Abstract: A hybrid analog and digital computational system is created by receiving equations in which a set of solution values is unknown. A residual iterative algorithm is implemented to solve the set of solution values for the equations. The residual iterative algorithm includes an outer update loop computed using a digital computing device with a set of residue values initially set to a first initial value and a set of solution update values set to a second initial value. The residual iterative algorithm includes an inner residual loop, which is iteratively computed using an analog accelerator until one or more inner residual loop stopping criteria is met and returning the set of solution update values. Next, the set of solution updates are used to update the set of residue values and a range of a next set of solution update values, thereby adjusting a computational precision of the inner residual loop.

Abstract: An image-based fluid characterization system may include a container configured to fully enclose a fluid, one or more illumination sources configured illuminate an interior portion of the container with illumination and one or more imaging systems. Each of the one or more imaging systems may include a multi-pixel sensor and an optical relay, where the multi-pixel sensor generates one or more images of the fluid in response to the illumination via the optical relay. The system may further include a controller to generate one or more measurements of the fluid based on the one or more images.

Abstract: An adaptive system and a method for adjusting a parameter in the adaptive system includes operating an adaptive system with an output signal produced from an input signal applied to an input, in which a parameter with a finite range is determined based on a difference between the output signal and a target output signal. In one example the parameter with the finite range is a fixed-point parameter or an analog parameter. The parameter is accessed from the adaptive system. A probability distribution of the parameter is assigned. The finite range for the parameter is updated based on the probability distribution which has been assigned. The probability distribution function may be updated alone with the finite range of the parameter. The probability distribution may be derived from one or more historical values of the parameter, and a plurality of system parameters belonging to an identical category of data as the parameter.

Abstract: An adaptive system and a method for adjusting a parameter in the adaptive system includes operating an adaptive system with an output signal produced from an input signal applied to an input, in which a parameter with a finite range is determined based on a difference between the output signal and a target output signal. In one example the parameter with the finite range is a fixed-point parameter or an analog parameter. The parameter is accessed from the adaptive system. A probability distribution of the parameter is assigned. The finite range for the parameter is updated based on the probability distribution which has been assigned. The probability distribution function may be updated alone with the finite range of the parameter. The probability distribution may be derived from one or more historical values of the parameter, and a plurality of system parameters belonging to an identical category of data as the parameter.