21 research outputs found
Fast Design Space Exploration of Nonlinear Systems: Part I
System design tools are often only available as blackboxes with complex
nonlinear relationships between inputs and outputs. Blackboxes typically run in
the forward direction: for a given design as input they compute an output
representing system behavior. Most cannot be run in reverse to produce an input
from requirements on output. Thus, finding a design satisfying a requirement is
often a trial-and-error process without assurance of optimality. Finding
designs concurrently satisfying multiple requirements is harder because designs
satisfying individual requirements may conflict with each other. Compounding
the hardness are the facts that blackbox evaluations can be expensive and
sometimes fail to produce an output due to non-convergence of underlying
numerical algorithms. This paper presents CNMA (Constrained optimization with
Neural networks, MILP solvers and Active Learning), a new optimization method
for blackboxes. It is conservative in the number of blackbox evaluations. Any
designs it finds are guaranteed to satisfy all requirements. It is resilient to
the failure of blackboxes to compute outputs. It tries to sample only the part
of the design space relevant to solving the design problem, leveraging the
power of neural networks, MILPs, and a new learning-from-failure feedback loop.
The paper also presents parallel 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 for seven nonlinear design problems of
8 (2 problems), 10, 15, 36 and 60 real-valued dimensions and one with 186
binary dimensions. It is shown that CNMA improves the performance of stable,
off-the-shelf implementations of Bayesian Optimization and Nelder Mead and
Random Search by 1%-87% for a given fixed time and function evaluation budget.
Note, that these implementations did not always return solutions.Comment: 14 pages, 26 figures. arXiv admin note: text overlap with
arXiv:2010.0984
A model for the degradation of polyimides due to oxidation
Polyimides, due to their superior mechanical behavior at high temperatures,
are used in a variety of applications that include aerospace, automobile and
electronic packaging industries, as matrices for composites, as adhesives etc.
In this paper, we extend our previous model in [S. Karra, K. R. Rajagopal,
Modeling the non-linear viscoelastic response of high temperature polyimides,
Mechanics of Materials, In press, doi:10.1016/j.mechmat.2010.09.006], to
include oxidative degradation of these high temperature polyimides. Appropriate
forms for the Helmholtz potential and the rate of dissipation are chosen to
describe the degradation. The results for a specific boundary value problem,
using our model compares well with the experimental creep data for PMR-15 resin
that is aged in air.Comment: 13 pages, 2 figures, submitted to Mechanics of Time-dependent
Material