DAGSENS: Directed acyclic graph based direct and adjoint transient sensitivity analysis for event-driven objective functions

Abstract

We present DAGSENS, a new approach to parametric transient sensitivity analysis of Differential Algebraic Equation systems (DAEs), such as SPICE-level circuits. The key ideas behind DAGSENS are, (1) to represent the entire sequence of computations from DAE parameters to the objective function (whose sensitivity is needed) as a Directed Acyclic Graph (DAG) called the “sensitivity DAG”, and (2) to compute the required sensitivites efficiently by using dynamic programming techniques to traverse the DAG. DAGSENS is simple, elegant, and easy-to-understand compared to previous approaches; for example, in DAGSENS, one can switch between direct and adjoint sensitivities simply by reversing the direction of DAG traversal. Also, DAGSENS is more powerful than previous approaches because it works for a more general class of objective functions, including those based on “events” that occur during a transient simulation (e.g., a node voltage crossing a threshold, a phase-locked loop (PLL) achieving lock, a circuit signal reaching its maximum/minimum value, etc.). In this paper, we demonstrate DAGSENS on several electronic and biological applications, including high-speed communication, statistical cell library characterization, and gene expression.