DAGSENS: Directed Acyclic Graph Based Direct and Adjoint Transient Sensitivity Analysis for Event-Driven Objective Functions
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
We present DAGSENS, a new theory for 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, starting from DAE parameters, all the way up to the objective function whose sensitivity is needed, as a Directed Acyclic Graph (DAG) called the "sensitivity DAG", and (2) to compute the required sensitivities efficiently (with time complexity linear in the size of the sensitivity DAG) by leveraging dynamic programming techniques to traverse the DAG. DAGSENS is simple, elegant, and easy-to-understand compared to existing sensitivity analysis approaches; for example, in DAGSENS, one can switch between direct and adjoint transient sensitivities just by changing the direction of DAG traversal (i.e., topological order vs. reverse topological order). Also, DAGSENS is significantly more powerful than existing sensitivity analysis approaches because it allows one to compute the sensitivities of a much more general class of objective functions, including those defined based on "events" that occur during a transient simulation (e.g., a node voltage crossing a particular threshold, a phase-locked loop (PLL) achieving lock, a signal reaching its maximum/minimum value during a transient run, etc.). In this paper, we apply DAGSENS to compute the sensitivities of important event-driven performance metrics in several real-world electronic and biological applications, including high-speed communication (featuring sub-systems such as I/0 links and PLLs), statistical cell library characterization, and gene expression in Drosophila embryos.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- AC04-94AL85000; NA0003525
- OSTI ID:
- 1761808
- Report Number(s):
- SAND-2017-8569; 671191
- Country of Publication:
- United States
- Language:
- English
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