A High-Efficiency and Versatile Reconfigurable Intelligent Surface Design Paradigm with Novel Topological Representation

Ying Juan Lu; Jia Nan Zhang; Yi Han Zhao; Jun Wei Zhang; Zhen Zhang; Rui Zhe Jiang; Jing Cheng Liang; Hui Dong Li; Jun Yan Dai; Tie Jun Cui; Qiang Cheng

doi:10.1016/j.eng.2024.11.028

Engineering ›› 2025, Vol. 48 ›› Issue (5) :163 -173. DOI: 10.1016/j.eng.2024.11.028

Research Metamaterials—Article

research-article

A High-Efficiency and Versatile Reconfigurable Intelligent Surface Design Paradigm with Novel Topological Representation

Ying Juan Lu ^a^,^b^,^#
, Jia Nan Zhang ^a^,^b^,^#^,^*
, Yi Han Zhao ^a^,^b
, Jun Wei Zhang ^a^,^b
, Zhen Zhang ^c
, Rui Zhe Jiang ^a^,^b
, Jing Cheng Liang ^a^,^b
, Hui Dong Li ^a^,^b
, Jun Yan Dai ^a^,^b^,^*
, Tie Jun Cui ^a^,^b^,^*
, Qiang Cheng ^a^,^b^,^*

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Abstract

With digital coding technology, reconfigurable intelligent surfaces (RISs) become powerful real-time systems for manipulating electromagnetic (EM) waves. However, most automatic RIS designs involve extensive numerical simulations of the unit, including the passive pattern and active devices, requiring high data acquisition and training costs. In addition, for passive patterns, the widely employed random pixelated method presents design efficiency and effectiveness challenges due to the massive pixel combinations and blocked excitation current flow in discrete patterns. To overcome these two critical problems, we propose a versatile RIS design paradigm with efficient topology representation and a separate design architecture. First, a non-uniform rational B-spline (NURBS) is introduced to represent continuous patterns and solve excitation current flow issues. This representation makes it possible to finely tune continuous patterns with several control points, greatly reducing the pattern solution space by 20-fold and facilitating RIS optimization. Then, employing multiport network theory to separate the passive pattern and active device from the unit, the separate design architecture significantly reduces the dataset acquisition cost by 62.5%. Through multistep multiport calculation, the multistate EM responses of the RIS under different structural combinations can be quickly obtained with only one prediction of pattern response, thereby achieving dataset and model reuse for different RIS designs. With a hybrid continuous-discrete optimization algorithm, three examples—including two typical high-performance RISs and an ultra-wideband multilayer RIS—are provided to validate the superiority of our paradigm. Our work offers an efficient solution for RIS automatic design, and the resulting structure is expected to boost RIS applications in the fields of wireless communication and sensing.

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Keywords

Reconfigurable intelligent surfaces / Non-uniform rational B-splines / Separate design architecture / Dataset reuse / Versatile metasurfaces design

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Ying Juan Lu, Jia Nan Zhang, Yi Han Zhao, Jun Wei Zhang, Zhen Zhang, Rui Zhe Jiang, Jing Cheng Liang, Hui Dong Li, Jun Yan Dai, Tie Jun Cui, Qiang Cheng. A High-Efficiency and Versatile Reconfigurable Intelligent Surface Design Paradigm with Novel Topological Representation. Engineering, 2025, 48 (5) : 163-173 DOI:10.1016/j.eng.2024.11.028

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1. Introduction

Programmable digital coding metasurfaces [1], [2] are two-dimensional (2D) artificial electromagnetic (EM) metamaterials that contain active devices for the precise control of EM waves, including their amplitude, phase, and frequency in real time. Such metasurfaces have extensive applications thanks to their fabrication simplicity, ultrathin profile, and reprogrammability, ranging from beam refraction [3], [4] and EM stealth [5], [6] to holographic imaging [7], [8]. Moreover, metasurfaces have demonstrated significant potential in enhancing the performance and functionality of modern antenna systems [9], [10], [11]. In the wireless communication community, programmable metasurfaces are also called reconfigurable intelligent surfaces (RISs); as they are renowned for their notable dynamic wireless channel control [12], [13], they have become crucial in fifth-generation (5G) and sixth-generation (6G) research. The evolution from passive metasurfaces to RISs highlights the growing demand for enhanced performance and expanded applications. However, metasurface unit structures exhibit variations, and a direct analytical formula to correlate them with the EM responses is lacking. Conventional designs mainly rely on classical structures and their variants. When these structures prove to be inadequate for design targets, researchers must continually adjust them, incurring very high costs.

Recently, the successful integration of machine learning (ML) with image processing [14], [15], object detection [16], [17], and natural language processing [18] has been demonstrated to have robust learning capability, ushering in new opportunities for EM designs [19], [20], [21], [22], [23]. Data-driven automatic metasurface design can be roughly classified into two types: inverse design [24], [25], [26], [27], [28], [29], [30], [31] and forward design [32], [33], [34], [35], [36]. Inverse design minimizes the dependence on designer expertise by efficiently generating unit structures tailored to the desired responses. This approach is effective for meeting design targets with similar requirements, but challenges emerge when the target response extends beyond the data space or is nonexistent [37]. Forward design uses the fitness function as the optimization goal to determine the optimal unit, thereby offering greater tolerance in target description, unlike the stringent input requirements in inverse design. However, forward design requires a re-simulation for each unit optimization. Both the forward and inverse design methods promote automatic metasurface designs, but ML-based methods present a challenge: the high data cost linked to effective design. Efforts have been made to alleviate this problem by integrating physical principles or laws (e.g. Maxwell’s equations [38], [39], physical analysis [36], [40], and equivalent circuit theory [33], [34], [41], [42]) into ML. However, these methods are generally confined to particular classic regular patterns and lack accuracy in the broadband range.

More importantly, most ML-assisted methods focus on passive metasurfaces, which are insufficient for RISs with more complex structures and characteristics. Firstly, as the key factor in determining the RIS modulation performance, different active devices exhibit diverse states that defy easy quantification and learning in neural networks. Secondly, the varying states of active devices correspond to distinct impedances, resulting in multiple EM responses from an RIS. Like a 1-bit RIS unit, an automatic design entails a link between two EM responses and a single unit, which makes training more difficult [31]. This multistate mapping dilemma intensifies with escalating coded quantization. Finally, a conventional random pixelated pattern is usually discrete, which hinders the smooth flow of excitation current from active devices and the maximum resonance ability of surface patterns.

In this work, we propose a resource-efficient design paradigm that includes a novel non-uniform rational B-splines topology representation method (NBTRM) and a transplantable separate design architecture. This paradigm enables the creation of multifunctional and structurally diverse RIS designs without the need for dataset re-collection and model retraining. Utilizing several spline control points and pattern mappings, NBTRM can quickly generate and finely tune continuous patterns for smooth current flow, effectively narrowing the pattern solution space by a factor of 20 and facilitating the optimization efficiency. Then, employing microwave multiport network theory, the RIS unit is separated into four subparts (i.e., active device, pattern layer, dielectric layer, and metal ground). In this separate design architecture, the multistate responses of units with different subpart combinations can be obtained in nearly 1 s with a pre-incremental learning network (PILN) and theoretical calculations, thus avoiding time-consuming simulations in the optimization process. This ingenious architecture solves the multistate mapping dilemma when various active devices are embedded into an RIS unit, extends the design freedom, and greatly reduces dataset acquisition costs by 62.5%. Three design examples—including two functional single-layer RISs and one ultra-wideband 1-bit multilayer RIS that match or surpass well-designed manual units—are presented to demonstrate our paradigm. The proposed method’s scalability allows it to be extended to other complex RIS designs as well, such as transmissive or dual-polarized RISs, without the need for specific equivalent circuit models for each configuration. This work not only enhances the efficiency and flexibility of RIS design but also provides a sustainable and scalable framework applicable to various EM device designs.

2. Overview of the automatic design paradigm for RISs

Current passive metasurface design research mainly focuses on finding a matching unit for a fixed EM response. This process disregards the EM responses in other states, especially when active devices transit with changing bias voltage. Thus, a separate passive pattern design and an independent active device selection are essential to expedite RIS design and reduce data training demands. Our paradigm offers a fresh design perspective: leveraging the unit’s inner cascading mechanism to design RISs. Utilizing microwave multiport network theory, the unit is split into four subparts (i.e., the active device, pattern layer, dielectric layer, and metal ground), which are parameterized as inputs to a hybrid continuous-discrete particle swarm optimization (PSO) algorithm [43], as indicated in Fig. 1(a).

As shown in Fig. 1(b), NBTRM is first adopted to generate surface patterns, mapping several spline control points to a continuous pattern for a smooth and exciting current flow. This method greatly facilitates pattern optimization with only a few variables, achieving pattern solution space compression. According to the optimization steps shown in Fig. 1(a), a separate design architecture for RIS responses calculation based on PILN and multiport network theory is presented in Fig. 1(c). The PILN is trained to predict the surface pattern’s scattering matrix, whereas the scattering matrices of other subparts are analytically calculated or provided by the manufacturer. By analyzing the internal connection scattering matrix in these subparts, the multistate EM responses of each parameterized particle (unit) can be calculated with two-step cascading operations. This architecture addresses the limitation in current RIS designs, achieves the independent optimization of separate subparts, and facilitates dataset and trained model reuse. Based on NBTRM and the separate design architecture, the multistate EM responses of an updated particle (unit) can be calculated by modifying the corresponding scattering matrices of updated continuous (i.e., control point coordinates) or discrete variables (i.e., the permittivity, thickness, and active device, as shown in Table 1), to achieve optimization with PSO processing. To elucidate this design concept, we provide a detailed exposition to highlight the specific content of each subblock diagram.

3. Theory and methods

3.1. NBTRM for dataset

The random pixelated method presents significant challenges in pattern design efficiency due to the vast number of possible pixel combinations. Moreover, discontinuity within pattern pixel blocks impedes the flow of the inner excitation current, constraining the capacity for pattern resonance. To overcome these challenges, NBTRM is introduced to generate continuous patterns using non-uniform rational B-splines (NURBSs) [44], [45]. A NURBS curve involves control points, weights, and a knot vector. In essence, a NURBS curve with n control points can be conceptualized as B-spline curves defined independently over multiple intervals, which are expressed as follows:

(1)

B (K) = \sum_{i = 0}^{n - 1} N_{i, m} (K) R_{i} B_{i} / \sum_{i = 0}^{n - 1} N_{i, m} (K) R_{i}

The basic functions

N_{i, m} (K)

is defined as follows:

(2)

N_{i, 0} (K) = \{\begin{matrix} 1, K_{i} \leq K \leq K_{i + 1} \\ 0, otherwise \end{matrix}, i \in [0, n - 1]

(3)

N_{i, m} (K) = \frac{(K - K_{i}) N_{i, m - 1} (K)}{K_{i + m} - K_{i}} + \frac{(K_{i + m + 1} - K) N_{i + 1, m - 1} (K)}{K_{i + m + 1} - K_{i + 1}}, m \geq 1, i \in [0, n - 1]

where the knot vector

K = \{K_{1}, K_{2}, . . ., K_{p}\}

defines the knots assembled in NURBS curve

B (K)

;

N_{i, m} (K)

is the associated basis function evaluated at knot K, with the ith control point of degree m;

B_{i}

is the ith control point with coordinate

(x_{i}, y_{i})

; and

R_{i}

is the weight factor for

B_{i}

. Among these equations,

p = n + m

. Eqs. (2), (3) express how

N_{i, m} (K)

is recursively generated from

N_{i, m - 1} (K)

and

N_{i + 1, m - 1} (K)

Fig. 2 exhibits a modeling flowchart of NBTRM that allows easy pattern updates via the control point’s movement. The design process begins with generating five control points, followed by constructing a NURBS curve using Eq. (1). The order is

m = 3

, and the weight factor for each point is set as 1. This curve is then discretized, quantized, mapped onto a coding matrix, and mirrored to form a 10 × 10 surface pattern. The unique non-uniformity of NURBS ensures that adjusting one control point

B_{2}

exclusively affects its associated curve segment without impacting other parts of the curve, enhancing the pattern optimization precision and flexibility. In this work, the pattern simulation spans the frequency range from 2 to 16 GHz with a 10 mm unit period. The coordinates

(x_{i}, y_{i})

of the control points are constrained in the range

x_{i} \in [- 1, 6]

y_{i} \in [- 1, 11]

, ensuring that the mapping pattern remains within the region

x \in [0, 5]

y \in [0, 10]

. The initial control point is aligned with the active device’s position on the surface pattern, while the control point range is slightly extended beyond the metal pattern boundary to allow for greater design flexibility. The y-axis symmetrical surface pattern is divided into 10

\times

10 blocks (0.8 mm each), including a central 0.3 mm-wide strip for active device welding. Employing only five control points, NBTRM reduces the topology domain for pattern iteration by a factor of 20 compared with the original 10 × 10 codes. Finally, 10 000 distinct curves are generated to map pattern layers with these patterns’ responses obtained through a CST Studio Suite–Python co-simulation method.

The NURBS topological representation method offers significant advantages over the traditional random pixelated method, particularly in design space compression, shape modification flexibility, and representation smoothness. By reducing the dimensionality of the design space and allowing for more efficient modifications, NBTRM enhances both the design efficiency and the accuracy of the modeling process. It should be noted that the permittivity of the exit plane wave space is consistent with the dielectric to ensure cascading calculation accuracy. Dual wave ports are concurrently configured to excite transverse electric (TE)-polarized EM waves and capture output waves with a distance of 30 mm to the reference plane, while the boundaries are set to “unit cell.” Specific NBTRM steps and simulation settings are detailed in Appendix A Sections S1 and S2, respectively.

As shown in Fig. 3, the permittivity changes will systematically impact the EM responses of the fixed pattern layer. For practical applications, the permittivity pre-list in Table 1 can guide the simulations, combining 20% of the pattern dataset with all permittivities and interleaving parameter values for the remaining patterns, as shown in Table 2. Finally, a dataset including 50 000 sets of combined patterns and responses is obtained.

3.2. Separate design architecture

Following the existing design paradigms, general thinking tends to employ deeper and more intricate neural networks, like that shown in Fig. 4(a), to learn the link between multistate responses and the entire unit. However, increasing the network complexity leads to challenges such as model convergence issues, higher data expenses, and increased computational requirements. To tackle these issues, we propose a separate design architecture. This architecture first compresses the complex network into a simpler neural network (i.e., the PILN) focusing solely on the pattern layer’s response. The overall unit responses are then computed using theoretical formulas. This decomposition extends the design flexibility of the RIS unit and allows for the transfer of collected pattern datasets and a trained PILN to transmissive RIS or multilayer RIS designs, thereby increasing the data reusability.

Fig. 4(b) shows the cascading relationship of the separate subparts: pattern layer A, dielectric layer B, active device C, and the metal ground. These subparts are treated as distributed components in a microwave circuit, with port 1 signifying the excitation port from the incident EM wave, and ports 4–7 denoting the interconnection ports between A, B, and C. Ports 2 and 3 are the ground side, which can be simplified as a short circuit. The transmission matrix of B (T_B) can be expressed as follows:

(4)

T_{B} = [\begin{matrix} c o s (ω n_{r} h / C_{0}) & j η s i n (ω n_{r} h / C_{0}) \\ j s i n (ω n_{r} h / C_{0}) / η & c o s (ω n_{r} h / C_{0}) \end{matrix}]

where ω is the angular frequency,

C_{0}

is the velocity of light, h is the thickness of the dielectric layer B,

n_{r} = \sqrt{ε_{r} μ_{r}}

is the refractive index,

ε_{r}

is the relative permittivity of the dielectric layer B,

μ_{r}

is the relative permeability of the dielectric layer B, and η is the dielectric wave impedance [46]. The scattering matrix of C is obtained from the product company or through measurement. Simulating the pattern layer reveals its scattering matrix. Due to the non-connection between B and C, two cascading calculations are crucial. Initially, we integrate A and B with the following formulation:

(5)

S (f) = S_{p p} (f) + S_{p c} {(Γ - S_{c c} (f))}^{- 1} S_{c p} (f)

where

f

is frequency,

Γ

is connection matrix,

S

is the scattering matrix of the RIS unit,

S_{p p}

represents the scattering matrix between internal ports,

S_{c c}

denotes the scattering matrix between external ports,

S_{p c}

represents the scattering matrix from the external to internal ports, and

S_{c p}

is the scattering matrix from the internal to external ports [47]. Detailed steps are provided in Appendix A Section S3.

We then cascade the passive part (the combined AB part and ground) with C. To account for multistate responses under different active device operation states, we simply replace the scattering matrix of C and repeat the two-step cascading calculation. This approach eliminates the need for additional predictions and simulations to determine the unit’s multistate response.

This architecture employs frequency-dependent scattering matrices for the response calculations, which could be extended to an infinite frequency band. The multiple sample analysis in Section S3 demonstrates this architecture’s calculation accuracy and its capability to substitute a portion of simulation tasks and networks. In this way, our architecture greatly reduces the dataset acquisition time costs, with an average simulation time of 47 s for a pattern layer (2 min and 3 s for the entire unit), cutting the data acquisition time from 24 to 9 days (62.5%). Moreover, the multistate responses of units in different combinations (i.e., units with a fixed pattern, different thicknesses, and different active devices) can be obtained through a single pattern layer numerical simulation, which could be used to achieve infinite expansion of a dataset in reverse design. These analyses demonstrate the power of our architecture, which enhances the design freedom, achieves data reuse, and overcomes band limitations in traditional models. Using this architecture, it becomes simple and easy to implement high-efficiency and versatile RIS designs. In addition, due to its independent design principle, this separate design architecture can be further extended to RIS structures involving increased geometric complexity, multilayer structures, or multiple active devices.

3.3. Structure and training of the PILN

The unit multistate EM responses are calculated using scattering matrices of the subparts. Since the pattern layer’s matrix cannot be directly obtained, we design a PILN (Fig. 5(a)) with a 50-bit pattern code and a 20-bit binary code for permittivity as input. Three custom convolutional channels after the pattern input are set to boost the network’s ability to learn complex pattern features. To prevent potential deep resonances and phase flips in amplitude and phase curves from complicating the neural network training, the real and imaginary components of the scattering parameters are collected during the dataset acquisition process. This conversion results in smoother dataset curves, thereby improving the stability of the neural network’s performance. Ultimately, the PILN is a dual-output neural network for the real and imaginary parts of the scattering coefficient and includes two training steps. It undergoes a pre-training step with 2000 × 10 sets of data, encompassing all permittivities, as shown in Table 2, and enabling the neural network to grasp the regular effect of permittivity on the pattern responses. Formal training continues with the same network structure to learn the link between the pattern and the EM response using the total dataset. During the training process, each pattern is paired with at least three permittivities to avoid forgetting knowledge from the pre-training step.

In the training process, the dataset is split into training, validation, and testing sets (80%, 10%, and 10%, respectively), with mean squared error (MSE) being employed as the training performance metric. The final loss of the PILN is the summation of

L_{r e}

and

L_{i m}

with the same weight.

L_{r e}

and

L_{i m}

represent the loss of real and imaginary outputs, respectively. The synthesized loss function is defined as follows:

(6)

F i n a l_L o s s = {0.5 \times L}_{r e} + {0.5 \times L}_{i m}

Apart from the MSE, the similarity in shape between two curves serves as a crucial criterion that must be assessed. The average cosine similarity of the testing set is used to evaluate the prediction effect of the trained model, which is calculated by the following equation:

(7)

C o s i n e S i m i l a r i t y = \frac{X_{1} ∙ X_{2}}{|X_{1}| |X_{2}|} \times 100 %

where

X_{1}

represents the vector of the curve predicted by our model, and

X_{2}

represents the vector of the actual curve obtained from the simulation (i.e., the ground truth).

Fig. 5(b) depicts the outcomes of the PILN’s two-step training process, showcasing average training losses of 0.0014 during the pre-training and 6.792 × 10^–4 for the final formal training. The final average cosine similarity across the total testing sets stands at 99.66%, which means that the PILN is credible for matrix prediction and response calculation. We further design an ablation experiment; that is, we remove the pre-training to verify the performance of the two-step trained model. The training loss in the ablation experiment is 8.64 × 10^–4, which is much higher than that of the PILN (6.792 × 10^–4) in Fig. 5(c). The strengths of the PILN are further verified with the testing set, for which the PILN exhibits a smaller prediction error of 4.676 × 10^–4 (compared with 1.111 × 10^–3 in the ablation experiment) and a higher accuracy of 99.66% (versus 98.61% in the ablation experiment). Moreover, compared with the multilayer perceptron (MLP) baseline, our model improves the accuracy by nearly 1.07% and reduces the prediction error by 7.434 × 10^–4, underscoring its superior performance. Three random pattern layers in the respective testing sets are selected to illustrate the prediction effect of the two-step training. Figs. 5(d) and (e) reveal a high level of consistency between the predicted and actual curves. The analysis and more training information on the PILN are provided in Appendix A Section S4.

4. Model validation and experimental verification

It should be noted that our paradigm enables multi-purpose use with one-time training. After training the PILN, designing RIS units with various functionalities and structures becomes seamless, requiring no additional EM simulations or secondary model training. In contrast, when using a traditional method, it is necessary to develop a new parametric model from scratch, which involves numerous simulations and extended training cost. Moreover, our trained PILN can even be transplanted and utilized for complex RIS structure design including transmissive and multilayer RISs. To further verify our paradigm, we design two different single-layer units that meet typical RIS demands and one ultra-wideband 1-bit multilayer RIS unit. The design procedure leverages NBTRM for precise control over the unit pattern, coupled with the separate design architecture to iteratively refine and optimize the design parameters. This paradigm ensures that the RIS units achieve the desired EM functionalities while maintaining physical feasibility and efficiency within the defined constraints.

In the first case, we design a 1-bit phase-modulation RIS unit, featuring an amplitude loss of less than 3 dB within 9–15 GHz and a relative bandwidth of 50%, which achieves better performance even in comparison with manually crafted units. In the optimization process, the design target is the following:

(8)

F i t n e s s = - E / M

(9)

E = \sum_{t = 1}^{M} χ \{|φ_{1} (f_{t}) - φ_{0} (f_{t})| > 160, 20 l g (a_{1} (f_{t})) > - 3, 20 l g (a_{0} (f_{t})) > - 3\}

where M is the total number of frequency points sampled with a 200 MHz interval in 9–15 GHz. The indicator function

χ \{c o n d i t i o n\}

is 1 if the condition is met and 0 otherwise. Thus, the sum E is the total number of frequency points satisfying the condition, where

f_{t}

represents the tth frequency points,

φ_{1}

and

a_{1}

denote the phase and amplitude of the S₁₁ of the unit in the “on” state, respectively, and

φ_{0}

and

a_{0}

represent the phase and amplitude of S₁₁ in the “off” state, respectively. With 500 sets of particles in the initial population and 50 iterations in 8 h, the final output unit achieves 1-bit phase-modulation in 9–15 GHz with MADP-000907-14020x as the load. Fig. 6(a) depicts the fitness curve of the optimization process. The structural parameters of this unit are given in Table 3. Due to the excellent training of the PILN, the predicted EM responses of this unit align well with the simulated results, as shown in Fig. 6(b), indicating that the designed RIS achieves the design demands and robustly validating the effectiveness of our paradigm.

Next, we aim to design a typical 3-bit phase-modulation RIS unit (315° shift) in the frequency band of 4–5 GHz with an amplitude loss of less than 4 dB. Varying voltages permit continuous changes in the varactor’s reverse-biased junction capacitance, enabling RIS reconfigurability. We designate the load’s serial number as the varactor SMV1405-040LF in Table 1. The design target is changed to the following:

(10)

E = \sum_{t = 1}^{M} χ \{|φ_{2} (f_{t}) - φ_{0} (f_{t})| > 315, 20 l g (a_{2} (f_{t})) > - 4, 20 l g (a_{0} (f_{t})) > - 4\}

where

φ_{2}

and

a_{2}

denote the phase and amplitude of S₁₁ with the varactor loaded by a −30 V voltage, respectively, The design procedure is consistent with that of the 1-bit phase-modulation unit, and the optimal unit in Fig. 6(c) achieves 3-bit phase modulation in 4.06–4.38 GHz with the structural parameters given in Table 3. It can be seen that the predicted responses in Fig. 6(d) are in good agreement with the simulated results, so the different functional RIS designs are finished without extra data acquisition and training costs. Detailed EM response information for the 3-bit RIS is provided in Appendix A Section S5.

As mentioned above, our paradigm can realize dataset reuse and cover the design range of multiple RIS structures. Here, the trained PILN model is used for a multilayer RIS design without secondary training. By changing only one additional step of matrix computation in the separate design architecture, we design an ultra-wideband 1-bit phase-modulation unit using the same PILN model, featuring an amplitude loss of less than 3 dB within 7–14.7 GHz, with a relative bandwidth of 71%. The fitness function is the same as Eq. (9). After 40 iterations, the final optimal unit in Fig. 6(e) is implemented on the F₄B substrate and polymethacrylimide foam, with MADP-000907-14020x as the load. Fig. 6(f) illustrates the computational results derived from our model in comparison with the simulation outcomes of the actual unit. The performance of the unit exhibits a level of excellence that even exceeds the results achieved by experienced researchers through exhaustive manual design. The design process of PILN integration into a multilayer RIS unit design is delineated in Appendix A Section S6.

As typical demands for RISs, these successful design examples not only validate the power of our paradigm to achieve a rapid design with no demand for experience but also highlight its practicality in addressing complex RIS design challenges in real-world scenarios. These designed RISs can be used for beamforming (Fig. 6(g)), scattering energy reduction (Fig. 6(h)), and information processing systems in the wireless communication field (Fig. 6(i)). A table comparing our proposed paradigm with previous approaches across several key metrics, including method, RIS design variety, 1-bit RIS unit performance, and relative bandwidth, is presented in Table 4 [29], [30], [31].

A mockup of the 1-bit phase-modulation RIS was fabricated using the conventional printed circuit board (PCB) technique for demonstration. The functional RIS consists of 12 × 16 units with a side length of 10 mm. The unit features additional feeding, with a copper column (radius: 0.25 mm) and a feed line width of 0.8 mm, as shown in Fig. 7(a). Adhesive and dielectric layers (with permittivities of 4.30 and 2.17, respectively) are positioned between the feed line and metal ground, with respective thicknesses of 0.10 and 0.25 mm. Fig. 7(b) illustrates the designed RIS and the measurement setup in a microwave anechoic chamber. The beam control function of the RIS is realized by generating different coding patterns, which are achieved by manipulating the reflection phase of each unit. The diodes within the same column share a common bias voltage, and the states can be altered synchronously. The far-field scattered beam is expressed as follows [2]:

(11)

D i r (θ, φ) = 4 π {|F (θ, φ)|}^{2} / \int_{0}^{2 π} \int_{0}^{π / 2} {|F (θ, φ)|}^{2} s i n θ d θ d φ

where

θ

and

φ

denote the elevation and azimuth angles of an arbitrary direction, respectively, and

F (θ, φ)

represents the pattern function of an array element. Based on this far-field equation, we design the RIS coding sequences to deflect the beams to the angles (15°, 30°, 45°) at 10 and 14 GHz, as illustrated in the upper panels of Fig. 7(c). The simulated and measured results of the radiation patterns under these coding sequences are presented in the lower panels of Fig. 7(c). More measured results within 9–15 GHz are provided in Appendix A Section S7. This approach, including improving the feed network for independent unit control and refining the surface 2D array coding, can be further adopted to improve the RIS’s radiation efficiency and accuracy. These two sets of results are generally consistent, showing the good beam-control capabilities of our designed RIS and further demonstrating our proposed design method.

The surface pattern and dielectric layers of the 1-bit phase-modulation multilayer RIS were fabricated using conventional PCB technology. This mockup consists of 12 × 12 units with a side length of 10 mm. In this multilayer structure, a foam layer is placed between the dielectric layer and the metal ground. Consequently, the feed lines, which are 0.15 mm in width and positioned perpendicular to the incident EM wave’s electric field (Fig. 8(a)), are located on the pattern layer. The dielectric board, foam, and copper foil are bonded with a 0.03 mm double-sided adhesive, as shown in Fig. 8(b). Despite some phase errors and amplitude losses around 7 and 14 GHz, the measurement results of this mockup generally align with its simulation results (Fig. 8(c)). Based on an analysis, the discrepancies likely result from the adhesive layers, manual assembly variations, and fluctuations in the foam layer’s permittivity. Measurement details are provided in Section S6.

The effectiveness and superiority of our design paradigm are strongly validated through these two distinct physical implementations. The results demonstrate that our paradigm solves the problem of multistate EM responses in RIS design, and the units designed using our paradigm significantly outperform those created via other approaches. Moreover, our paradigm allows dataset and model reuse for multifunctional and complex RIS designs, such as 3-bit RIS and multilayer RIS units. To a certain degree, it represents substantial progress toward the goals of automating design and mitigating reliance on experiential knowledge.

5. Conclusions

This work proposed an efficient and universal design paradigm for the automatic design of RISs with different functions and structures. A pivotal advancement is the introduction of a novel topology representation method, which realizes equivalent mapping from 100-dimensional continuous patterns to five-dimensional NURBS control points, extensively reducing the pattern solution space by 20 times. Compared with the traditional random pixelated method, the proposed method ensures a smooth excitation current flow in RIS surface patterns, effectively achieving maximum pattern resonance capability.

In addition, a separate design architecture was proposed to solve the multistate mapping dilemma in RIS automatic design. Based on the PILN and multiport network theory, this proposed architecture can quickly predict the multistate responses of an RIS within 1 s, avoiding the need for time-consuming numerical simulation constraints. In particular, our separate design architecture reduces the dataset acquisition cost by 62.5% and achieves dataset reuse in multiple structural RIS designs compared with traditional methods. As proof of the proposed design paradigm, we designed three examples, including two typical high-performance RISs and an ultra-wideband multilayer RIS with a relative bandwidth reaching 71%.

In general, the proposed architecture achieves a strategic shift toward minimizing dataset costs, fostering data reuse, and liberating design freedom. The proposed paradigm paves the way for automatic EM design and can effectively accelerate the development of multifunctional and multi-structure RISs to meet the increasing property demands for RIS in radar, sensing, and wireless communication systems. However, several aspects of this paradigm require further refinement, including the incorporation of effective non-continuous patterns into the dataset, the establishment of more general rules for pattern domain representation, addressing minor deviations caused by interlayer coupling, and considering the impact of complex permittivity on scattering parameters. To further reduce the design time, future research will also focus on overcoming challenges related to the RIS inverse design, such as the increased complexity in model training. Addressing these issues and adopting a more comprehensive strategy for RIS manufacturing will be key areas of focus in future work.

CRediT authorship contribution statement

Ying Juan Lu: Writing – review & editing, Writing – original draft, Validation, Methodology, Data curation. Jia Nan Zhang: Writing – review & editing, Supervision, Writing – original draft. Yi Han Zhao: Formal analysis, Data curation. Jun Wei Zhang: Methodology, Formal analysis, Conceptualization. Zhen Zhang: Formal analysis, Conceptualization. Rui Zhe Jiang: Validation, Investigation. Jing Cheng Liang: Validation, Investigation. Hui Dong Li: Supervision, Formal analysis. Jun Yan Dai: Project administration, Funding acquisition. Tie Jun Cui: Writing – review & editing, Funding acquisition, Conceptualization. Qiang Cheng: Writing – review & editing, Methodology, Funding acquisition.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the National Key Research and Development Program of China (2023YFB3811502), the National Science Foundation of China (62225108), the Fundamental Research Funds for the Central Universities (2242022k60003), the National Natural Science Foundation of China (62288101 and 62201139), the Jiangsu Province Frontier Leading Technology Basic Research Project (BK20212002), the Jiangsu Provincial Scientific Research Center of Applied Mathematics (BK20233002), the Fundamental Research Funds for the Central Universities (2242024RCB0005 and 2242024K30009), and the 111 Project (111-2-05).

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.eng.2024.11.028.

References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Chen HT, Taylor AJ, Yu N.A review of metasurfaces: physics and applications.Rep Prog Phys 2016; 79(7):076401.

[2]	Cui TJ, Qi MQ, Wan X, Zhao J, Cheng Q.Coding metamaterials, digital metamaterials and programmable metamaterials.Light Sci Appl 2014; 3(10):e218.

[3]	Liang JC, Zhang L, Cheng ZW, Zhang P, Cui TJ.Flexible beam manipulations by reconfigurable intelligent surface with independent control of amplitude and phase.Front Mater 2022; 9:946163.

[4]	Bai X, Zhang FR, Sun L, Cao A, Zhang J, He C, et al.Time-modulated transmissive programmable metasurface for low sidelobe beam scanning.Research 2022; 2022:9825903.

[5]	Ramaccia D, Tobia A, Toscano A, Bilotti F.Antenna arrays emulate metamaterial-based carpet cloak over a wide angular and frequency bandwidth.IEEE Trans Antennas Propag 2018; 66(5):2346-2353.

[6]	Yang H, Li T, Jidi L, Gao K, Li Q, Qiao J, et al.From metasurface to low-RCS array antenna: a fast and efficient route to design stealthy array antennas.IEEE Trans Antennas Propag 2023; 71(5):4075-4084.

[7]	Wu JW, Wang ZX, Zhang L, Cheng Q, Liu S, Zhang S, et al.Anisotropic metasurface holography in 3-D space with high resolution and efficiency.IEEE Trans Antennas Propag 2021; 69(1):302-316.

[8]	Zhang F, Wang C, Feng W, Liu T, Wang Z, Wang Y, et al.Holographic communication using programmable coding metasurface.Nanophotonics 2024; 13(8):1509-1519.

[9]	Alibakhshi-Kenari M, Naser-Moghadasi M, Sadeghzadeh RA, Virdee BS, Limiti E.Traveling-wave antenna based on metamaterial transmission line structure for use in multiple wireless communication applications.AEU Int J Electron Commun 2016; 70(12):1645-1650.

[10]	Alibakhshikenari M, Virdee BS, Limiti E.Wideband planar array antenna based on SCRLH-TL for airborne synthetic aperture radar application.J Electromagn Waves Appl 2018; 32(12):1586-1599.

[11]	Alibakhshikenari M, Virdee BS, Shukla P, Wang Y, Azpilicueta L, Naser-Moghadasi M, et al.Impedance bandwidth improvement of a planar antenna based on metamaterial-inspired T-matching network.IEEE Access 2021; 9:67916-67927.

[12]	Wei M, Zhao H, Galdi V, Li L, Cui TJ.Metasurface-enabled smart wireless attacks at the physical layer.Nat Electron 2023; 6(8):610-618.

[13]	Li H, Xin K, Ding H, Li T, Hu G, Xu HX.Programmable metasurface for front-back scattering communication.Nanophotonics 2023; 12(18):3653-3661.

[14]

Kate C, Kalpana C, Sharma A, Yadav AS, Kumar A, Kumar SS.Investigation of machine learning algorithms for pattern recognition in image processing.In: Proceedings of the 2023 5th International Conference on Inventive Research in Computing Applications (ICIRC A); 2023 Aug 3–5; Coimbatore, India. New York City: IEE E; 2023. p. 898–904.

[15]	Stoel BC, Staring M, Reijnierse M, van AHM der Helm-van Mil.Deep learning in rheumatological image interpretation.Nat Rev Rheumatol 2024; 20(3):182-195.

[16]	Zhou H, Qiao B, Yang L, Lai J, Xie X.Texture-guided saliency distilling for unsupervised salient object detection.In: Proceedings of the 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR); 2023 Jun 17–24; Vancouver, BC, Canada. New York City: IEEE; 2023. p. 7257–67.

[17]	Diwan T, Anirudh G, Tembhurne JV.Object detection using YOLO: challenges, architectural successors, datasets and applications.Multimedia Tools Appl 2023; 82(6):9243-9275.

[18]	Ohmae K, Ohmae S.Emergence of syntax and word prediction in an artificial neural circuit of the cerebellum.Nat Commun 2024; 15:927.

[19]	Isaksson M, Wisell D, Ronnow D.Wide-band dynamic modeling of power amplifiers using radial-basis function neural networks.IEEE Trans Microw Theory Tech 2005; 53(11):3422-3428.

[20]	Koziel S, Abdullah M.Machine-learning-powered EM-based framework for efficient and reliable design of low scattering metasurfaces.IEEE Trans Microw Theory Tech 2021; 69(4):2028-2041.

[21]	Gupta A, Karahan EA, Bhat C, Sengupta K, Khankhoje UK.Tandem neural network based design of multiband antennas.IEEE Trans Antennas Propag 2023; 71(8):6308-6317.

[22]	Ma W, Liu Z, Kudyshev ZA, Boltasseva A, Cai W, Liu Y.Deep learning for the design of photonic structures.Nat Photonics 2021; 15(2):77-90.

[23]	Malkiel I, Mrejen M, Nagler A, Arieli U, Wolf L, Suchowski H.Plasmonic nanostructure design and characterization via deep learning.Light Sci Appl 2018; 7:60.

[24]	Zhu R, Qiu T, Wang J, Sui S, Hao C, Liu T, et al.Phase-to-pattern inverse design paradigm for fast realization of functional metasurfaces via transfer learning.Nat Commun 2021; 12:2974.

[25]	Naseri P, Hum SV.A generative machine learning-based approach for inverse design of multilayer metasurfaces.IEEE Trans Antennas Propag 2021; 69(9):5725-5739.

[26]	Zhang J, Qian C, Fan Z, Chen J, Li E, Jin J, et al.Heterogeneous transfer-learning-enabled diverse metasurface design.Adv Opt Mater 2022; 10(17):2200748.

[27]	Naseri P, Pearson S, Wang Z, Hum SV.A combined machine-learning/optimization-based approach for inverse design of nonuniform bianisotropic metasurfaces.IEEE Trans Antennas Propag 2022; 70(7):5105-5119.

[28]	Jia Y, Qian C, Fan Z, Cai T, Li EP, Chen H.A knowledge-inherited learning for intelligent metasurface design and assembly.Light Sci Appl 2023; 12:82.

[29]	Wang P, Li Z, Luo C, Wei Z, Wu T, Jiang W, et al.Preprocessing-based fast design of multiple EM structures with one deep neural network.IEEE Trans Antennas Propag 2024; 72(5):4298-4310.

[30]	Wang P, Li Z, Wei Z, Wu T, Luo C, Jiang W, et al.Space–time-coding digital metasurface element design based on state recognition and mapping methods with CNN–LSTM–DNN.IEEE Trans Antennas Propag 2024; 72(6):4962-4975.

[31]	Wang P, Wei Z, Wu T, Jiang W, Hong T, Pedersen GF, et al.A machine learning framework for the design of STCDME structures in RIS applications.IEEE Trans Microw Theory Tech 2024; 72(3):1467-1479.

[32]	Jafar-Zanjani S, Inampudi S, Mosallaei H.Adaptive genetic algorithm for optical metasurfaces design.Sci Rep 2018; 8:11040.

[33]	Wei Z, Zhou Z, Wang P, Ren J, Yin Y, Pedersen GF, et al.Equivalent circuit theory-assisted deep learning for accelerated generative design of metasurfaces.IEEE Trans Antennas Propag 2022; 70(7):5120-5129.

[34]	Wu B, Wang G, Liu K, Hu G, Xu HX.Equivalent-circuit-intervened deep learning metasurface.Mater Des 2022; 218:110725.

[35]	Brown T, Mojabi P.Cascaded metasurface design using electromagnetic inversion with gradient-based optimization.IEEE Trans Antennas Propag 2022; 70(3):2033-2045.

[36]	Zhang J, You JW, Feng F, Na W, Lou ZC, Zhang QJ, et al.Physics-driven machine-learning approach incorporating temporal coupled mode theory for intelligent design of metasurfaces.IEEE Trans Microw Theory Tech 2023; 71(7):2875-2887.

[37]	Ji W, Chang J, Xu HX, Gao JR, Gröblacher S, Urbach HP, et al.Recent advances in metasurface design and quantum optics applications with machine learning, physics-informed neural networks, and topology optimization methods.Light Sci Appl 2023; 12:169.

[38]	Chen Z, Liu Y, Sun H.Physics-informed learning of governing equations from scarce data.Nat Commun 2021; 12:6136.

[39]	Khatib O, Ren S, Malof J, Padilla WJ.Learning the physics of all-dielectric metamaterials with deep Lorentz neural networks.Adv Opt Mater 2022; 10(13):2200097.

[40]	Liu P, Chen L, Chen ZN.Prior-knowledge-guided deep-learning-enabled synthesis for broadband and large phase shift range metacells in metalens antenna.IEEE Trans Antennas Propag 2022; 70(7):5024-5034.

[41]	Ghosh S, Bhattacharyya S, Srivastava KV.Design, characterisation and fabrication of a broadband polarisation-insensitive multi-layer circuit analogue absorber.IET Microw Antennas Propag 2016; 10(8):850-855.

[42]	Zhang Z, Zhang JW, Wu JW, Liang JC, Wang ZX, Cheng Q, et al.Macromodeling of reconfigurable intelligent surface based on microwave network theory.IEEE Trans Antennas Propag 2022; 70(10):8707-8717.

[43]	Lampinen J, Zelinka I.Mixed integer-discrete-continuous optimization by differential evolution-part 1: the optimization method.In: Proceedings of the 5th International Mendel Conference on Soft Computing; 1999 Jun 9–12; Brno, Czech Republic. Berlin: Springer; 1999. p. 71–6.

[44]	Echter R, Oesterle B, Bischoff M.A hierarchic family of isogeometric shell finite elements.Comput Methods Appl Mech Eng 2013; 254:170-180.

[45]	Schillinger D, Ruess M.The finite cell method: a review in the context of higher-order structural analysis of CAD and image-based geometric models.Arch Comput Methods Eng 2015; 22(3):391-455.

[46]	Smith DR, Vier DC, ThKoschny , Soukoulis CM.Electromagnetic parameter retrieval from inhomogeneous metamaterials.Phys Rev E Stat Nonlin Soft Matter Phys 2005; 71(3):036617.

[47]	Monaco VA, Tiberio P.Computer-aided analysis of microwave circuits.IEEE Trans Microw Theory Tech 1974; 22(3):249-263.

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Cite this article

1. Introduction

2. Overview of the automatic design paradigm for RISs

3. Theory and methods

3.1. NBTRM for dataset

3.2. Separate design architecture

3.3. Structure and training of the PILN

4. Model validation and experimental verification

5. Conclusions

CRediT authorship contribution statement

Declaration of competing interest

Acknowledgments

Appendix A. Supplementary data

References

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