Intrinsic Voltage Offsets in Memcapacitive Bio-Membranes Enable High-Performance Physical Reservoir Computing

TL;DR

This work addresses the pre-processing and scalability bottlenecks in physical reservoir computing by introducing a heterogeneous memcapacitor reservoir that exploits intrinsic internal voltage offsets $v_\Phi$ from asymmetric biomembrane leaflets. By fabricating twelve memcapacitors with varying asymmetry, the authors demonstrate tunable input-state correlations ranging from monotonic to non-monotonic, underpinned by a quartic capacitance response $C_m(v_{app}) \propto v_{app}^4$ and memory evidenced by PPF/PPD. The reservoir solves the SONDS problem with extremely low prediction error, $PE \approx 1.7\times10^{-4}$, and predicts the chaotic Hénon map with $NRMSE$ as low as $0.080$, without input masking; external offsets can generalize the approach to devices lacking offsets. Collectively, the results reveal a low-overhead, energy-efficient path toward real-time full in-materia PRCs with broad applicability to neuromorphic hardware and bio-compatible interfaces.

Abstract

Reservoir computing is a brain-inspired machine learning framework for processing temporal data by mapping inputs into high-dimensional spaces. Physical reservoir computers (PRCs) leverage native fading memory and nonlinearity in physical substrates, including atomic switches, photonics, volatile memristors, and, recently, memcapacitors, to achieve efficient high-dimensional mapping. Traditional PRCs often consist of homogeneous device arrays, which rely on input encoding methods and large stochastic device-to-device variations for increased nonlinearity and high-dimensional mapping. These approaches incur high pre-processing costs and restrict real-time deployment. Here, we introduce a novel heterogeneous memcapacitor-based PRC that exploits internal voltage offsets to enable both monotonic and non-monotonic input-state correlations crucial for efficient high-dimensional transformations. We demonstrate our approach's efficacy by predicting a second-order nonlinear dynamical system with an extremely low prediction error (0.00018). Additionally, we predict a chaotic Hénon map, achieving a low normalized root mean square error (0.080). Unlike previous PRCs, such errors are achieved without input encoding methods, underscoring the power of distinct input-state correlations. Most importantly, we generalize our approach to other neuromorphic devices that lack inherent voltage offsets using externally applied offsets to realize various input-state correlations. Our approach and unprecedented performance are a major milestone towards high-performance full in-materia PRCs.

Figures (31)

• Figure 1: An illustration of symmetric and asymmetric memcapacitors, their response to voltage stimuli, and the resulting heterogeneous memcapacitor-based reservoir. We show in Fig. S4 real device photos we took using an inverted microscope. a A symmetric memcapacitor consists of two leaflets of the same composition (e.g., DPhPC-DPhPC). In the case of a symmetric membrane, as shown on the left side, experiencing a voltage stimulus forces a faster increase in the interfacial area (electrowetting) and a slower decrease in hydrophobic thickness (electrocompression) due to oil expulsion Taylor2015DirectBilayerNajem2019DynamicalMembranes. For an asymmetrical bilayer, an intrinsic voltage offset (see Supplementary Note 3 and Supplementary Fig. S3) arises from a mismatch between the two phospholipids' head dipoles Taylor2019ElectrophysiologicalFlip-flop. At rest, an asymmetric membrane possesses higher capacitance than a symmetric membrane due to the internal offset, represented by the bilayer areas and thicknesses for the cases of $v_{app} = 0$. For a negative internal voltage offset shown on the right side, a positive applied stimulus acts against the internal offset, leading to a decrease in the membrane interfacial area and an increase in the hydrophobic thickness since the overall membrane potential has decreased. b Representative capacitance responses for six different devices, namely 0-0, 60-0, 100-0, 100-100, 0-60, and 0-100, to a pulse train of 5000 pulses (Supplementary Fig. S6 shows the response of all twelve devices). Each input pulse is 3 ms long with 2 ms of ON time and 1 ms of OFF time, as shown by the top-right inset. As observed, the starting capacitance is larger for asymmetrical devices compared to symmetrical cases. While the steady-state capacitances for the symmetrical cases are comparable, their transient responses are different as they exhibit dissimilar temporal dynamics, as discussed later. c A visual representation of the heterogeneous memcapacitor-based reservoir. Supplementary Fig. S5 displays a full guide on the twelve devices, and their representing visuals
• Figure 2: Characterizing the inherent voltage offsets and their influence on input-state correlations. a the internal voltage offset corresponding to different membrane compositions. Mirroring the membrane composition switches the sign of the obtained internal voltage offset. Regardless of the composition, symmetric membrane leaflets have no internal voltage offsets. b Charge versus applied potential curves for seven distinct devices, namely, 100-0, 60-0, 20-0, 0-40, 0-80, and 100-100. The applied potential sweeps are of 50-mHz frequency. Supplementary Fig. S7 shows the curves for all twelve devices. The larger markers refer to the pinching point for curves of the same color. c Steady-state capacitance as a function of applied potential for same devices listed in panel b. As observed in this panel, the input-state correlation across different memcapacitors has varying degrees of positive, negative, and negative, followed by positive correlations. Supplementary Fig. S8 shows the steady-state capacitance for all twelve devices. d The capacitance vs applied potential slopes ($\Delta C_m/\Delta v_{app}$) are shown to represent the diversity of input-state correlations qualitatively. The red and blue regions correspond to positive and negative input-state correlations.
• Figure 3: PPF and PPD indices as functions of PD and IPI and memory-related characteristics as functions of change in transmembrane potential across varying memcapacitor compositions. We averaged all displayed experimental data across five samples, representing the memcapacitors used in the RC tasks. Supplementary Fig. S16-S18 display the information and statistics on the cycle-to-cycle and device-to-device variability of these memcapacitors. a 2D maps of the PPF and PPD indices as functions of PD and IPI for four devices, namely 100-100, 100-0, 80-0, and 0-100. Supplementary Fig. S13 showcases the 2D maps for all twelve devices. b Horizontal and vertical projections of the four maps. In the horizontal case, we fixed the IPI to 250 ms, and the PPF and PPD are plotted against varying PD in the top and bottom panels, respectively. We fixed The PD to 250 ms for the vertical projection, and the PPF and PPD are plotted against varying IPI in the top and bottom panels, respectively. The PPF and PPD projections for the remaining eight devices can be found in Supplementary Fig. S14. c A plot of the temporal parameter $\zeta_{ew}$ as a function of membrane potential change $\Delta_{v_m}$ for seven devices, namely 100-0, 80-0, 60-0, 40-0, 20-0, 0-0, and 100-100. Since $\zeta_{ew}$ only varies with the absolute membrane composition, mirroring the listed asymmetric membranes to yield devices 0-100, 0-80, 0-60, 0-40, and 0-20 generates similar $\zeta_{ew}$ data, in the same listing order. d A qualitative representation of the capacitance drop rate, which is indirectly influenced by $\zeta_{ew}$ (see Supplementary Methods), for different $\Delta_{v_m}$.
• Figure 4: A visual representation of the process flow of solving SONDS and a summary of the prediction results obtained by the heterogeneous memcapacitor-based RC system. a The process flow of solving SONDS. The training random input stream $u$$\mathrm{_{Train}}$ is linearly interpolated and sampled into pulses with a specific voltage range, pulse width, and duty cycle using a voltage encoder. We channeled the resulting pulses into the reservoir layer comprising twelve distinct memcapacitors, and the capacitance is recorded at the end of each pulse, yielding an N-by-K state matrix (N = 12 and K = 1000 in this case). The state matrix trains a linear readout layer using linear regression. The trained readout layer is then multiplied by the training state matrix to yield a prediction for the $y$$\mathrm{_{Train}}$. The resulting $y$$\mathrm{_{Train}}$ is then compared to the true $y$$\mathrm{_{Train}}$ using a defined prediction error metric (see Supplementary Methods section). b The predicted training data set $y$$\mathrm{_{Train}}$ over the true values of $y$$\mathrm{_{Train}}$ for time steps 150-250. These results correspond to a $1.73\times10^{-4}$ prediction error. c The predicted testing data set $y$$\mathrm{_{Test}}$ over the true values of $y$$\mathrm{_{Test}}$ for time steps 150-250. These results correspond to a $1.80\times10^{-4}$ prediction error. d The training (top) and (bottom) testing prediction errors for the five different pulse widths for voltage ranges of 1) -150 mV to +150 mV (circles) and 2) -200 mV to +200 mV (squares) for a heterogeneous reservoir with internal voltage offsets (blue) and a homogeneous reservoir with externally applied offsets (red). e A visual comparison of testing prediction errors achieved previously by Du2017ReservoirProcessingNishioka2022Edge-of-chaosReservoirArmendarez2024Brain-InspiredPlasticity and this work as well as the number of reservoir nodes needed to achieve these testing prediction errors.
• Figure 5: A summary of the results obtained by the heterogeneous memcapacitor-based RC system for the Hénon Map. a The predicted training data set $z$$\mathrm{_{Train}}$ over the true values of $z$$\mathrm{_{Train}}$ for time steps 150-250. These results correspond to an NRMSE of 0.059. b The predicted testing data set $z$$\mathrm{_{Test}}$ over the true values of $z$$\mathrm{_{Test}}$ for time steps 150-250. These results correspond to an NRMSE of 0.080. c The predicted training data 2-D map set $z$$\mathrm{_{Train}}$ against $x$$\mathrm{_{Train}}$ over the true 2-D map for all 1000 time steps. d The predicted testing data 2-D map set $z$$\mathrm{_{Test}}$ against $x$$\mathrm{_{Test}}$ over the true 2-D map for all 1000 time steps. e The training (top) and (bottom) testing NRMSEs for the five different pulse widths for voltage ranges of 1) -150 mV to +150 mV (circles) and 2) -200 mV to +200 mV (squares) for a heterogeneous reservoir with internal voltage offsets (blue) and a homogeneous reservoir with externally applied offsets (red). f A visual comparison of NRMSEs achieved previously by Zhong2021DynamicProcessingWu2024ACuInP2S6Pei2023Power-EfficientArraysChen2023All-ferroelectricComputingFang2024Oxide-BasedComputingFeng2023FullyStates and this work as well as the number of reservoir nodes needed to achieve these NRMSEs.