Robust DC and efficient time-domain fast fault simulation

Purpose – Imperfections in manufacturing processes may cause unwanted connections (faults) that are added to the nominal, "golden", design of an electronic circuit. By fault simulation one simulates all situations. Normally this leads to a large list of simulations in which for each defect a steady-state (DC) solution is determined followed by a transient simulation. We improve the robustness and the e¿iciency of these simulations. Design/methodology/approach – Determining the DC solution can be very hard. For this we present an adaptive time domain source stepping procedure that can deal with controlled sources. The method can easily be combined with existing pseudo-transient procedures. The method is robust and e¿cient. In the subsequent transient simulation the solution of a fault is compared to a golden, fault-free, solution. A strategy is developed to e¿ciently simulate the faulty solutions until their moment of detection. Finding – We fully exploit the hierarchical structure the circuit in the simulation process to bypass parts of the circuit that appear to be una¿ected by the fault. Accurate prediction and e¿cient solution procedures lead to fast fault simulation. Originality/value – Our fast fault simulation helps to store a database with detectable deviations for each fault. If such a detectable output "matches" a result of a product that has been returned because of malfunctioning it helps to identify the subcircuit that may contain the real fault. One aims to detect as much as possible candidate faults. Because of the many options the simulations must be very e¿cient

Robust DC and efficient time-domain fast fault simulation

Purpose – Imperfections in manufacturing processes may cause unwanted connections (faults) that are added to the nominal, "golden", design of an electronic circuit. By fault simulation one simulates all situations. Normally this leads to a large list of simulations in which for each defect a steady-state (DC) solution is determined followed by a transient simulation. We improve the robustness and the e¿iciency of these simulations. Design/methodology/approach – Determining the DC solution can be very hard. For this we present an adaptive time domain source stepping procedure that can deal with controlled sources. The method can easily be combined with existing pseudo-transient procedures. The method is robust and e¿cient. In the subsequent transient simulation the solution of a fault is compared to a golden, fault-free, solution. A strategy is developed to e¿ciently simulate the faulty solutions until their moment of detection. Finding – We fully exploit the hierarchical structure the circuit in the simulation process to bypass parts of the circuit that appear to be una¿ected by the fault. Accurate prediction and e¿cient solution procedures lead to fast fault simulation. Originality/value – Our fast fault simulation helps to store a database with detectable deviations for each fault. If such a detectable output "matches" a result of a product that has been returned because of malfunctioning it helps to identify the subcircuit that may contain the real fault. One aims to detect as much as possible candidate faults. Because of the many options the simulations must be very e¿cient

Heavy-tailed kernels reveal a finer cluster structure in t-SNE visualisations

T-distributed stochastic neighbour embedding (t-SNE) is a widely used data visualisation technique. It differs from its predecessor SNE by the low-dimensional similarity kernel: the Gaussian kernel was replaced by the heavy-tailed Cauchy kernel, solving the "crowding problem" of SNE. Here, we develop an efficient implementation of t-SNE for a $t$-distribution kernel with an arbitrary degree of freedom $\nu$, with $\nu\to\infty$ corresponding to SNE and $\nu=1$ corresponding to the standard t-SNE. Using theoretical analysis and toy examples, we show that $\nu<1$ can further reduce the crowding problem and reveal finer cluster structure that is invisible in standard t-SNE. We further demonstrate the striking effect of heavier-tailed kernels on large real-life data sets such as MNIST, single-cell RNA-sequencing data, and the HathiTrust library. We use domain knowledge to confirm that the revealed clusters are meaningful. Overall, we argue that modifying the tail heaviness of the t-SNE kernel can yield additional insight into the cluster structure of the data