Showing papers on "Parametric statistics published in 2020"

Fourier Neural Operator for Parametric Partial Differential Equations

Abstract: The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For partial differential equations (PDEs), neural operators directly learn the mapping from any functional parametric dependence to the solution. Thus, they learn an entire family of PDEs, in contrast to classical methods which solve one instance of the equation. In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on Burgers' equation, Darcy flow, and Navier-Stokes equation. The Fourier neural operator is the first ML-based method to successfully model turbulent flows with zero-shot super-resolution. It is up to three orders of magnitude faster compared to traditional PDE solvers. Additionally, it achieves superior accuracy compared to previous learning-based solvers under fixed resolution.

Gravitational Test beyond the First Post-Newtonian Order with the Shadow of the M87 Black Hole

Abstract: The 2017 Event Horizon Telescope (EHT) observations of the central source in M87 have led to the first measurement of the size of a black-hole shadow. This observation offers a new and clean gravitational test of the black-hole metric in the strong-field regime. We show analytically that spacetimes that deviate from the Kerr metric but satisfy weak-field tests can lead to large deviations in the predicted black-hole shadows that are inconsistent with even the current EHT measurements. We use numerical calculations of regular, parametric, non-Kerr metrics to identify the common characteristic among these different parametrizations that control the predicted shadow size. We show that the shadow-size measurements place significant constraints on deviation parameters that control the second post-Newtonian and higher orders of each metric and are, therefore, inaccessible to weak-field tests. The new constraints are complementary to those imposed by observations of gravitational waves from stellar-mass sources.

Model Reduction and Neural Networks for Parametric PDEs

Abstract: We develop a general framework for data-driven approximation of input-output maps between infinite-dimensional spaces. The proposed approach is motivated by the recent successes of neural networks and deep learning, in combination with ideas from model reduction. This combination results in a neural network approximation which, in principle, is defined on infinite-dimensional spaces and, in practice, is robust to the dimension of finite-dimensional approximations of these spaces required for computation. For a class of input-output maps, and suitably chosen probability measures on the inputs, we prove convergence of the proposed approximation methodology. We also include numerical experiments which demonstrate the effectiveness of the method, showing convergence and robustness of the approximation scheme with respect to the size of the discretization, and compare it with existing algorithms from the literature; our examples include the mapping from coefficient to solution in a divergence form elliptic partial differential equation (PDE) problem, and the solution operator for viscous Burgers' equation.

IBM SPSS statistics

Abstract: IBM SPSS Statistics (“Statistical Package for the Social Sciences”) is a software used for the statistical analysis, data management, and data documentation. This short chapter introduces the SPSS software, including an overview of its capabilities. Topics such as data preparation, data import, options of parametric and nonparametric statistical tests, export and editing of statistical results, and creation of charts and tables are covered.

Path Tracking and Direct Yaw Moment Coordinated Control Based on Robust MPC With the Finite Time Horizon for Autonomous Independent-Drive Vehicles

Abstract: It is a striking fact that the characteristics of parametric uncertainties, external disturbance, time-varying and nonlinearities are available in the constructed model of autonomous independent-drive vehicles; therefore, in this paper, the robust model predictive control (MPC) with the finite time horizon is proposed to realize the coordinated path tracking and direct yaw moment control (DYC) for autonomous four in-wheel motor independent-drive electric vehicles (AMIDEV). Firstly, considering the time-varying and uncertain feature of the tire cornering stiffness and the vehicle velocity in the state space equation constructed by 2 degrees of freedom (DoF) vehicle model and the path tracking preview model, the linear parameter varying (LPV) discrete model with four polytypic vertexes is constructed. Then, based on the linear matrix inequality (LMI) method, the novel robust MPC theory with the finite time horizon is put forward to solve the min-max optimization problem after updating four polytypic vertexes in real time, which could deal with the inevitable model mismatch problem caused by the time-varying, uncertain vehicle dynamic characteristics and external disturbance. Finally, the simulation and experimental results have verified that the proposed novel robust MPC theory could emerge from the stranglehold exercised by the conservativeness of the traditional robust MPC theory with the infinite time horizon, which strengthens the robustness of this control system as well as achieves better path tracking accuracy and handling ability of AMIDEV.

Adaptive Control for Pneumatic Artificial Muscle Systems With Parametric Uncertainties and Unidirectional Input Constraints

Abstract: Pneumatic artificial muscle (PAM) systems are a kind of tube-like actuators, which can act roughly like human muscles by performing contractile or extensional motions actuated by pressurized air. At present, it is still an open and challenging issue to tackle positioning and tracking control problems of PAM systems, due to inherent characteristics, e.g., unidirectional inputs, high nonlinearities, hysteresis, time-varying characteristics, etc. In this paper, a new adaptive control method is proposed for PAM systems, which achieves satisfactory tracking performance. To this end, an update law is designed to estimate unknown system parameters online. Also, some control input transforming operations are applied to address unidirectional constraints (i.e., control inputs of PAM systems should always be positive). As far as we know, compared with most of the existing control methods, this paper gives the first continuous control solution for PAM systems that can simultaneously compensate parametric uncertainties, reject external disturbances, and meet unidirectional constraints. Without linearizing the nonlinear dynamics, the closed-loop system is theoretically proven to be asymptotically stable at the equilibrium point with the stability analysis. In addition, a series of hardware experiments are implemented on a self-built hardware platform, indicating that the proposed method achieves satisfactory tracking control and exhibits robustness against parametric uncertainties and disturbances.

Total-Body Dynamic Reconstruction and Parametric Imaging on the uEXPLORER.

Abstract: The world's first 194-cm-long total-body PET/CT scanner (uEXPLORER) has been built by the EXPLORER Consortium to offer a transformative platform for human molecular imaging in clinical research and health care. Its total-body coverage and ultra-high sensitivity provide opportunities for more accurate tracer kinetic analysis in studies of physiology, biochemistry, and pharmacology. The objective of this study was to demonstrate the capability of total-body parametric imaging and to quantify the improvement in image quality and kinetic parameter estimation by direct and kernel reconstruction of the uEXPLORER data. Methods: We developed quantitative parametric image reconstruction methods for kinetic analysis and used them to analyze the first human dynamic total-body PET study. A healthy female subject was recruited, and a 1-h dynamic scan was acquired during and after an intravenous injection of 256 MBq of 18F-FDG. Dynamic data were reconstructed using a 3-dimensional time-of-flight list-mode ordered-subsets expectation maximization (OSEM) algorithm and a kernel-based algorithm with all quantitative corrections implemented in the forward model. The Patlak graphical model was used to analyze the 18F-FDG kinetics in the whole body. The input function was extracted from a region over the descending aorta. For comparison, indirect Patlak analysis from reconstructed frames and direct reconstruction of parametric images from the list-mode data were obtained for the last 30 min of data. Results: Images reconstructed by OSEM showed good quality with low noise, even for the 1-s frames. The image quality was further improved using the kernel method. Total-body Patlak parametric images were obtained using either indirect estimation or direct reconstruction. The direct reconstruction method improved the parametric image quality, having a better contrast-versus-noise tradeoff than the indirect method, with a 2- to 3-fold variance reduction. The kernel-based indirect Patlak method offered image quality similar to the direct Patlak method, with less computation time and faster convergence. Conclusion: This study demonstrated the capability of total-body parametric imaging using the uEXPLORER. Furthermore, the results showed the benefits of kernel-regularized reconstruction and direct parametric reconstruction. Both can achieve superior image quality for tracer kinetic studies compared with the conventional indirect OSEM for total-body imaging.

PaMIR: Parametric Model-Conditioned Implicit Representation for Image-based Human Reconstruction

Abstract: Modeling 3D humans accurately and robustly from a single image is very challenging, and the key for such an ill-posed problem is the 3D representation of the human models. To overcome the limitations of regular 3D representations, we propose Parametric Model-Conditioned Implicit Representation (PaMIR), which combines the parametric body model with the free-form deep implicit function. In our PaMIR-based reconstruction framework, a novel deep neural network is proposed to regularize the free-form deep implicit function using the semantic features of the parametric model, which improves the generalization ability under the scenarios of challenging poses and various clothing topologies. Moreover, a novel depth-ambiguity-aware training loss is further integrated to resolve depth ambiguities and enable successful surface detail reconstruction with imperfect body reference. Finally, we propose a body reference optimization method to improve the parametric model estimation accuracy and to enhance the consistency between the parametric model and the implicit function. With the PaMIR representation, our framework can be easily extended to multi-image input scenarios without the need of multi-camera calibration and pose synchronization. Experimental results demonstrate that our method achieves state-of-the-art performance for image-based 3D human reconstruction in the cases of challenging poses and clothing types.

DeepLPF: Deep Local Parametric Filters for Image Enhancement

Abstract: Digital artists often improve the aesthetic quality of digital photographs through manual retouching. Beyond global adjustments, professional image editing programs provide local adjustment tools operating on specific parts of an image. Options include parametric (graduated, radial filters) and unconstrained brush tools. These highly expressive tools enable a diverse set of local image enhancements. However, their use can be time consuming, and requires artistic capability. State-of-the-art automated image enhancement approaches typically focus on learning pixel-level or global enhancements. The former can be noisy and lack interpretability, while the latter can fail to capture fine-grained adjustments. In this paper, we introduce a novel approach to automatically enhance images using learned spatially local filters of three different types (Elliptical Filter, Graduated Filter, Polynomial Filter). We introduce a deep neural network, dubbed Deep Local Parametric Filters (DeepLPF), which regresses the parameters of these spatially localized filters that are then automatically applied to enhance the image. DeepLPF provides a natural form of model regularization and enables interpretable, intuitive adjustments that lead to visually pleasing results. We report on multiple benchmarks and show that DeepLPF produces state-of-the-art performance on two variants of the MIT-Adobe 5k dataset, often using a fraction of the parameters required for competing methods.

Neural Source-Filter Waveform Models for Statistical Parametric Speech Synthesis

Abstract: Neural waveform models have demonstrated better performance than conventional vocoders for statistical parametric speech synthesis. One of the best models, called WaveNet, uses an autoregressive (AR) approach to model the distribution of waveform sampling points, but it has to generate a waveform in a time-consuming sequential manner. Some new models that use inverse-autoregressive flow (IAF) can generate a whole waveform in a one-shot manner but require either a larger amount of training time or a complicated model architecture plus a blend of training criteria. As an alternative to AR and IAF-based frameworks, we propose a neural source-filter (NSF) waveform modeling framework that is straightforward to train and fast to generate waveforms. This framework requires three components to generate waveforms: a source module that generates a sine-based signal as excitation, a non-AR dilated-convolution-based filter module that transforms the excitation into a waveform, and a conditional module that pre-processes the input acoustic features for the source and filter modules. This framework minimizes spectral-amplitude distances for model training, which can be efficiently implemented using short-time Fourier transform routines. As an initial NSF study, we designed three NSF models under the proposed framework and compared them with WaveNet using our deep learning toolkit. It was demonstrated that the NSF models generated waveforms at least 100 times faster than our WaveNet-vocoder, and the quality of the synthetic speech from the best NSF model was comparable to that from WaveNet on a large single-speaker Japanese speech corpus.

Composite Learning Adaptive Dynamic Surface Control of Fractional-Order Nonlinear Systems

Abstract: Adaptive dynamic surface control (ADSC) is effective for solving the complexity problem in adaptive backstepping control of integer-order nonlinear systems. This article focuses on the ADSC design for parametric uncertain fractional-order nonlinear systems (FONSs). In each backstepping step, the virtual controller is driven to pass through a fractional dynamic surface whose fractional-order derivative can be calculated easily. An ADSC law that ensure tracking error convergence is designed. The proposed ADSC requires a stringent condition called persistent excitation (PE) to achieve parameter convergence. To relax this limitation, a prediction error is defined by using online recorded data and instantaneous data, and a composite learning law is proposed to utilize both the prediction error and the tracking error. Then, a composite learning ADSC (CLADSC) method is developed to guarantee tracking error convergence and accurate parameter estimation under an interval excitation condition that is weaker than the PE one. Finally, an illustrative example is presented to show the performance of our methods.

Combining Implicit Function Learning and Parametric Models for 3D Human Reconstruction

Abstract: Implicit functions represented as deep learning approximations are powerful for reconstructing 3D surfaces. However, they can only produce static surfaces that are not controllable, which provides limited ability to modify the resulting model by editing its pose or shape parameters. Nevertheless, such features are essential in building flexible models for both computer graphics and computer vision. In this work, we present methodology that combines detail-rich implicit functions and parametric representations in order to reconstruct 3D models of people that remain controllable and accurate even in the presence of clothing. Given sparse 3D point clouds sampled on the surface of a dressed person, we use an Implicit Part Network (IP-Net) to jointly predict the outer 3D surface of the dressed person, the inner body surface, and the semantic correspondences to a parametric body model. We subsequently use correspondences to fit the body model to our inner surface and then non-rigidly deform it (under a parametric body + displacement model) to the outer surface in order to capture garment, face and hair detail. In quantitative and qualitative experiments with both full body data and hand scans we show that the proposed methodology generalizes, and is effective even given incomplete point clouds collected from single-view depth images. Our models and code will be publicly released (http://virtualhumans.mpi-inf.mpg.de/ipnet).

On the Iteration Complexity of Hypergradient Computation

Abstract: We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation Important instances arising in machine learning include hyperparameter optimization, meta-learning, and certain graph and recurrent neural networks Typically the gradient of the upper-level objective (hypergradient) is hard or even impossible to compute exactly, which has raised the interest in approximation methods We investigate some popular approaches to compute the hypergradient, based on reverse mode iterative differentiation and approximate implicit differentiation Under the hypothesis that the fixed point equation is defined by a contraction mapping, we present a unified analysis which allows for the first time to quantitatively compare these methods, providing explicit bounds for their iteration complexity This analysis suggests a hierarchy in terms of computational efficiency among the above methods, with approximate implicit differentiation based on conjugate gradient performing best We present an extensive experimental comparison among the methods which confirm the theoretical findings

Combining Implicit Function Learning and Parametric Models for 3D Human Reconstruction

Abstract: Implicit functions represented as deep learning approximations are powerful for reconstructing 3D surfaces. However, they can only produce static surfaces that are not controllable, which provides limited ability to modify the resulting model by editing its pose or shape parameters. Nevertheless, such features are essential in building flexible models for both computer graphics and computer vision. In this work, we present methodology that combines detail-rich implicit functions and parametric representations in order to reconstruct 3D models of people that remain controllable and accurate even in the presence of clothing. Given sparse 3D point clouds sampled on the surface of a dressed person, we use an Implicit Part Network (IP-Net)to jointly predict the outer 3D surface of the dressed person, the and inner body surface, and the semantic correspondences to a parametric body model. We subsequently use correspondences to fit the body model to our inner surface and then non-rigidly deform it (under a parametric body + displacement model) to the outer surface in order to capture garment, face and hair detail. In quantitative and qualitative experiments with both full body data and hand scans we show that the proposed methodology generalizes, and is effective even given incomplete point clouds collected from single-view depth images. Our models and code can be downloaded from this http URL.

Multi-criteria COPRAS Method Based on Parametric Measures for Intuitionistic Fuzzy Sets: Application of Green Supplier Selection

Abstract: In this manuscript, we present complex proportional assessment (COPRAS) method to solve multi-criteria decision-making (MCDM) problems with intuitionistic fuzzy information, known as IF-COPRAS method. In this method, a new formula is developed to evaluate the criterion weights, in which the objective weights are calculated from divergence measure method. For this, new parametric divergence and entropy measures are investigated and some desirable properties are also discussed. Since the vagueness or uncertainty is an unavoidable characteristic of MCDM problems, the proposed approach can be a useful tool for decision making in an uncertain atmosphere. Further, a decision-making problem of green supplier selection is presented to demonstrate the usefulness of the proposed method. To illustrate the validity of the proposed method, comparison with existing methods is presented and the stability is also discussed through a sensitivity analysis with different values of criterion weights.

Data-driven recovery of hidden physics in reduced order modeling of fluid flows

Abstract: In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on using first principles to model the known physics in conjunction with utilizing the data-driven machine learning tools to model the remaining residual that is hidden in data. This framework employs proper orthogonal decomposition as a compression tool to construct orthonormal bases and a Galerkin projection (GP) as a model to build the dynamical core of the system. Our proposed methodology, hence, compensates structural or epistemic uncertainties in models and utilizes the observed data snapshots to compute true modal coefficients spanned by these bases. The GP model is then corrected at every time step with a data-driven rectification using a long short-term memory (LSTM) neural network architecture to incorporate hidden physics. A Grassmann manifold approach is also adopted for interpolating basis functions to unseen parametric conditions. The control parameter governing the system’s behavior is, thus, implicitly considered through true modal coefficients as input features to the LSTM network. The effectiveness of the HAM approach is then discussed through illustrative examples that are generated synthetically to take hidden physics into account. Our approach, thus, provides insights addressing a fundamental limitation of the physics-based models when the governing equations are incomplete to represent underlying physical processes.

The Random Feature Model for Input-Output Maps between Banach Spaces

Abstract: Well known to the machine learning community, the random feature model, originally introduced by Rahimi and Recht in 2008, is a parametric approximation to kernel interpolation or regression methods. It is typically used to approximate functions mapping a finite-dimensional input space to the real line. In this paper, we instead propose a methodology for use of the random feature model as a data-driven surrogate for operators that map an input Banach space to an output Banach space. Although the methodology is quite general, we consider operators defined by partial differential equations (PDEs); here, the inputs and outputs are themselves functions, with the input parameters being functions required to specify the problem, such as initial data or coefficients, and the outputs being solutions of the problem. Upon discretization, the model inherits several desirable attributes from this infinite-dimensional, function space viewpoint, including mesh-invariant approximation error with respect to the true PDE solution map and the capability to be trained at one mesh resolution and then deployed at different mesh resolutions. We view the random feature model as a non-intrusive data-driven emulator, provide a mathematical framework for its interpretation, and demonstrate its ability to efficiently and accurately approximate the nonlinear parameter-to-solution maps of two prototypical PDEs arising in physical science and engineering applications: viscous Burgers' equation and a variable coefficient elliptic equation.

Multi-variate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows

Abstract: Time series forecasting is often fundamental to scientific and engineering problems and enables decision making. With ever increasing data set sizes, a trivial solution to scale up predictions is to assume independence between interacting time series. However, modeling statistical dependencies can improve accuracy and enable analysis of interaction effects. Deep learning methods are well suited for this problem, but multivariate models often assume a simple parametric distribution and do not scale to high dimensions. In this work we model the multivariate temporal dynamics of time series via an autoregressive deep learning model, where the data distribution is represented by a conditioned normalizing flow. This combination retains the power of autoregressive models, such as good performance in extrapolation into the future, with the flexibility of flows as a general purpose high-dimensional distribution model, while remaining computationally tractable. We show that it improves over the state-of-the-art for standard metrics on many real-world data sets with several thousand interacting time-series.

Artificial Intelligence and Parametric Construction Cost Estimate Modeling: State-of-the-Art Review

Abstract: This study reviews the common practices and procedures conducted to identify the cost drivers that the past literature has classified into two main categories: qualitative and quantitative ...

Photonic-Crystal Josephson Traveling-Wave Parametric Amplifier

Abstract: A new solution to the phase-matching problem common to so-called traveling-wave parametric amplifiers is achieved with a simple design that's easy to fabricate.

Active Learning for Nonlinear System Identification with Guarantees.

Abstract: While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and actions or for systems that can be identified from data generated by iid random inputs Nonetheless, many interesting dynamical systems have continuous states and actions and can only be identified through a judicious choice of inputs Motivated by practical settings, we study a class of nonlinear dynamical systems whose state transitions depend linearly on a known feature embedding of state-action pairs To estimate such systems in finite time identification methods must explore all directions in feature space We propose an active learning approach that achieves this by repeating three steps: trajectory planning, trajectory tracking, and re-estimation of the system from all available data We show that our method estimates nonlinear dynamical systems at a parametric rate, similar to the statistical rate of standard linear regression

Performance Scaling in Magnetized Liner Inertial Fusion Experiments

Abstract: We present experimental results from the first systematic study of performance scaling with drive parameters for a magnetoinertial fusion concept. In magnetized liner inertial fusion experiments, the burn-averaged ion temperature doubles to 3.1 keV and the primary deuterium-deuterium neutron yield increases by more than an order of magnitude to 1.1×10^{13} (2 kJ deuterium-tritium equivalent) through a simultaneous increase in the applied magnetic field (from 10.4 to 15.9 T), laser preheat energy (from 0.46 to 1.2 kJ), and current coupling (from 16 to 20 MA). Individual parametric scans of the initial magnetic field and laser preheat energy show the expected trends, demonstrating the importance of magnetic insulation and the impact of the Nernst effect for this concept. A drive-current scan shows that present experiments operate close to the point where implosion stability is a limiting factor in performance, demonstrating the need to raise fuel pressure as drive current is increased. Simulations that capture these experimental trends indicate that another order of magnitude increase in yield on the Z facility is possible with additional increases of input parameters.