scholarly journals Geometry of sample sets in derivative-free optimization: polynomial regression and underdetermined interpolation

2008 ◽  
Vol 28 (4) ◽  
pp. 721-748 ◽  
Author(s):  
A. R. Conn ◽  
K. Scheinberg ◽  
L. N. Vicente
Keyword(s):  
Polynomial Regression ◽  
Derivative Free Optimization ◽  
Derivative Free

scholarly journals Optimal Wells Placement to Maximize the Field Coverage Using Derivative-Free Optimization

2020 ◽  
Vol 178 ◽  
pp. 65-74
Author(s):  
Ksenia Balabaeva ◽  
Liya Akmadieva ◽  
Sergey Kovalchuk
Keyword(s):  
Derivative Free Optimization ◽  
Derivative Free

Benchmarking and Field-Testing of the Distributed Quasi-Newton Derivative-Free Optimization Method for Field Development Optimization

2021 ◽  
Author(s):  
Faruk Alpak ◽  
Yixuan Wang ◽  
Guohua Gao ◽  
Vivek Jain
Keyword(s):  
Optimization Problems ◽  
Field Testing ◽  
Optimization Method ◽  
Training Data ◽  
Local Optima ◽  
Field Development ◽  
Derivative Free Optimization ◽  
Derivative Free ◽  
Data Points ◽  
Quasi Newton

Abstract Recently, a novel distributed quasi-Newton (DQN) derivative-free optimization (DFO) method was developed for generic reservoir performance optimization problems including well-location optimization (WLO) and well-control optimization (WCO). DQN is designed to effectively locate multiple local optima of highly nonlinear optimization problems. However, its performance has neither been validated by realistic applications nor compared to other DFO methods. We have integrated DQN into a versatile field-development optimization platform designed specifically for iterative workflows enabled through distributed-parallel flow simulations. DQN is benchmarked against alternative DFO techniques, namely, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method hybridized with Direct Pattern Search (BFGS-DPS), Mesh Adaptive Direct Search (MADS), Particle Swarm Optimization (PSO), and Genetic Algorithm (GA). DQN is a multi-thread optimization method that distributes an ensemble of optimization tasks among multiple high-performance-computing nodes. Thus, it can locate multiple optima of the objective function in parallel within a single run. Simulation results computed from one DQN optimization thread are shared with others by updating a unified set of training data points composed of responses (implicit variables) of all successful simulation jobs. The sensitivity matrix at the current best solution of each optimization thread is approximated by a linear-interpolation technique using all or a subset of training-data points. The gradient of the objective function is analytically computed using the estimated sensitivities of implicit variables with respect to explicit variables. The Hessian matrix is then updated using the quasi-Newton method. A new search point for each thread is solved from a trust-region subproblem for the next iteration. In contrast, other DFO methods rely on a single-thread optimization paradigm that can only locate a single optimum. To locate multiple optima, one must repeat the same optimization process multiple times starting from different initial guesses for such methods. Moreover, simulation results generated from a single-thread optimization task cannot be shared with other tasks. Benchmarking results are presented for synthetic yet challenging WLO and WCO problems. Finally, DQN method is field-tested on two realistic applications. DQN identifies the global optimum with the least number of simulations and the shortest run time on a synthetic problem with known solution. On other benchmarking problems without a known solution, DQN identified compatible local optima with reasonably smaller numbers of simulations compared to alternative techniques. Field-testing results reinforce the auspicious computational attributes of DQN. Overall, the results indicate that DQN is a novel and effective parallel algorithm for field-scale development optimization problems.

scholarly journals Optimization based Layer-wise Magnitude-based Pruning for DNN Compression

2018 ◽  
Author(s):  
Guiying Li ◽  
Chao Qian ◽  
Chunhui Jiang ◽  
Xiaofen Lu ◽  
Ke Tang
Keyword(s):  
Deep Neural Network ◽  
Optimization Problem ◽  
State Of The Art ◽  
Automatic Tuning ◽  
Constrained Optimization Problem ◽  
Derivative Free Optimization ◽  
Derivative Free ◽  
Threshold Tuning ◽  
Model Subject ◽  
Pruning Methods

Layer-wise magnitude-based pruning (LMP) is a very popular method for deep neural network (DNN) compression. However, tuning the layer-specific thresholds is a difficult task, since the space of threshold candidates is exponentially large and the evaluation is very expensive. Previous methods are mainly by hand and require expertise. In this paper, we propose an automatic tuning approach based on optimization, named OLMP. The idea is to transform the threshold tuning problem into a constrained optimization problem (i.e., minimizing the size of the pruned model subject to a constraint on the accuracy loss), and then use powerful derivative-free optimization algorithms to solve it. To compress a trained DNN, OLMP is conducted within a new iterative pruning and adjusting pipeline. Empirical results show that OLMP can achieve the best pruning ratio on LeNet-style models (i.e., 114 times for LeNet-300-100 and 298 times for LeNet-5) compared with some state-of-the- art DNN pruning methods, and can reduce the size of an AlexNet-style network up to 82 times without accuracy loss.

An empirical study on the GEOtop hydrological model optimal estimation and uncertainty reduction using supercomputers

2021 ◽  
Author(s):  
Giacomo Bertoldi ◽  
Stefano Campanella ◽  
Emanuele Cordano ◽  
Alberto Sartori
Keyword(s):  
Learning Community ◽  
Hydrological Model ◽  
Computing Time ◽  
Optimal Estimation ◽  
Search Space ◽  
Water Retention Curve ◽  
Derivative Free Optimization ◽  
Derivative Free ◽  
Discretionary Choices ◽  
Computational Aspects

<p>Proper characterization of uncertainty remains a major research and operational challenge in Earth and Environmental Systems Models (EESMs). In fact, model calibration is often more an art than a science: one must make several discretionary choices, guided more by his own experience and intuition than by the scientific method. In practice, this means that the result of calibration (CA) could be suboptimal. One of the challenges of CA is the large number of parameters involved in EESM, which hence are usually selected with the help of a preliminary sensitivity analysis (SA). Finally, the computational burden of EESMs models and the large volume of the search space make SA and CA very time-consuming processes.</p><p>This work applies a modern HPC approach to optimize a complex, over parameterized hydrological model, improving the computational efficiency of SA/CA. We apply the derivative-free optimization algorithms implemented in the Facebook Nevergrad Python library (Rapin and Teytaud, 2018) on a HPC cluster, thanks to the Dask framework (Dask Development Team, 2016).</p><p>The approach has been applied to the GEOtop hydrological model (Rigon et al., 2006; Endrizzi et al., 2014) to predict the time evolution of variables as soil water content and evapotranspiration for several mountain agricultural sites in South Tyrol with different elevation, land cover (pasture, meadow, orchard), soil types.</p><p>We performed simulations on one-dimensional domains, where the model solves the energy and water budget equations in a column of soil and neglects the lateral water fluxes.  Even neglecting the distribution of parameters across layers of soil, considering a homogeneous column, one has tens of parameters, controlling soil and vegetation properties, where only a few of them are experimentally available. </p><p>Because the interpretation of global SA could be difficult or misleading and the number of model evaluations needed by SA is comparable with CA, we employed the following strategy. We performed CA using a full set of continuous parameters and SA after CA, using the samples collected during CA, to interpret the results. However, given the above-mentioned computational challenges, this strategy is possible only using HPC resources. For this reason, we focused on the computational aspects of calibration from an HPC perspective and examined the scaling of these algorithms and their implementation up to 1024 cores on a cluster. Other issues that we had to address were the complex shape of the search space and robustness of CA and SA against model convergence failure.</p><p>HPC  techniques allow to calibrate models with a high number of parameters within a reasonable computing time and  exploring the parameters space properly. This is particularly important with noisy, multimodal objective functions. In our case, HPC was essential to determine the  parameters controlling the water retention curve, which is highly not linear.  The developed  framework, which is published and freely available on GitHub, shows also how libraries and tools used within the machine learning community could be useful and easily adapted to EESMs CA.</p>

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