Fig. 3: In-memory differential computing for solving mathematical derivative functions.

a A schematic diagram showing how the domain configuration in 14 ferroelectric capacitors stores data with values varying from −7 to 7. Inset shows the function f(x)=−x, where ∆x = 1, a = −4 and b = 4. b A schematic diagram showing how the ferroelectric domains switching calculates the differential value. The upward (downward) domain switching is labeled in blue and red, respectively. c, d The evolution of transient currents (left) and integral charges (right) with time. In the case of (c), as time increases periodically, the number of capacitors with upward domain switching increases monotonically from 1 to 14 in steps of 1 (inset of c). In the case of (d), as time increases periodically, the number of capacitors with upward domain switching increases monotonically from 0 to 7 in steps of 1 and then remains constant at 7, while the number of capacitors with downward domain switching first remains constant at 7 and then decreases monotonically from 7 to 0 in steps of 1 (inset of d). e The parabolic function g(x)=x²-2x + 1. f The evolution of transient currents (left) and integral charges (right) as a function of time. As time increases periodically, the switching of domains computes g(0)-g(−1), g(1)-g(0), g(2)-g(1) and g(3)-g(2), respectively. g By dividing with the ∆x of 1, that is [g(0)-g(−1)]/[0-(−1)] = g’(−0.5), [g(1)-g(0)]/[1-0] = g’(0.5), [g(2)-g(1)]/[2-1] = g’(1.5) and [g(3)-g(2)]/[3-2] = g’(2.5), the domains switching gives the first-order derivative function g’(x) = 2x−2. The experimental measurements are repeated 12 times to exclude randomness. h The evolution of transient currents (left) and integral charges (right) with time. As time increases periodically, the domains switching calculates g’(0.5)-g’(−0.5), g’(1.5)-g’(0.5) and g’(2.5)-g’(1.5), respectively. i By dividing with the ∆x of 1, that is [g’(0.5)-g’(−0.5)]/[0.5-(−0.5)] = g”(0), [g’(1.5)-g’(0.5)]/[1.5-0.5] = g”(1) and [g’(2.5)-g’(1.5)]/[2.5-1.5] = g”(2), the domains switching gives the second-order derivative function g”(x) = 2. The experimental measurements are repeated 12 times to exclude randomness. Source data are provided as a Source Data file.