Parallel Mechanical Computing: Metamaterials That Can Multitask

Academic Background

Decades after being replaced by digital computing platforms, analog computing has regained significant interest due to advancements in metamaterials and intricate fabrication techniques. Particularly, wave-based analog computers, which perform spatial transformations on an incident wavefront to achieve desired mathematical operations, have gained traction because they can directly encode input signals in their unprocessed form, bypassing analog-to-digital conversion. However, these systems are inherently limited to single-task configurations, and their inability to perform multiple tasks concurrently or compute in parallel represents a major obstacle to advancing mechanical computing devices with broader computational capabilities. This paper presents a pathway to simultaneously process independent computational tasks within the same architected structure. By breaking time invariance in a set of metasurface building blocks, multiple frequency-shifted beams are self-generated, which absorb significant energy from the fundamental signal. The emergence of these tunable harmonics allows distinct computational tasks to be assigned to different independent “channels,” effectively enabling an analog mechanical computer to multitask.

Paper Source

This paper was authored by Mohamed Mousa and Mostafa Nouh, affiliated with the Department of Mechanical and Aerospace Engineering and the Department of Civil, Structural and Environmental Engineering at the University at Buffalo (State University of New York). The paper was published on December 18, 2024, in the journal PNAS.

Research Process

1. Research Objectives and Methods

The goal of this study is to develop a mechanical computing system capable of simultaneously processing multiple independent computational tasks within the same architected structure. To achieve this, the researchers employed a metasurface-based approach, where time-modulated metasurface building blocks generate multiple frequency-shifted beams, enabling parallel processing of different computational tasks.

2. Metasurface Approach

The mechanical computing system (AMC) consists of three main components: a spatial Fourier transform subblock (FT), an operator metasurface or space-filtering subblock (SF), and an inverse Fourier transform subblock (IFT). The input function ( f(y) ) is spatially encoded in the form of an incident wave and transformed into the corresponding output ( g(y) ) through the following scheme:

[ g(y) = \text{IFT}[H(k_y) \cdot \text{FT}[f(y)]] ]

where ( k_y ) is the spatial frequency, and ( H(k_y) ) is the transfer function describing the desired mathematical operation. For instance, the transfer functions for differentiation and integration operations involve multiplying and dividing the input by ( (ik_y) ), respectively.

3. Unit Cell Design

The dynamics of the AMC require a unit cell with a wide range of transmission amplitudes and phase angles. To this end, the researchers adopted a subwavelength unit cell consisting of a straight pipe coupled with four shunted Helmholtz resonators (HRs). By adjusting the height of the straight pipe ( h_1 ) and the resonator height ( h_3 ), precise control over the transmission amplitude and phase is achieved.

4. Temporal Modulation

To enable parallel computing in the AMC, the researchers exploited changes in the frequency content of a propagating signal associated with periodic media that carry a momentum bias. By temporally modulating the properties of the unit cells, significant portions of the bulk wave energy were redistributed into sidebands representing up- and down-converted harmonics of the fundamental frequency. In the numerical finite element model, each resonator domain was defined as a moving mesh, with deformed mesh positions introduced as degrees of freedom in the system dynamics.

Main Results

1. Single Computing

As a sanity check, the researchers first introduced uniform temporal modulation to a system originally designed to perform a single mathematical operation, such as differentiation. Despite the expected energy redistribution from the fundamental frequency channel to other harmonics, the AMC’s functionality remained consistent across all frequency channels due to the uniformity of the imposed modulation. The results demonstrated that the AMC could successfully compute the spatial derivative of the input load at both the fundamental and down-converted frequency channels.

2. Parallel Computing

After confirming single computing functionality, the researchers configured the AMC to concurrently run two independent operations. By carefully selecting modulation parameters and tunable heights, the highest pressure amplitudes were achieved at the fundamental and down-converted frequency channels. The results showed that the AMC could perform the primary mathematical operation (e.g., differentiation) at the fundamental frequency while simultaneously executing a secondary operation (e.g., integration) at the down-converted frequency, thus achieving parallel computing.

3. Insensitivity to Task Type

The researchers emphasized that the embedded parallel computing capability of the AMC is highly robust. Regardless of the required operation or the frequency channel in which it is implemented, the system maintains its functionality. To demonstrate this, the researchers showcased the AMC as a full-fledged ordinary differential equation (ODE) solver. The results confirmed that the AMC could solve two different second-order ODEs simultaneously at distinct frequency channels, further proving the system’s robustness and design flexibility.

Conclusion

This study successfully demonstrated parallel computing through frequency multiplexing in a mechanical computing system. By utilizing time-modulated metasurface units, the system decomposed a monochromatic incident wave into multiple supplementary signals, enabling the concurrent execution of different mathematical operations within the same system. This approach paves the way for the design of metamaterials with multitasking capabilities, offering significant scientific and practical value.

Research Highlights

1. Multitasking Capability: This study is the first to achieve parallel computing in a mechanical computing system, breaking the single-task limitations of traditional analog computers.
2. Frequency Multiplexing Technology: By using time-modulated metasurface units, the researchers successfully assigned multiple computational tasks to different frequency channels, enabling parallel processing.
3. Robustness and Flexibility: The system’s insensitivity to task type and frequency channels demonstrates its broad applicability in practical scenarios.
4. Potential Applications: This research opens new avenues for exploration in physical computing and reservoir computing, particularly in mechanical media.

Other Valuable Information

The study also discussed the system’s robustness under complex loading conditions, showing that the AMC can effectively perform parallel computations even when the input signal is polluted by broadband noise or contains a broader range of frequencies. Additionally, the researchers provided detailed information on the availability of materials and software, with all study data included in the article and supporting information.