Metasurfaces-Integrated Neural Network (MINN)

• MINN is a computational system that integrates neural network operations with metasurfaces engineered for tailored amplitude and phase control.
• It leverages diverse physical implementations—optical, photonic, and wireless—to perform analog matrix operations at significantly lower energy and latency.
• The approach uses physics-aware training and stackable metasurface layers to achieve high accuracy in tasks such as image convolution and classification.

A Metasurfaces-Integrated Neural Network (MINN) is a computational system in which a neural network architecture is physically realized by integrating metasurfaces—spatially patterned arrays of subwavelength scatterers with engineered amplitude and phase response—with optical, photonic, or wireless electronic signal processing. The metasurface acts as trainable or programmable layers that perform neural network operations, either as complex-valued weight matrices, optical analog convolution kernels, mode-converters, or over-the-air linear transforms, in direct analogy to digital neural network layers. MINN architectures exploit the passive, ultrafast, and parallel nature of light and electromagnetic waves to implement inference or learning tasks at orders-of-magnitude lower energy and latency than conventional electronics. MINN research encompasses implementations in free-space optics, integrated photonics, diffractive and multiplexed domains, and wireless over-the-air intelligence systems.

1. Physical Foundations and Metasurface Layer Modeling

MINNs leverage metasurfaces, which are two- or three-dimensional lattices of nanostructures (pillars, disks, antennas), tailored to control the local amplitude ($A$) and phase ($\phi$) of incident waves. In optical MINN architectures, each metasurface layer applies a complex transmission function $T(x)=A(x)\,e^{i\phi(x)}$; in photonics, programmable phase-change metasurfaces (e.g., GST) allow nonvolatile, multi-level (6-bit) control of local coupling coefficients representing analog neural network weights (Wu et al., 2019, Wu et al., 2020). In wireless implementations, programmable electronic metasurfaces (RIS, SIM) effect tunable phase shifts $\phi_n$ for each reflecting or diffracting element, thereby controlling the propagation channel between transmitter and receiver (Stylianopoulos et al., 31 Mar 2025, Stylianopoulos et al., 23 Dec 2025).

Each metasurface layer can act as a linear mapping—analogous to a neural network layer—by imposing a spatially varying amplitude and phase map, with interlayer free-space (or guided-mode) propagation enacting convolutional or matrix multiplication operations. The precise theoretical framework varies:

• Optical stacking: $$E_n^{(l)}(x) = \mathcal{F}^{-1}\{E_f^{(l-1)}(k)e^{i\delta_k}\} * [A^{(l)}(w^{(l)}(x))e^{i\phi^{(l)}(w^{(l)}(x))}]$$, followed by far-field propagation via a Hankel kernel $G(x,x')$ (Wu et al., 2019).
• Photonic MVM: Waveguide-integrated phase-gradient metasurfaces convert TE$_0$ to TE$_1$ modes with programmable contrast $I(s)$, forming a 6-bit weight matrix for matrix-vector multiplication (Wu et al., 2020).
• Wireless OTA: Stacked metasurfaces (SIM) act as trainable hidden layers, with RF channel modeled as $y = [H_D + H_2 \Phi H_1^\dagger]s + n$ and $\Phi$ a multi-layer product of phase shift matrices and diffraction kernels (Stylianopoulos et al., 23 Dec 2025).

2. Architectures, Programming, and Training Methodologies

MINNs span several physical architectures:

• Neuromorphic metasurfaces: Stack of TiO$_2$ pillars, each width $w$ mapped to local transmission $A(w)e^{i\phi(w)}$. Training is performed by numerical backpropagation through the optics—using precomputed FDTD response curves for amplitude and phase versus geometry and updating $w$ via gradient descent (Wu et al., 2019).
• Programmable phase-change metasurface on waveguide: GST phase gradient elements with discrete crystallization states $s=0\ldots63$ map to refractive index $n(s)$ and multi-level modal mixing, trained to represent signed real-valued weights. The system can perform image convolution and classification tasks by programming the contrast $I(s)$ at each converter and reading out summed detector intensity (Wu et al., 2020).
• Multiplexed diffractive neural networks: On-chip TiO$_2$ metasurfaces (rectangular nanopillars) with polarization multiplexing can realize dual neural networks for multitasking (e.g., MNIST and Fashion-MNIST) at $>$99% accuracy. Each meta-neuron encodes independent phase for $x$- and $y$-polarized light (Luo et al., 2021).
• Wireless over-the-air inference: The transmitter and receiver portions of a DNN are interconnected via programmable metasurface layers, which play the role of trainable hidden layers, their phase response tuned during joint DNN training using full E2E backpropagation through the channel equations. Both static and reconfigurable modes are possible, with power-control DNN modules enabling joint optimization of classification error and average transmit power (Stylianopoulos et al., 23 Sep 2025, Stylianopoulos et al., 31 Mar 2025, Stylianopoulos et al., 23 Dec 2025).

Training combines physics-aware loss functions, chain-rule gradients through the transmission matrices, and possibly additional constraints (e.g., phase wrapping, energy conservation enforced via special neural layers (Saadabad et al., 8 Apr 2025)). For analog optical convolution, large 2D kernels (e.g. $75 \times 75$) are learned in the frequency domain—ensuring computational tractability and global receptive field (Liang et al., 2024).

3. Performance Metrics and Experimental Results

MINN systems are characterized by distinctive hardware and algorithmic metrics:

Platform	Classification Accuracy	Energy per Inference	Hardware Footprint	Throughput
TiO$_2$ Neuromorphic MS (5 layer) (Wu et al., 2019)	90% (MNIST)	fJ–pJ	2–5 layers $\times$ 400 pillars	ns, passive
GST Photonic Waveguide (Wu et al., 2020)	91% ("1" vs "2" MNIST)	few fJ/MAC	$80\,\mu$m$\times 20\,\mu$m	$>$10 Gbit/s
Large-kernel analog conv MS (Liang et al., 2024)	98.59% (MNIST, exp.)	$10^{-12}$ J/op	2 mm$\diameter$, Si-on-Sapphire	$>1$ TOPS
Stacked SIM (wireless) (Stylianopoulos et al., 23 Sep 2025, Stylianopoulos et al., 23 Dec 2025)	98–99% (MNIST, EI)	$\sim$mJ$\rightarrow$ few mW	4–32$\times$4–100 elements/layer	Real-time RF
Nano-3D Depth Imaging (Li et al., 20 Mar 2025)	AbsRel 0.13 (sim)	N/A	3 mm$\diameter$, TiO$_2$	ps–ms, passive

Additional metrics include bandwidth (optical: $\pm 10$–$40$ nm), area density ($\sim$6.25$\times 10^6$/mm$^2$), power–accuracy tradeoff curves (up to two orders magnitude TX power savings for fixed accuracy via power-control DNN (Stylianopoulos et al., 23 Sep 2025)), and computational acceleration ($>67\times$ speedup over full-wave solvers for Maxwell’s equations surrogate MINN (Furat et al., 17 Dec 2025)).

4. Integration Table: Physical Mechanisms and Application Domains

Mechanism/Platform	Task/Class	Key Engineering Principle	Applications
Free-space optical stack	Classification	Subwavelength phase/amplitude mod	Machine vision, embedded inference
Phase-change PCM photonic	Convolution/MVM	Multi-level refractive index	On-chip AI accelerators
Multiplexed diffractive	Multitask inference	Polarization/wavelength division	On-chip sensor-compute
Analog convolution (Si MS)	Large-kernel conv	Spatial-frequency domain training	Edge-AI, low-power imaging
Wireless SIM/RIS	Channel-DNN	Programmable RF phase/diffraction	Over-the-air inference, 6G edge nodes

5. Challenges, Limitations, and Future Directions

MINN realizations face ongoing technical constraints:

• Linearity: Current metasurface-based layers are strictly linear; physical realization of nonlinear activations (on-chip saturable absorbers, phase-change devices for reconfigurability) remains a challenge (Wu et al., 2019, Stylianopoulos et al., 23 Dec 2025).
• Fabrication accuracies/tolerances: Lithography-induced width/height variances yield phase noise; multi-layer stacking can amplify errors, requiring error-correcting designs or compensation algorithms (Wu et al., 2019, Luo et al., 2021).
• Non-reconfigurability vs. dynamic programming: Passive metasurfaces offer zero run-time power, but fixed kernels after fabrication; recent works report nonvolatile programmable PCM metasurfaces for high-density photonic computation (Wu et al., 2020).
• Scalability: High-density (megapixel/mm$^2$) metasurfaces allow deep and wide analog networks, yet bandwidth and coupling losses grow with array size and depth (Luo et al., 2021).
• Channel dynamics (wireless MINN): In time-varying environments, adaptive MS control—possibly via onboard sensing and real-time DNN modules—is needed; static fixed-MS approaches perform best in quasi-static channels (Stylianopoulos et al., 31 Mar 2025).

Research directions include multi-modal multiplexing (polarization, wavelength, orbital angular momentum), physics-constrained learning (embedded Maxwell/PDE residuals (Saadabad et al., 8 Apr 2025, Furat et al., 17 Dec 2025)), co-design of photonic hardware and DNN architectures, and potentially in-situ, all-optical or OTA backpropagation (Stylianopoulos et al., 23 Dec 2025).

6. Significance and Implications for Computational Intelligence

MINNs provide a physical analog to digital neural networks, offloading key operations—matrix multiplication, convolution, analog signal mixing—into the passive or low-power wave domain. This yields transformative reductions in energy and latency, especially in ultra-compact or edge scenarios (e.g., vision sensors, embedded wireless inference (Li et al., 20 Mar 2025, Liang et al., 2024)). By treating electromagnetic propagation environments as trainable neural layers, MINN architectures unify materials science, computational physics, and deep learning theory.

Emergent research substantiates that:

• Fixed or reconfigurable metasurface layers, when trained end-to-end with encoder and decoder DNNs, match digital DNN accuracy under practical hardware and channel configurations (Stylianopoulos et al., 23 Dec 2025, Wu et al., 2020).
• Physics-constrained training (embedding physical laws and symmetries directly into the network) improves data efficiency, generalization, and physical interpretability for metasurface modeling and inverse design (Saadabad et al., 8 Apr 2025, Furat et al., 17 Dec 2025).
• MINN architectures—across optics, photonics, and RF domains—enable robust, scalable, and energy-efficient intelligence, with measurable gains over conventional digital implementations in throughput, area density, and power scaling (Stylianopoulos et al., 31 Mar 2025, Liang et al., 2024, Stylianopoulos et al., 23 Sep 2025).

A plausible implication is that advances in programmable and reconfigurable metasurfaces, when coupled with neural network co-design and physics-informed surrogate modeling, may lead to general-purpose, domain-specific AI accelerators with unprecedented energy and form-factor advantages. Research continues toward incorporating nonlinear layers, multi-modal coding, OTA learning, and direct in-situ gradient feedback to expand MINN capabilities.