Thallo – Scheduling for High-Performance Large-Scale Non-Linear Least-Squares Solvers

Large-scale optimization problems at the core of many graphics, vision, and imaging applications are often implemented by hand in tedious and error-prone processes in order to achieve high performance (in particular on GPUs), despite recent developments in libraries and DSLs. At the same time, these hand-crafted solver implementations reveal that the key for high performance is a problem-specific schedule that enables efficient usage of the underlying hardware. In this work, we incorporate this insight into Thallo, a domain-specific language for large-scale non-linear least squares optimization problems. We observe various code reorganizations performed by implementers of high-performance solvers in the literature, and then define a set of basic operations that span these scheduling choices, thereby defining a large scheduling space. Users can either specify code transformations in a scheduling language or use an autoscheduler. Thallo takes as input a compact, shader-like representation of an energy function and a (potentially auto-generated) schedule, translating the combination into high-performance GPU solvers. Since Thallo can generate solvers from a large scheduling space, it can handle a large set of large-scale non-linear and non-smooth problems with various degrees of non-locality and compute-to-memory ratios, including diverse applications such as bundle adjustment, face blendshape fitting, and spatially-varying Poisson deconvolution, as seen in Figure 1. Abstracting schedules from the optimization, we outperform state-of-the-art GPU-based optimization DSLs by an average of 16× across all applications introduced in this work, and even some published hand-written GPU solvers by 30%+.

GM(1,1;λ) with Constrained Linear Least Squares

The only parameters of the original GM(1,1) that are generally estimated by the ordinary least squares method are the development coefficient a and the grey input b. However, the weight of the background value, denoted as λ, cannot be obtained simultaneously by such a method. This study, therefore, proposes two simple transformation formulations such that the unknown parameters, and can be simultaneously estimated by the least squares method. Therefore, such a grey model is termed the GM(1,1;λ). On the other hand, because the permission zone of the development coefficient is bounded, the parameter estimation of the GM(1,1) could be regarded as a bound-constrained least squares problem. Since constrained linear least squares problems generally can be solved by an iterative approach, this study applies the Matlab function lsqlin to solve such constrained problems. Numerical results show that the proposed GM(1,1;λ) performs better than the GM(1,1) in terms of its model fitting accuracy and its forecasting precision.

Design and Analysis of High-precision Weighted Linear Least-Squares Fitting Algorithm for Fluorescent Optical Fiber Temperature Sensor

Microwave hyperthermia is a new method of treating cancer, where the therapeutic effect is determined by the heating temperature. Traditional active temperature sensors are interfered by high frequency so that the accuracy of temperature measurement cannot be guaranteed. It is of great significance to study the high-precision fluorescent optical fiber temperature sensor with complete insulation. This paper has realized a compact and practical fluorescent optical fiber temperature sensor after studying the optical path, circuit, data processing algorithm. In order to improve the accuracy of the system, the weighted linear least-squares fitting algorithm is improved in this paper. Through experimental tests, compared with the standard linear least-squares fitting algorithm and the unimproved weighted linear least-squares fitting algorithm, the accuracy of the algorithm is improved by about 98% and 65.5%, respectively. In addition, the response time is reduced by about 36.5%, compared with the unimproved weighted linear least-squares fitting algorithm. This algorithm fully meets the precision requirements of microwave hyperthermia.

Empirical Models to Characterize the Structural and Physiochemical Properties of Vacuum Gas Oils with Different Saturate Contents

Inter-criteria analysis was employed in VGO samples having a saturate content between 0.8 and 93.1 wt.% to define the statistically significant relations between physicochemical properties, empirical structural models and vacuum gas oil compositional information. The use of a logistic function and employment of a non-linear least squares method along with the aromatic ring index allowed for our newly developed correlation to accurately predict the saturate content of VGOs. The empirical models developed in this study can be used not only for obtaining the valuable structural information necessary to predict the behavior of VGOs in the conversion processes but can also be utilized to detect incorrectly performed SARA analyses. This work confirms the possibility of predicting the contents of VGO compounds from physicochemical properties and empirical models.