Fast Design Space Exploration of Nonlinear Systems: Part I

Sanjai Narain, Emily Mak, Dana Chee, Brendan Englot, Kishore Pochiraju, Niraj K. Jha, Karthik Narayan

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


System design tools are often only available as input-output blackboxes: for a given design as input they compute an output representing system behavior. Blackboxes are intended to be run in the forward direction. This paper presents a new method of solving the “inverse design problem” namely, given requirements or constraints on output, find an input that also optimizes an objective function. This problem is challenging for several reasons. First, blackboxes are not designed to be run in reverse. Second, inputs and outputs can be discrete and continuous. Third, finding designs concurrently satisfying a set of requirements is hard because designs satisfying individual requirements may conflict with each other. Fourth, blackbox evaluations can be expensive. Finally, evaluations can sometimes fail to produce an output due to non-convergence of underlying numerical algorithms. This paper presents CNMA, a new method of solving the inverse problem that overcomes these challenges. CNMA tries to sample only the part of the design space relevant to solving the inverse problem, leveraging the power of neural networks, Mixed Integer Linear Programs, and a new learning-from-failure feedback loop. The paper also presents a parallel version of CNMA that improves the efficiency and quality of solutions over the sequential version, and tries to steer it away from local optima. CNMA’s performance is evaluated against conventional optimization methods for seven nonlinear design problems of 8 (two problems), 10, 15, 36 and 60 real-valued dimensions and one with 186 binary dimensions. Conventional methods evaluated are stable, off-the-shelf implementations of Bayesian Optimization with Gaussian Processes, Nelder Mead and Random Search. The first two do not even produce a solution for problems that are high-dimensional, have both discrete and continuous variables or whose blackboxes fail to return values for some inputs. CNMA produces solutions for all problems. When conventional methods do produce solutions, CNMA improves upon their performance by 1%-87%.

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering


  • Blackbox optimization
  • Feedback loop
  • Integrated circuits
  • Inverse problems
  • Linear programming
  • Metamodeling
  • Mixed-Integer Linear Program (MILP)
  • Neural networks
  • Optimization methods
  • constrained optimization
  • neural networks
  • optimization
  • sample efficiency.


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