetic environment adaptive optimization.

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