scholarly journals Efficient Bayesian inference for large chaotic dynamical systems

2021 ◽  
Vol 14 (7) ◽  
pp. 4319-4333
Author(s):  
Sebastian Springer ◽  
Heikki Haario ◽  
Jouni Susiluoto ◽  
Aleksandr Bibov ◽  
Andrew Davis ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Dynamical Systems ◽  
Spatial Data ◽  
Large Scale ◽  
Likelihood Function ◽  
Computational Cost ◽  
Local Approximation ◽  
Physical Models ◽  
Chaotic Dynamical Systems ◽  
Time Required

Abstract. Estimating parameters of chaotic geophysical models is challenging due to their inherent unpredictability. These models cannot be calibrated with standard least squares or filtering methods if observations are temporally sparse. Obvious remedies, such as averaging over temporal and spatial data to characterize the mean behavior, do not capture the subtleties of the underlying dynamics. We perform Bayesian inference of parameters in high-dimensional and computationally demanding chaotic dynamical systems by combining two approaches: (i) measuring model–data mismatch by comparing chaotic attractors and (ii) mitigating the computational cost of inference by using surrogate models. Specifically, we construct a likelihood function suited to chaotic models by evaluating a distribution over distances between points in the phase space; this distribution defines a summary statistic that depends on the geometry of the attractor, rather than on pointwise matching of trajectories. This statistic is computationally expensive to simulate, compounding the usual challenges of Bayesian computation with physical models. Thus, we develop an inexpensive surrogate for the log likelihood with the local approximation Markov chain Monte Carlo method, which in our simulations reduces the time required for accurate inference by orders of magnitude. We investigate the behavior of the resulting algorithm with two smaller-scale problems and then use a quasi-geostrophic model to demonstrate its large-scale application.

scholarly journals Efficient Bayesian inference for large chaotic dynamical systems

2020 ◽  
Author(s):  
Sebastian Springer ◽  
Heikki Haario ◽  
Jouni Susiluoto ◽  
Aleksandr Bibov ◽  
Andrew Davis ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Dynamical Systems ◽  
Spatial Data ◽  
Large Scale ◽  
Likelihood Function ◽  
Computational Cost ◽  
Local Approximation ◽  
Physical Models ◽  
Chaotic Dynamical Systems ◽  
Time Required

Abstract. Estimating parameters of chaotic geophysical models is challenging due to these models' inherent unpredictability. With temporally sparse long-range observations, these models cannot be calibrated using standard least squares or filtering methods. Obvious remedies, such as averaging over temporal and spatial data to characterize the mean behavior, do not capture the subtleties of the underlying dynamics. We perform Bayesian inference of parameters in high-dimensional and computationally demanding chaotic dynamical systems by combining two approaches: (i) measuring model-data mismatch by comparing chaotic attractors, and (ii) mitigating the computational cost of inference by using surrogate models. Specifically, we construct a likelihood function suited to chaotic models by evaluating a distribution over distances between points in the phase space; this distribution defines a summary statistic that depends on the attractor's geometry, rather than on pointwise matching of trajectories. This statistic is computationally expensive to simulate, compounding the usual challenges of Bayesian computation with physical models. Thus we develop an inexpensive surrogate for the log-likelihood via local approximation Markov chain Monte Carlo, which in our simulations reduces the time required for accurate inference by orders of magnitude. We investigate the behavior of the resulting algorithm on model problems, and then use a quasi-geostrophic model to demonstrate its large-scale application.

Variable Fidelity Modeling in Closed Loop Dynamical Systems

2014 ◽  
Author(s):  
Matthew A. Williams ◽  
Andrew G. Alleyne
Keyword(s):  
Dynamical Systems ◽  
Closed Loop ◽  
System Development ◽  
Computational Cost ◽  
Computational Effort ◽  
High Fidelity ◽  
Vapor Compression System ◽  
Variable Fidelity ◽  
Time Required ◽  
Fidelity Model

In the early stages of control system development, designers often require multiple iterations for purposes of validating control designs in simulation. This has the potential to make high fidelity models undesirable due to increased computational complexity and time required for simulation. As a solution, lower fidelity or simplified models are used for initial designs before controllers are tested on higher fidelity models. In the event that unmodeled dynamics cause the controller to fail when applied on a higher fidelity model, an iterative approach involving designing and validating a controller’s performance may be required. In this paper, a switched-fidelity modeling formulation for closed loop dynamical systems is proposed to reduce computational effort while maintaining elevated accuracy levels of system outputs and control inputs. The effects on computational effort and accuracy are investigated by applying the formulation to a traditional vapor compression system with high and low fidelity models of the evaporator and condenser. This sample case showed the ability of the switched fidelity framework to closely match the outputs and inputs of the high fidelity model while decreasing computational cost by 32% from the high fidelity model. For contrast, the low fidelity model decreases computational cost by 48% relative to the high fidelity model.

scholarly journals Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems

2020 ◽  
Author(s):  
Waad Subber ◽  
Sayan Ghosh ◽  
Piyush Pandita ◽  
Yiming Zhang ◽  
Liping Wang
Keyword(s):  
Bayesian Inference ◽  
Dynamical Systems ◽  
Uncertainty Quantification ◽  
Computational Cost ◽  
Three Dimensional ◽  
Region Of Interest ◽  
System Response ◽  
User Interest ◽  
Operation Conditions ◽  
Random Material Properties

Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem

scholarly journals Super-resolution emulator of cosmological simulations using deep physical models

2020 ◽  
Vol 495 (4) ◽  
pp. 4227-4236 ◽  
Author(s):  
Doogesh Kodi Ramanah ◽  
Tom Charnock ◽  
Francisco Villaescusa-Navarro ◽  
Benjamin D Wandelt
Keyword(s):  
Large Scale ◽  
Initial Conditions ◽  
Computational Cost ◽  
Physical Modelling ◽  
Real Space ◽  
Physical Models ◽  
Small Scale ◽  
Cosmological Simulations ◽  
Scale Structures ◽  
Small Scale Structures

ABSTRACT We present an extension of our recently developed Wasserstein optimized model to emulate accurate high-resolution (HR) features from computationally cheaper low-resolution (LR) cosmological simulations. Our deep physical modelling technique relies on restricted neural networks to perform a mapping of the distribution of the LR cosmic density field to the space of the HR small-scale structures. We constrain our network using a single triplet of HR initial conditions and the corresponding LR and HR evolved dark matter simulations from the quijote suite of simulations. We exploit the information content of the HR initial conditions as a well-constructed prior distribution from which the network emulates the small-scale structures. Once fitted, our physical model yields emulated HR simulations at low computational cost, while also providing some insights about how the large-scale modes affect the small-scale structure in real space.

scholarly journals Surrogate-assisted Bayesian inversion for landscape and basin evolution models

2019 ◽  
Author(s):  
Rohitash Chandra ◽  
Danial Azam ◽  
Arpit Kapoor ◽  
R. Dietmar Mulller
Keyword(s):  
Parallel Computing ◽  
Uncertainty Quantification ◽  
High Performance ◽  
Large Scale ◽  
Likelihood Function ◽  
Computational Cost ◽  
Optimization Methods ◽  
Parallel Tempering ◽  
Model Parameters ◽  
Basin Evolution

Abstract. The complex and computationally expensive features of the forward landscape and sedimentary basin evolution models pose a major challenge in the development of efficient inference and optimization methods. Bayesian inference provides a methodology for estimation and uncertainty quantification of free model parameters. In our previous work, parallel tempering Bayeslands was developed as a framework for parameter estimation and uncertainty quantification for the landscape and basin evolution modelling software Badlands. Parallel tempering Bayeslands features high-performance computing with dozens of processing cores running in parallel to enhance computational efficiency. Although parallel computing is used, the procedure remains computationally challenging since thousands of samples need to be drawn and evaluated. In large-scale landscape and basin evolution problems, a single model evaluation can take from several minutes to hours, and in certain cases, even days. Surrogate-assisted optimization has been with successfully applied to a number of engineering problems This motivates its use in optimisation and inference methods suited for complex models in geology and geophysics. Surrogates can speed up parallel tempering Bayeslands by developing computationally inexpensive surrogates to mimic expensive models. In this paper, we present an application of surrogate-assisted parallel tempering where that surrogate mimics a landscape evolution model including erosion, sediment transport and deposition, by estimating the likelihood function that is given by the model. We employ a machine learning model as a surrogate that learns from the samples generated by the parallel tempering algorithm and the likelihood from the model. The entire framework is developed in a parallel computing infrastructure to take advantage of parallelization. The results show that the proposed methodology is effective in lowering the overall computational cost significantly while retaining the quality of solutions.

scholarly journals Surrogate-assisted Bayesian inversion for landscape and basin evolution models

2020 ◽  
Vol 13 (7) ◽  
pp. 2959-2979
Author(s):  
Rohitash Chandra ◽  
Danial Azam ◽  
Arpit Kapoor ◽  
R. Dietmar Müller
Keyword(s):  
Uncertainty Quantification ◽  
High Performance ◽  
Large Scale ◽  
Likelihood Function ◽  
Landscape Evolution ◽  
Computational Cost ◽  
Evolution Model ◽  
Parallel Tempering ◽  
Model Parameters ◽  
Computationally Expensive

Abstract. The complex and computationally expensive nature of landscape evolution models poses significant challenges to the inference and optimization of unknown model parameters. Bayesian inference provides a methodology for estimation and uncertainty quantification of unknown model parameters. In our previous work, we developed parallel tempering Bayeslands as a framework for parameter estimation and uncertainty quantification for the Badlands landscape evolution model. Parallel tempering Bayeslands features high-performance computing that can feature dozens of processing cores running in parallel to enhance computational efficiency. Nevertheless, the procedure remains computationally challenging since thousands of samples need to be drawn and evaluated. In large-scale landscape evolution problems, a single model evaluation can take from several minutes to hours and in some instances, even days or weeks. Surrogate-assisted optimization has been used for several computationally expensive engineering problems which motivate its use in optimization and inference of complex geoscientific models. The use of surrogate models can speed up parallel tempering Bayeslands by developing computationally inexpensive models to mimic expensive ones. In this paper, we apply surrogate-assisted parallel tempering where the surrogate mimics a landscape evolution model by estimating the likelihood function from the model. We employ a neural-network-based surrogate model that learns from the history of samples generated. The entire framework is developed in a parallel computing infrastructure to take advantage of parallelism. The results show that the proposed methodology is effective in lowering the computational cost significantly while retaining the quality of model predictions.

A Method for Three-Dimensional Navier–Stokes Simulations of Large-Scale Regions of the Human Lung Airway

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
D. Keith Walters ◽  
William H. Luke
Keyword(s):  
Large Scale ◽  
Cfd Simulation ◽  
Computational Cost ◽  
Three Dimensional ◽  
Mesh Size ◽  
Flow Path ◽  
Physical Models ◽  
Navier Stokes ◽  
Small Scale ◽  
Flow Geometry

A new methodology for CFD simulation of airflow in the human bronchopulmonary tree is presented. The new approach provides a means for detailed resolution of the flow features via three-dimensional Navier–Stokes CFD simulation without the need for full resolution of the entire flow geometry, which is well beyond the reach of available computing power now and in the foreseeable future. The method is based on a finite number of flow paths, each of which is fully resolved, to provide a detailed description of the entire complex small-scale flowfield. A stochastic coupling approach is used for the unresolved flow path boundary conditions, yielding a virtual flow geometry that allows accurate statistical resolution of the flow at all scales for any set of flow conditions. Results are presented for multigenerational lung models based on the Weibel morphology and the anatomical data of Hammersley and Olson (1992, “Physical Models of the Smaller Pulmonary Airways,” J. Appl. Physiol., 72(6), pp. 2402–2414). Validation simulations are performed for a portion of the bronchiole region (generations 4–12) using the flow path ensemble method, and compared with simulations that are geometrically fully resolved. Results are obtained for three inspiratory flowrates and compared in terms of pressure drop, flow distribution characteristics, and flow structure. Results show excellent agreement with the fully resolved geometry, while reducing the mesh size and computational cost by up to an order of magnitude.

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