A surrogate modeling and adaptive sampling toolbox for computer based design

An exceedingly large number of scientific and engineering fields are confronted with the need for computer simulations to study complex, real world phenomena or solve challenging design problems. However, due to the computational cost of these high fidelity simulations, the use of neural networks, kernel methods, and other surrogate modeling techniques have become indispensable. Surrogate models are compact and cheap to evaluate, and have proven very useful for tasks such as optimization, design space exploration, prototyping, and sensitivity analysis. Consequently, in many fields there is great interest in tools and techniques that facilitate the construction of such regression models, while minimizing the computational cost and maximizing model accuracy. This paper presents a mature, flexible, and adaptive machine learning toolkit for regression modeling and active learning to tackle these issues. The toolkit brings together algorithms for data fitting, model selection, sample selection (active learning), hyperparameter optimization, and distributed computing in order to empower a domain expert to efficiently generate an accurate model for the problem or data at hand

Evolutionary model type selection for global surrogate modeling

Due to the scale and computational complexity of currently used simulation codes, global surrogate (metamodels) models have become indispensable tools for exploring and understanding the design space. Due to their compact formulation they are cheap to evaluate and thus readily facilitate visualization, design space exploration, rapid prototyping, and sensitivity analysis. They can also be used as accurate building blocks in design packages or larger simulation environments. Consequently, there is great interest in techniques that facilitate the construction of such approximation models while minimizing the computational cost and maximizing model accuracy. Many surrogate model types exist ( Support Vector Machines, Kriging, Neural Networks, etc.) but no type is optimal in all circumstances. Nor is there any hard theory available that can help make this choice. In this paper we present an automatic approach to the model type selection problem. We describe an adaptive global surrogate modeling environment with adaptive sampling, driven by speciated evolution. Different model types are evolved cooperatively using a Genetic Algorithm ( heterogeneous evolution) and compete to approximate the iteratively selected data. In this way the optimal model type and complexity for a given data set or simulation code can be dynamically determined. Its utility and performance is demonstrated on a number of problems where it outperforms traditional sequential execution of each model type

Likelihood-free inference of experimental Neutrino Oscillations using Neural Spline Flows

In machine learning, likelihood-free inference refers to the task of performing an analysis driven by data instead of an analytical expression. We discuss the application of Neural Spline Flows, a neural density estimation algorithm, to the likelihood-free inference problem of the measurement of neutrino oscillation parameters in Long Baseline neutrino experiments. A method adapted to physics parameter inference is developed and applied to the case of the disappearance muon neutrino analysis at the T2K experiment.Comment: 10 pages, 3 figure

Combining domain knowledge and statistical models in time series analysis

This paper describes a new approach to time series modeling that combines subject-matter knowledge of the system dynamics with statistical techniques in time series analysis and regression. Applications to American option pricing and the Canadian lynx data are given to illustrate this approach.Comment: Published at http://dx.doi.org/10.1214/074921706000001049 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels

We present Spline-based Convolutional Neural Networks (SplineCNNs), a variant of deep neural networks for irregular structured and geometric input, e.g., graphs or meshes. Our main contribution is a novel convolution operator based on B-splines, that makes the computation time independent from the kernel size due to the local support property of the B-spline basis functions. As a result, we obtain a generalization of the traditional CNN convolution operator by using continuous kernel functions parametrized by a fixed number of trainable weights. In contrast to related approaches that filter in the spectral domain, the proposed method aggregates features purely in the spatial domain. In addition, SplineCNN allows entire end-to-end training of deep architectures, using only the geometric structure as input, instead of handcrafted feature descriptors. For validation, we apply our method on tasks from the fields of image graph classification, shape correspondence and graph node classification, and show that it outperforms or pars state-of-the-art approaches while being significantly faster and having favorable properties like domain-independence.Comment: Presented at CVPR 201

An adaptive orthogonal search algorithm for model subset selection and non-linear system identification

A new adaptive orthogonal search (AOS) algorithm is proposed for model subset selection and non-linear system identification. Model structure detection is a key step in any system identification problem. This consists of selecting significant model terms from a redundant dictionary of candidate model terms, and determining the model complexity (model length or model size). The final objective is to produce a parsimonious model that can well capture the inherent dynamics of the underlying system. In the new AOS algorithm, a modified generalized cross-validation criterion, called the adjustable prediction error sum of squares (APRESS), is introduced and incorporated into a forward orthogonal search procedure. The main advantage of the new AOS algorithm is that the mechanism is simple and the implementation is direct and easy, and more importantly it can produce efficient model subsets for most non-linear identification problems