An analog computing system with coupled non-linear oscillators can solve complex combinatorial optimization problems using the weighted Ising model. The system is composed of a fully-connected LC oscillator network with low-cost electronic components and compatible with traditional integrated circuit technologies. Each LC oscillator, or node, in the network can be coupled to each other node in the array with a multiply and accumulate crossbar array or optical interconnects. When implemented with four nodes, the system performs with single-run ground state accuracies of 98% on randomized MAX-CUT problem sets with binary weights and 84% with five-bit weight resolutions. The four-node system can obtain solutions within five oscillator cycles with a time-to-solution that scales directly with oscillator frequency. A scaling analysis suggests that larger coupled oscillator networks may be used to solve computationally intensive problems faster and more efficiently than conventional algorithms.

An analog computing system with coupled non-linear oscillators can solve complex combinatorial optimization problems using the weighted Ising model. The system is composed of a fully-connected LC oscillator network with low-cost electronic components and compatible with traditional integrated circuit technologies. Each LC oscillator, or node, in the network can be coupled to each other node in the array with a multiply and accumulate crossbar array or optical interconnects. When implemented with four nodes, the system performs with single-run ground state accuracies of 98% on randomized MAX-CUT problem sets with binary weights and 84% with five-bit weight resolutions. The four-node system can obtain solutions within five oscillator cycles with a time-to-solution that scales directly with oscillator frequency. A scaling analysis suggests that larger coupled oscillator networks may be used to solve computationally intensive problems faster and more efficiently than conventional algorithms.

Systems and methods provide for efficiently and accurately determining a simplified path that conforms to the geometry of an original path by simultaneously minimizing the deviation from the original path and reducing the number of anchor points in the simplified path. A simplified path may be iteratively generated by updating parametric values and anchor points for candidate simplified paths at epochs. A deviation in distance between points on the original path and corresponding points on candidate paths may be iteratively decreased to ensure that the resulting simplified path follows the geometry of the original path to a predetermined threshold. Continuity constrains can also be applied to ensure smoothness of the simplified path.

Systems and methods provide for efficiently and accurately determining a simplified path that conforms to the geometry of an original path by simultaneously minimizing the deviation from the original path and reducing the number of anchor points in the simplified path. A simplified path may be iteratively generated by updating parametric values and anchor points for candidate simplified paths at epochs. A deviation in distance between points on the original path and corresponding points on candidate paths may be iteratively decreased to ensure that the resulting simplified path follows the geometry of the original path to a predetermined threshold. Continuity constrains can also be applied to ensure smoothness of the simplified path.

A system includes a motor, a memory storing instructions and at least one controller configured to execute the instructions to cause the system to obtain at least one message over a network, the at least one message indicating a target position for a rotor of the motor and a target time associated with the target position, determine a position command and a speed command based on the target position and the target time, and control the motor based on the position command and the speed command.

A system includes a motor, a memory storing instructions and at least one controller configured to execute the instructions to cause the system to obtain at least one message over a network, the at least one message indicating a target position for a rotor of the motor and a target time associated with the target position, determine a position command and a speed command based on the target position and the target time, and control the motor based on the position command and the speed command.

A flow analysis apparatus is provided. The flow analysis apparatus includes a model deriver configured to generate a flow analytic model for performing a flow analysis for a plurality of cells by using analytic data including a plurality of input signals used for performing multiple times iterations of numerical analysis by Computational Fluid Dynamics (CFD) and a plurality of output signals corresponding to each of the plurality of input signals, and a flow analyzer configured to perform the flow analysis for the plurality of cells that divide the space around a design target component by using the generated flow analytic model.

Disclosed are techniques for simulating a physical process and for determining boundary conditions for a specific energy dissipation rate of a k-Omega turbulence fluid flow model of a fluid flow, by computing from a cell center distance and fluid flow variables a value of the specific energy dissipation rate for a turbulent flow that is valid for a viscous layer, buffer layer, and logarithmic region of a boundary defined in the simulation space. The value is determined by applying a buffer layer correction factor as a first boundary condition for the energy dissipation rate and by applying a viscous sublayer correction factor as a second boundary condition for the energy dissipation rate.

Disclosed are techniques for simulating a physical process and for determining boundary conditions for a specific energy dissipation rate of a k-Omega turbulence fluid flow model of a fluid flow, by computing from a cell center distance and fluid flow variables a value of the specific energy dissipation rate for a turbulent flow that is valid for a viscous layer, buffer layer, and logarithmic region of a boundary defined in the simulation space. The value is determined by applying a buffer layer correction factor as a first boundary condition for the energy dissipation rate and by applying a viscous sublayer correction factor as a second boundary condition for the energy dissipation rate.

The disclosure following relates generally to complex simulations, and fault diagnosis. In some embodiments, a component that is causing a delayed simulation time of a system is determined. A component of reduced complexity is designed, and the component of reduced complexity is used to replace the original component in the system. Fault diagnosis may then be conducted using the updated system with the reduced complexity component, thus decreasing the time taken to diagnose the fault.