Self-Programming Synaptic Resistor Circuit for Intelligent Systems

Vehicle (FA9550-16-1-0087) ” and “ Brain Inspired Networks for Multifunctional Intelligent Systems in Aerial Vehicles (FA9550-19-0213). ”


Introduction
The human brain has long served as the inspiration of artificial intelligent systems. A neural network (Figure 1a) processes voltage pulses at M presynaptic neurons inducing currents via synapses at N postsynaptic neurons by following the signal processing algorithm where w ¼ ðw nm Þ ∈ ℝ NÂM denotes a matrix with w nm as the weight (conductance) of a synapse connecting the m th presynaptic and the n th postsynaptic neuron, x ¼ ðx m Þ ∈ ℝ M denotes a vector with x m as the voltage pulses at the m th presynaptic neuron, and I ¼ ðI n Þ ∈ ℝ N denotes a vector with I n as the current flowing into the n th postsynaptic neuron, which triggers the voltage pulses y ¼ ðy n Þ ∈ ℝ N with y n as the pulses output from the n th postsynaptic neuron. Concurrently, the synaptic weight matrix, w, is modified by following the learning algorithm [1,2] w where α denotes the modification coefficient, z ¼ ðz n Þ ∈ ℝ N denotes a function of y ¼ ðy n Þ ∈ ℝ N with y n as the voltage pulses at the n th postsynaptic neuron (Equation S1, Supporting Information), and z ⊗ x represents the outer product between z and x. By integrating signal processing, memory, and correlative learning functions in each synapse, a neural network concurrently executes the signal-processing (Equation (1)) and learning (Equation (2)) algorithms in analog parallel mode to dynamically self-program w and create new functions in real time in unpredictable and arbitrary environments with general intelligence. [1,3,4] Computers embedded in artificial intelligent systems can execute arbitrary signal-processing algorithms [5] to outperform humans at specific tasks such as pattern recognition [6] and the Go game, [7] but they have to be preprogrammed by humans and cannot adapt or develop new functions in unpredictable and arbitrary environments as humans do. [4] The time and energy consumption to compute machine learning algorithms from a dataset with M-dimensional variables increase versus DOI: 10.1002/aisy.202100016 Unlike artificial intelligent systems based on computers which have to be programmed for specific tasks, the human brain "self-programs" in real time to create new tactics and adapt to arbitrary environments. Computers embedded in artificial intelligent systems execute arbitrary signal-processing algorithms to outperform humans at specific tasks, but without the real-time self-programming functionality, they are preprogrammed by humans, fail in unpredictable environments beyond their preprogrammed domains, and lack general intelligence in arbitrary environments. Herein, a synaptic resistor circuit that self-programs in arbitrary and unpredictable environments in real time is demonstrated. By integrating the synaptic signal processing, memory, and correlative learning functions in each synaptic resistor, the synaptic resistor circuit processes signals and self-programs the circuit concurrently in real time with an energy efficiency about six orders higher than those of computers. In comparison with humans and a preprogrammed computer, the self-programming synaptic resistor circuit dynamically modifies its algorithm to control a morphing wing in an unpredictable aerodynamic environment to improve its performance function with superior self-programming speeds and accuracy. The synaptic resistor circuits potentially circumvent the fundamental limitations of computers, leading to a new intelligent platform with real-time self-programming functionality for artificial general intelligence.
M exponentially, [8] referred to as the "curse of dimensionality." [9] Therefore learning algorithms are executed in off-site highspeed computers with high-power consumptions and bulky volumes. [7,10,11] Despite improved parallelism and computational energy efficiencies, transistor-based computing circuits, such as the Summit supercomputer, [12] graphics processing units (GPUs), [7,11,13] tensor processing units (TPUs), [14] fieldprogrammable gate arrays (FPGAs), [15] TrueNorth, [16] and Tianjic [17] neuromorphic circuits, are still based on the Turing computing model by executing algorithms with data transmissions between physically separated logic and memory transistors. Existing neuromorphic devices such as transistors, [18,19] memristors, [20,21] and phase-change memory resistors [22] execute signal-processing algorithms (without conductance change) and learning algorithms (with conductance change) by applying voltage pulses with different amplitudes. To avoid change of conductance during signal processing, the voltage pulses for signal processing are decreased to smaller magnitudes than the voltage pulses for learning. When the signal-processing algorithm is executed in the circuits, the learning algorithm is interrupted and vice versa. [22][23][24][25] Therefore, unlike neurobiological networks, the existing neuromorphic circuits cannot execute signalprocessing and learning algorithms concurrently and have to be trained or preprogrammed before executing signal-processing algorithms. Due to these limitations, the energy efficiencies for existing electronic circuits to compute learning algorithms are limited to the range of %10 7 À 10 13 OPS=W (operations per second per watt), [7,[11][12][13][14][15][16][17]20,22,24] which are significantly lower than that of the human brain (% 10 15 OPS=W) [26] and largely prevent artificial intelligent systems from self-programming on site in real time. Without real-time self-programming functionality, artificial intelligent systems fail in unpredictable environments beyond their preprogrammed domains [27] and lack the brain-like general intelligence in arbitrary environments. [4] Recently we developed a synaptic resistor, [28] abbreviated as synstor hereafter, to emulate a synapse. A synstor processes voltage pulses x by following I ¼ wx, Equation (1), and learns from voltage pulses x and z by following w Equation (2). Unlike existing electronic devices such as transistors, memristors, and phase-change memory resistors, the ðF ÀFÞ 2 is plotted versus S and V a in the typical morphing wing control processes by SNIC (left), human (middle), and computer (right). The black arrows indicate the evolving directions of the system. The illustration of d) a human and e) a computer receiving F ÀF signals and adjusting V a to modify wing shapes. synstors process and learn from the x and z voltage pulses with the same magnitudes, and the signal-processing (I ¼ wx, Equation (1)) and learning (w : ¼ αz ⊗ x, Equation (2)) algorithms can be executed concurrently in a synstor circuit without interrupting each other. A synstor circuit circumvents the energy consumption on data transmission and memory between logic and memory circuits for executing the signal-processing and learning algorithms separately in conventional computing circuits, and facilitates computations in analog parallel mode by integrating signal processing, memory, and correlative learning functions in each synstor. In this article, we demonstrate a synstor-based self-programming neuromorphic integrated circuit (abbreviated as SNIC hereafter) based on synstors (Figure 1a), which executes the signal-processing (I ¼ wx, Equation (1)) and correlative learning [1,3] (w : ¼ αz ⊗ x, Equation (2)) algorithms concurrently in parallel analog mode to self-program the synstor conductance matrix, w, toward its optimal values,ŵ, and improve the performance function of a system spontaneously with an energy efficiency (% 3.3 Â 10 17 OPS=W) significantly higher than the energy efficiencies of computing circuits (% 10 7 À 10 13 OPS=W) [7,[11][12][13][14][15][16]20,22,24] and the human brain (% 10 15 OPS=W). [26] 2

. Experiment and Results
We fabricated a crossbar synstor circuit ( Figure S1, Supporting Information), and each synstor [28] has a p-type semiconducting carbon nanotube (CNT) channel which forms Schottky contacts with Al input and output electrodes as a resistor. A HfO 2 /TiO 2 / HfO 2 charge trap heterojunction is sandwiched between the CNT channel and a grounded Al reference electrode as a capacitor ( Figure S2, Supporting Information). As shown in Figure 1a, voltage pulses, x m , on the input electrodes induce currents flowing through the CNT channels to the n th output neuron circuit by following the signal-processing algorithm, I n ¼ P m w nm x m (Equation (1)). When paired negative (positive) voltage pulses, x m and z n , are applied on the m th input and n th output electrodes of a synstor simultaneously, the pulses generate a potential difference between the CNT channel and the TiO 2 charge storage layer to drive electrons to hop through the HfO 2 dielectric layer, increasing the negative (positive) charge stored in the charge storage layer and in turn attracting (repelling) the holes in the p-type CNT channel to increase (decrease) the synstor conductance by following the learning algorithm, w : nm ¼ αz n x m (Equation (2)), with α > 0 (α < 0). Otherwise, when z n ¼ 0 and/or x m ¼ 0, the x m or z n voltage pulse mainly decreases beyond the recessed TiO 2 charge storage layer, and the potential differences between the CNT channel and the TiO 2 charge storage layer are below the threshold values to modify the charge stored in the charge storage layer, so, w : nm ¼ αz n x m ¼ 0 ( Figure S3 and S4, Supporting Information). The synstor circuit executes the signal-processing (I ¼ wx, Equation (1)) and correlative learning (w : ¼ αz ⊗ x, Equation (2)) algorithms concurrently without interrupting each other (Experimental Section).
To test SNIC in a practical challenging environment, an SNIC composed of a 2 Â 2 crossbar synstor circuit and two input and two output integrate-and-fire neuron circuits was connected to a morphing wing [29,30] in a wind tunnel (Figure 1a,b, Experimental Section). The synstor conductance matrix, w, had random values before a self-programming process, and the goal was to set w in the real-time self-programming process to tune the lift-force on the wing, F, toward the target value,F ¼ 0.3 N, and minimize an objective function E ¼ 1 2 ðF ÀFÞ 2 . The wind speed, S, changed randomly in the wind tunnel in the range of 17 À 29 m=s to emulate an unpredictable aerodynamic environment which caused the lift-force on the wing, F, to vary randomly in the range of 0 À 1 N. F was also influenced by the shape of the wing, which was controlled by a voltage, V a , applied on a piezoactuator in the wing (Figure 1b, Experimental Section). F was detected by a sensor in the wind tunnel, and the sensory signals were processed by input neurons to trigger 10 ns-wide input voltage pulses, x, with an amplitude of 1.5 V or À1.75 V (Figure 2a). When F >F, the pulses were triggered from the first input neuron only; when F <F, the pulses were triggered from the second input neuron only. The firing rates of the x input pulses were a nonlinear monotonically increasing sigmoid function of jF ÀFj (Experimental Section, Figure S5, Supporting Information).
x induced currents I via the synstor circuit by following Equation (1), I ¼ wx, and I flowed into integrate-and-fire output neuron circuits to generate output pulses, y, and feedback pulses, z, at the output electrodes of the circuit. The firing rates of the y and z pulses were nonlinear monotonically increasing functions of jIj (Experimental Section, Figure S6, Supporting Information). The actuation voltage, V a , was modified by y following V : a ¼ ρðr y1 À r y2 Þ with r y1 and r y2 as the firing rates of output pulses from the first and second output neurons, respectively, and ρ ¼ 8 mV. V a was applied on a piezoactuator to modify the wing shape, lift-force F, and objective function E (Figure 1c). A wave of 10 ns-wide 1.5 V (À1.75 V) z pulses was triggered at the first (second) output electrodes at % 575 ms before a wave of y pulses were triggered, and a train of 10 ns-wide À1.75 V (1.5 V) z pulses was triggered at the first (second) output electrodes at % 575 ms after the train of y pulses were triggered. (Figure 2a, Experimental Section, Equation S1, Supporting Information). The time shifts between y and z pulses were mainly set to accommodate the system time delay between the wing and SNIC. The synstor conductance matrix w was modified by the z and x voltage pulses by following the learning algorithm, (2)) in the real-time self-programming process to change V a and minimize the objective function E under the wind conditions with randomly varied speed S (Figure 1c). To compare the self-programming processes between SNIC and the human brain, 14 human participants without any preknowledge about the morphing wing and its control system received F ÀF signals visually and were instructed to minimize the difference between F andF and the objective function E ¼ 1 2 ðF ÀFÞ 2 by sending output signals y by pressing two keys preset randomly in a keyboard to increase or decrease the actuation voltage V a on the wing (Figures 1d and 2b, Experimental Section). In the real-time self-programming processes, E was reduced by dynamically modifying V a under wind with the same randomly varied speed S as that in the SNIC trials ( Figure 1c). To compare the self-programming control processes by SNIC and human brains with control processes by a preprogrammed computer, a proportional-integral-derivative (PID) controller implemented on a computer received F ÀF signals and output www.advancedsciencenews.com www.advintellsyst.com V a signals to modify the wing shape and F (Figure 1e). The PID controller with various gains was tested to control V a and the shape of the wing experiencing wind with a static speed S ¼ 28.7 m=s, and the optimal PID gains leading to the minimal average E were identified ( Figure S7, Supporting Information). After the PID controller was preprogrammed to the optimal gains, the PID controller modified the shape of the wing while experiencing wind with the same randomly varied speed S as that in the SNIC and human trials, emulating an unpredictable aerodynamic environment beyond the preprogrammed condition (Figure 1e and 2c).

Self-Programming Process
In an SNIC or human self-programming process, when F ¼F, (2)), w reaches an equilibrium stateŵ ¼ argmin w E. Although w andŵ were not experimentally measured, the relative deviation of effective w fromŵ, ΔwðtÞ ¼ ½wðtÞ Àŵ=jwð0Þ Àŵj, was extrapolated (Equation S2, Supporting Information). The average E over a fixed moving time window, 〈E〉, is shown versus t in Figure 3a, versus Δw and the wind speed S in Figure 3b, and versus jΔwj in Figure 3c. Although w for SNIC and humans was not preprogrammed, and had random positive or negative initial deviations fromŵ, w was modified toŵ, decreasing 〈E〉 toward equilibrium values, E eq , within %5.1 s for SNIC and %10 s for humans in their self-programming processes. When the wind speed S changed chaotically, leading to increases in jΔwj and E, w was spontaneously modified towardŵ under the varied S, decreasing 〈E〉 monotonically versus t in the selfprogramming processes (Figure 3). The dynamic change of E in the self-programming process can be expressed as (Supporting Information, Theorem 1) where β ≥ 0, and δE is related to the environmental influence and nonlinear term of E. In the self-programming processes for SNIC and humans, δE < βhEi and E : ¼ ÀβhEi þ δE < 0. Thus 〈E〉 represented a Lyapunov function and was asymptotically decreased toward its dynamic equilibrium value E eq , leading hwi to be modified toward hŵi in the self-programming process; when δE ¼ βhEi, E : ¼ 0, and E reached its dynamic equilibrium value E eq ¼ δE=β under hwi ¼ hŵi. The solution of Equation (3) gives hEi ¼ E eq þ ðhEi À E eq Þe Àβt þ δE Ã e Àβt , where δE Ã e Àβt represents the convolution between δE and e Àβt . When βt ≫ 1, hEi % E eq ; thus, β represents the selfprogramming speed to modify 〈E〉 toward E eq and w towardŵ (Equation (S5), Supporting Information). With its gains preprogrammed to their optimal values under a static wind speed, the PID controller decreased E initially, but the gains were not modified toward their optimal values dynamically under the varied S, leading to E significantly larger than those of the SNIC and humans (Figure 1c).
In a self-programming process, β in Equation (3) represents the speed to reduce 〈E〉 toward E eq and modify w toward w (Equation S5, Supporting Information). As shown in Figure 2. a) The lift-force on the wing F, its target valueF, input voltage pulses x m , feedback voltage pulses z n , output voltage pulses y n , and V a in a typical trial by SNIC are plotted versus time t (left) and at moments t 1 , t 2 , t 3 , t 4 , and t 5 equal to 0.498, 0.516, 0.549, 1.080, and 1.099s, respectively (right). F,F, y n , and V a are plotted versus t in typical trials by b) the human and c) a computer.
www.advancedsciencenews.com www.advintellsyst.com Figure 4a, β increases with increasing average change rate of w at the initial stage of the self-programming process, jw : j i , which can be increased by increasing the firing rates of x, y, and z pulses and decreasing the capacitances and leakage currents in the input and output neurons in SNIC ( Figure S5 and S6, Supporting Information). The equilibrium objective function E eq defined in Equation (3) represents the accuracy to modify w towardŵ (Equation S3, Supporting Information). As shown in Figure 4b, E eq reached its minimal values (data points 2 and 5) when the average change rate of w was near the equilibrium stage of the self-programming process, hjw : ji e ¼ 0.62=s for SNIC and hjw : ji e ¼ 0.32=s for humans. When hjw : ji e is decreased from its optimal values (data points 1 and 4), the β value is decreased, and E eq ¼ δE=β, leading to the increase in E eq as E eq ¼ δE=β.
When β is decreased to zero in a control experiment without z pulses or self-programming, hE (3)) and E eq reaches the maximal value in Figure 4b. When hjw : ji e is increased from its optimal values (data points 3 and 6), w is modified at a high rate, and w overshoots with respect toŵ near w, leading to the fluctuation of jΔwj and E and the increase in E eq (Figure 4c,). In the self-programming processes, when w is close toŵ, the pulse firing rates are decreased by the leakage current in the integrate-and-fire neuron circuits to avoid the overshoot of w with respect toŵ and reduce E eq ; when w deviates fromŵ, the pulse firing rates are increased as a nonlinear function of input signals to the neuron circuits to increase β and decrease E at high speed ( Figure S5 and S6, Supporting Information). By optimizing the neuron circuits in SNIC, the average self-programming 〈E〉 is plotted versus the relative deviations of the device conductances from the optimal conductances, Δw 11 , Δw 12 , Δw 21 , and Δw 22 , and wind speed, S. c) E is plotted at logarithmic scale in 3D plots versus jΔw 11 j, jΔw 12 j, jΔw 21 j, and jΔw 22 j at different azimuthal angles in linear scale. The evolving directions of Δw are indicated by arrows at the base planes of the 3D plots. 〈E〉 versus hΔwi is best fitted by hEi ¼ 1 2 g E=w hΔwi 2 þ E eq and shown as 3D surfaces, with E eq marked by red crosshairs. speed β (0.46s À1 ) and E eq (7.2 Â 10 À5 N 2 ) in the selfprogramming process of SNIC are superior to β (0.37s À1 ) and E eq (3.4 Â 10 À4 N 2 ) of the humans (Figure 3 and 4).

Conclusion
In summary, we demonstrated an SNIC based on synstors to emulate a neurobiological network based on synapses to execute the signal-processing (I ¼ wx, Equation (1)) and correlative learning (w : ¼ αz ⊗ x, Equition 2) algorithms concurrently in parallel analog mode. Unlike a programmable computer, the synstor conductance matrix w does not have to be preprogrammed and can be spontaneously modified toward the optimal matrixŵ, minimizing the objective function E in a self-programming process in complex and unpredictable environments. An SNIC controlled a morphing wing, modified its lift force F toward a targeted valueF, and minimized the objective function E ¼ 1 2 ðF ÀFÞ 2 toward its equilibrium value E eq in a wind with randomly varied speeds. The correlative learning algorithm executed in the synstor circuit can be extended to various learning algorithms including supervised, unsupervised, and reinforcement learning algorithms, leading to the optimization of predefined or self-organized objective functions in intelligent systems. [3,31] Unlike artificial intelligent systems based on computers which have to be preprogrammed for specific tasks, SNIC does not have to be preprogrammed and can "self-program" heuristically by executing the correlative learning algorithm in real time in arbitrary environments for general intelligence. In comparison with humans and a preprogrammed computer, an SNIC demonstrated self-programming speeds and E eq superior to those of the humans and computer. SNIC circumvents the energy consumptions on data transmissions in conventional computing circuits, facilitating a computing energy efficiency of % 3.3 Â 10 17 OPS=W (Experimental Section, Equation (6), Figure 5) significantly higher than the energy efficiencies of computing circuits (%10 7 À 10 13 OPS=W) [7,[11][12][13][14][15][16]20,22,24] and the human brain (% 10 15 OPS=W). [26] The speed to compute parallel hEi is plotted at logarithmic scale in 3D plots versus jΔw 11 j, jΔw 12 j, jΔw 21 j, and jΔw 22 j, which are shown versus time at the base planes of the 3D plots, at different azimuthal angles by blue, redÀorange, yellow, and violet lines, respectively. The arrows at the starting points of the lines indicate the evolving directions. 〈E〉 is best fitted as a function Δw by hEi ¼ 1 2 g E=w hΔwi 2 þ E eq and shown in 3D surfaces, with hE eq i marked by red crosshairs in (d) and dashed lines in (c).
www.advancedsciencenews.com www.advintellsyst.com signal-processing and learning algorithms in a SNIC increases linearly with increasing circuit scale (Experimental Section, Equation (4), Figure 5), the power consumption of an SNIC increases with increasing circuit scale (Experimental Section, Equation (5)), and the computing energy efficiency of an SNIC approximately does not change with increasing circuit scale (Experimental Section, Equation (6), Figure 5). A circuit of 10 6 synstors will have a speed (6 Â 10 14 OPS) comparable with the speeds (%10 12 À 10 14 OPS) of TPU, GPU, and FPGA circuits with~10 9 À 10 11 transistors and consume much less power (% 30 μW) than those of the transistor-based circuits (%40 W). [13][14][15] A circuit of 10 9 synstors will have a speed (6 Â 10 16 OPS) comparable with the speeds of the human brain (%10 16 OPS) and the Summit supercomputer (%10 17 OPS) and consumes a power (% 40 mW) much less than those of the human brain (%30 W with %10 14 synapses) [26] and Summit supercomputer (%10 7 W with %10 14 transistors). [12] There is "plenty of room at the bottom" to scale up synstor circuits with high speed, low power consumption, high energy efficiency, and small circuit scale/volume for a new computing platform that can self-program in real time in arbitrary and unpredictable environments for artificial general intelligence.

Experimental Section
Learning Algorithm in a Synstor Circuit: In the self-programming process of a synstor, the feedback pulses, z, follow z ¼ y Ãθ (Equation S1, Supporting Information), wherẽ θðtÞ ¼

<
: θðtÞ when À τ À < t < 0 ÀθðtÞ when τ þ > t > 0 0 when t ¼ 0 or t ≥ τ þ or t ≤ Àτ À , the time constants τ þ > 0 and τ À > 0, the function θðtÞ > 0. For the averageθ over learning period T, hθi ¼ 0, and the average z over learning period T, hzi ¼ 0, and z ¼ z Àz ¼ z. To generate feedback pulses with z n ¼ y n Ãθ, a train of positive (negative) feedback pulses with a pulse firing rate proportional to θðt À t n Þ within the time window t n À τ À < t < t n at the n th (complimentary) output electrode and a train of negative (positive) feedback pulses with a pulse firing rate proportional to θðt À t n Þ within the time window t n < t < t n þ τ þ were triggered at the n th output electrode.
Synstor Circuit Fabrication: The synstor circuit was fabricated by the process reported previously. [28] Si wafers with a 100 nm-thick SiO 2 layer were diced into 3 cm Â 3 cm square chips. A 10 μm-long and 50 nm-thick Al reference electrode ( Figure S1a, Supporting Information) was deposited by electron beam (e-beam) evaporation (CHA Industries, CHA Mark 40) and patterned by photolithography and wet chemical etching with tetramethylammonium hydroxide (TMAH)-based photoresist developer (AZ 300 MIF Developer). A 22 nm-thick HfO 2 barrier layer and a 2.5 nm-thick TiO 2 charge storage layer ( Figure S1b, Supporting Information) were deposited by atomic layer deposition (Cambridge NanoTech, Fiji Thermal and Plasma Atomic Layer Deposition (ALD)). The TiO 2 film was patterned ( Figure S1c SNIC Testing: Voltage pulses, x and z, were generated by function generators (Agilent 33250 A) with voltage amplitudes ranging between À2 V and 2 V, a duration ranging between 10 ns and 5 ms, and a frequency ranging between 50 MHz and 100 Hz and were applied to the input and output electrodes of synstor circuits. The x and z voltage pulses were gated by switches (Maxim, MAX383), which were activated by a digital voltage module (National Instruments, 9403 E Digital Input/Output). The synchronized input and output pulses from a single generator prevented phase shifts between the pulses. Output voltage pulses, y, were also read by the digital voltage module. The input, output, feedback, actuation, and reference voltage signals were measured by an analog module (National Instruments, 9205 Analog Input). To extrapolate the synstor conductance w, input pulses x ¼ À1.75 V were applied to a synstor, and the output current from the synstor was measured by an operational amplifier (Microchip Technologies, MPC6022).
Morphing Wing: The morphing wing was a wing section with a 12-inch chord and a morphing trailing edge, which used a macrofiber composite (MFC) piezoelectric actuator and a flexure box mechanism to modify the camber of the trailing edge. [30,32] The actuator had a 3D-printed elastomeric honeycomb skin for tailored stiffness, and the piezoelectric mechanism allowed for fast response time. The morphing wing had applications in stall recovery during wind gusts, optimizing the lift distribution to increase aerodynamic efficiency and reducing turbulence. The design was scalable to multiple piezoelectric actuators along the spanwise edge (spanwise morphing trail edge) to achieve continuous wing shape change, but the hysteresis of the piezoelectric actuator increased the difficulty of controlling the wing, which was adapted by the real-time selfprogramming functionality of the synstor circuit. The output voltage signals from the synstor circuit, y, triggered an analog actuation voltage, Figure 5. A 3D plot displays the computing energy efficiencies, speeds, and device numbers in a 2 Â 2 synstor circuit in this work (green), projected 10 Â 10, 10 2 Â 10 2 , 10 3 Â 10 3 , and 10 2 Â 10 3 Â 10 3 synstor circuits (green), the human brain (blue), Summit supercomputer, Volta V100 GPUs from Nvidia, Stratrix 10 FPGA from Intel, TPUs from Google, TrueNorth neuromorphic circuit from IBM, Tianjic neuromorphic circuits from Tsinghua University, phase-change memory circuit from IBM (signal processing only, learning excluded), and memristor circuits from UMass/ HP (signal processing only, learning excluded).
www.advancedsciencenews.com www.advintellsyst.com V a , from an analog voltage module (National Instruments, NI-9264). V a was amplified by a high-voltage driver (Avid LLC, AVID-EHV-MFC.B2) to a range from À0.5 to 1.5 kV to control the piezoelectric actuators and modify the wing shape.
Wind Tunnel: The morphing wing was tested in a laminar flow and an open-circuit wind tunnel (Aerolab) with a 24 Â 24 in. test section. A fan in the wind tunnel was driven by a high-voltage driver (ABB, ACS550-01-046 A-2 AC) to randomly change wind speed, S, in the range between 17.3 and 28.7m s À1 . S was measured by a pitot tube and air velocity transducer (TSI, 8455). The lift-force on the wing, F, was measured using a forceÀtorque multiaxis load cell (JR3, 30E12A-4-I40-EF 40N3.1S) with a measurement range of AE80 N and resolution of 0.01 N, attached to a morphing wing mounting shaft. The sensory signals of S and F were read by a voltage I/O device (National Instruments, PCIe 6353 Multifunction I/O Device).
Human Controllers: The F ÀF values were dynamically displayed to the participants, who pressed two keys on a keyboard to increase or decrease the actuation voltage, V a . The change rate of V a was determined by the key- when key 1 is pressed 0 when key 1 is not pressed and a k2 ¼ 1 when key2ispressed 0 when key 2 is not pressed , and ρ h was randomly set to 31 mV=ms or À31 mV=ms before each experiment started. V a was modified by the humans to minimize the objective function E ¼ 1 2 ðF ÀFÞ 2 under the randomly changed wind speed S.
PID Controller: The lift-force error, e F ¼ F ÀF, was sent to the PID controller to induce the actuation voltage V a following the PID control algorithm, V : F , where K p denotes the proportional gain, K i denotes the integral gain, and K d denotes the derivative gain. After the gains of the PID controller were set to various combinations of K p ¼ 10 À4 , 10 À3 , or 10 À2 V=N ⋅ s; K i ¼ 10 À3 , 10 À2 , or 10 À1 V=N ⋅ s 2 ; and K d ¼ 10 À2 , 10 À1 , or 1 V=N, the PID controller modified V a and the shape of the wing while experiencing wind with static speed S ¼ 28.7 m=s. The average objective function hEi ¼ 1 2 ðF ÀFÞ 2 during the control processes is shown as a function of K p , K i , and K d in Figure S7, Supporting Information, and 〈E〉 approaches its minimal value under the optimal gains with K p ¼ 10 À5 V=N ⋅ s, K i ¼ 10 À4 V=N ⋅ s 2 , and K d ¼ 10 À3 V=N. After the PID controller was preprogrammed to the optimal gains, the PID controller modified V a and the shape of the wing experienced the randomly changed wind speeds S, emulating an unpredictable aerodynamic environment beyond the static wind speed.
SNIC Computing Speed and Energy Efficiency: In comparison with computers, the equivalent computing operations in an M Â N synstor circuit were approximately equal to 3MN to implement the signal-processing algorithm (I ¼ wx, Equation (1)), 2MN for multiplications between w and x (MN for accumulations), and 3MN to implement the learning algorithm (w : ¼ αz ⊗ x Equation (2)), 2MN outer products between α, x, and z, MN for w modifications. The speed for the synstor circuit to implement 6MN equivalent computing operations for parallel signal processing and learning is where f c denotes the operation frequency of the circuit. When voltage pulses are applied on its input or output electrode of an M Â N synstor circuit connected with N output integrate-and-fire neuron circuits, the average power consumption in an M Â N synstor circuit is P c % MNhwiV 2 a D p þ NE p hr y i where hwi denotes the average conductance of the synstors, V a denotes the magnitude of pulses, D p denotes the average duty-cycle of the pulses, E p denotes the average energy consumption to trigger a pulse from integrate-and-fire neuron circuits, and hr y i denotes the average firing rates of pulses from output neuron circuits. The input neurons are part of the circuit of last layer, so their energy consumption is not included in the SNIC energy consumption of the current layer. The computing energy efficiency of a synstor circuit is equal to its computing speed V c divided by its power consumption P c C E ¼ 6f c =ðhwiV 2 a D p þ E p hr y i=MÞ The computing energy efficiency of SNIC operated with operation frequency f c ¼ 100 MHz, average synstor conductances hwi ¼ 10 nS, V a ¼ 1.75V, D p ¼ 0.06, E p ¼ 10 pJ, r in ¼ 300 kHz, and hr y i ¼ 160 Hz and was approximately equal to 3.3 Â 10 17 OPS=W.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.