Optimal designs for rational function regression

We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The proposed method treats D-, E-, A-, and $\Phi_p$-optimal designs in a unified manner, and generates a polynomial whose zeros are the support points of the optimal approximate design, generalizing a number of previously known results of the same flavor. The method is based on a mathematical optimization model that can incorporate various criteria of optimality and can be solved efficiently by well established numerical optimization methods. In contrast to previous optimization-based methods proposed for similar design problems, it also has theoretical guarantee of its algorithmic efficiency; in fact, the running times of all numerical examples considered in the paper are negligible. The stability of the method is demonstrated in an example involving high degree polynomials. After discussing linear models, applications for finding locally optimal designs for nonlinear regression models involving rational functions are presented, then extensions to robust regression designs, and trigonometric regression are shown. As a corollary, an upper bound on the size of the support set of the minimally-supported optimal designs is also found. The method is of considerable practical importance, with the potential for instance to impact design software development. Further study of the optimality conditions of the main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory and additional example

RTL2RTL Formal Equivalence: Boosting the Design Confidence

Increasing design complexity driven by feature and performance requirements and the Time to Market (TTM) constraints force a faster design and validation closure. This in turn enforces novel ways of identifying and debugging behavioral inconsistencies early in the design cycle. Addition of incremental features and timing fixes may alter the legacy design behavior and would inadvertently result in undesirable bugs. The most common method of verifying the correctness of the changed design is to run a dynamic regression test suite before and after the intended changes and compare the results, a method which is not exhaustive. Modern Formal Verification (FV) techniques involving new methods of proving Sequential Hardware Equivalence enabled a new set of solutions for the given problem, with complete coverage guarantee. Formal Equivalence can be applied for proving functional integrity after design changes resulting from a wide variety of reasons, ranging from simple pipeline optimizations to complex logic redistributions. We present here our experience of successfully applying the RTL to RTL (RTL2RTL) Formal Verification across a wide spectrum of problems on a Graphics design. The RTL2RTL FV enabled checking the design sanity in a very short time, thus enabling faster and safer design churn. The techniques presented in this paper are applicable to any complex hardware design.Comment: In Proceedings FSFMA 2014, arXiv:1407.195

Learning Optimal Control of Synchronization in Networks of Coupled Oscillators using Genetic Programming-based Symbolic Regression

Networks of coupled dynamical systems provide a powerful way to model systems with enormously complex dynamics, such as the human brain. Control of synchronization in such networked systems has far reaching applications in many domains, including engineering and medicine. In this paper, we formulate the synchronization control in dynamical systems as an optimization problem and present a multi-objective genetic programming-based approach to infer optimal control functions that drive the system from a synchronized to a non-synchronized state and vice-versa. The genetic programming-based controller allows learning optimal control functions in an interpretable symbolic form. The effectiveness of the proposed approach is demonstrated in controlling synchronization in coupled oscillator systems linked in networks of increasing order complexity, ranging from a simple coupled oscillator system to a hierarchical network of coupled oscillators. The results show that the proposed method can learn highly-effective and interpretable control functions for such systems.Comment: Submitted to nonlinear dynamic

Evolutionary-based sparse regression for the experimental identification of duffing oscillator

In this paper, an evolutionary-based sparse regression algorithm is proposed and applied onto experimental data collected from a Duffing oscillator setup and numerical simulation data. Our purpose is to identify the Coulomb friction terms as part of the ordinary differential equation of the system. Correct identification of this nonlinear system using sparse identification is hugely dependent on selecting the correct form of nonlinearity included in the function library. Consequently, in this work, the evolutionary-based sparse identification is replacing the need for user knowledge when constructing the library in sparse identification. Constructing the library based on the data-driven evolutionary approach is an effective way to extend the space of nonlinear functions, allowing for the sparse regression to be applied on an extensive space of functions. The results show that the method provides an effective algorithm for the purpose of unveiling the physical nature of the Duffing oscillator. In addition, the robustness of the identification algorithm is investigated for various levels of noise in simulation. The proposed method has possible applications to other nonlinear dynamic systems in mechatronics, robotics, and electronics